On the stability of the Atlantic meridional overturning circulation.

PubMed

Hofmann, Matthias; Rahmstorf, Stefan

2009-12-08

One of the most important large-scale ocean current systems for Earth's climate is the Atlantic meridional overturning circulation (AMOC). Here we review its stability properties and present new model simulations to study the AMOC's hysteresis response to freshwater perturbations. We employ seven different versions of an Ocean General Circulation Model by using a highly accurate tracer advection scheme, which minimizes the problem of numerical diffusion. We find that a characteristic freshwater hysteresis also exists in the predominantly wind-driven, low-diffusion limit of the AMOC. However, the shape of the hysteresis changes, indicating that a convective instability rather than the advective Stommel feedback plays a dominant role. We show that model errors in the mean climate can make the hysteresis disappear, and we investigate how model innovations over the past two decades, like new parameterizations and mixing schemes, affect the AMOC stability. Finally, we discuss evidence that current climate models systematically overestimate the stability of the AMOC.

Steady MHD free convection heat and mass transfer flow about a vertical porous surface with thermal diffusion and induced magnetic field

NASA Astrophysics Data System (ADS)

Touhid Hossain, M. M.; Afruz-Zaman, Md.; Rahman, Fouzia; Hossain, M. Arif

2013-09-01

In this study the thermal diffusion effect on the steady laminar free convection flow and heat transfer of viscous incompressible MHD electrically conducting fluid above a vertical porous surface is considered under the influence of an induced magnetic field. The governing non-dimensional equations relevant to the problem, containing the partial differential equations, are transformed by usual similarity transformations into a system of coupled non-linear ordinary differential equations and will be solved analytically by using the perturbation technique. On introducing the non-dimensional concept and applying Boussinesq's approximation, the solutions for velocity field, temperature distribution and induced magnetic field to the second order approximations are obtained for large suction with different selected values of the established dimensionless parameters. The influences of these various establish parameters on the velocity and temperature fields and on the induced magnetic fields are exhibited under certain assumptions and are studied graphically in the present analysis. It is observed that the effects of thermal-diffusion and large suction have great importance on the velocity, temperature and induced magnetic fields and mass concentration for several fluids considered, so that their effects should be taken into account with other useful parameters associated. It is also found that the dimensionless Prandtl number, Grashof number, Modified Grashof number and magnetic parameter have an appreciable influence on the concerned independent variables.

Multi-Scale Modeling and the Eddy-Diffusivity/Mass-Flux (EDMF) Parameterization

NASA Astrophysics Data System (ADS)

Teixeira, J.

2015-12-01

Turbulence and convection play a fundamental role in many key weather and climate science topics. Unfortunately, current atmospheric models cannot explicitly resolve most turbulent and convective flow. Because of this fact, turbulence and convection in the atmosphere has to be parameterized - i.e. equations describing the dynamical evolution of the statistical properties of turbulence and convection motions have to be devised. Recently a variety of different models have been developed that attempt at simulating the atmosphere using variable resolution. A key problem however is that parameterizations are in general not explicitly aware of the resolution - the scale awareness problem. In this context, we will present and discuss a specific approach, the Eddy-Diffusivity/Mass-Flux (EDMF) parameterization, that not only is in itself a multi-scale parameterization but it is also particularly well suited to deal with the scale-awareness problems that plague current variable-resolution models. It does so by representing small-scale turbulence using a classic Eddy-Diffusivity (ED) method, and the larger-scale (boundary layer and tropospheric-scale) eddies as a variety of plumes using the Mass-Flux (MF) concept.

Numerical applications of the advective-diffusive codes for the inner magnetosphere

NASA Astrophysics Data System (ADS)

Aseev, N. A.; Shprits, Y. Y.; Drozdov, A. Y.; Kellerman, A. C.

2016-11-01

In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.

Cross-diffusion-driven hydrodynamic instabilities in a double-layer system: General classification and nonlinear simulations

NASA Astrophysics Data System (ADS)

Budroni, M. A.

2015-12-01

Cross diffusion, whereby a flux of a given species entrains the diffusive transport of another species, can trigger buoyancy-driven hydrodynamic instabilities at the interface of initially stable stratifications. Starting from a simple three-component case, we introduce a theoretical framework to classify cross-diffusion-induced hydrodynamic phenomena in two-layer stratifications under the action of the gravitational field. A cross-diffusion-convection (CDC) model is derived by coupling the fickian diffusion formalism to Stokes equations. In order to isolate the effect of cross-diffusion in the convective destabilization of a double-layer system, we impose a starting concentration jump of one species in the bottom layer while the other one is homogeneously distributed over the spatial domain. This initial configuration avoids the concurrence of classic Rayleigh-Taylor or differential-diffusion convective instabilities, and it also allows us to activate selectively the cross-diffusion feedback by which the heterogeneously distributed species influences the diffusive transport of the other species. We identify two types of hydrodynamic modes [the negative cross-diffusion-driven convection (NCC) and the positive cross-diffusion-driven convection (PCC)], corresponding to the sign of this operational cross-diffusion term. By studying the space-time density profiles along the gravitational axis we obtain analytical conditions for the onset of convection in terms of two important parameters only: the operational cross-diffusivity and the buoyancy ratio, giving the relative contribution of the two species to the global density. The general classification of the NCC and PCC scenarios in such parameter space is supported by numerical simulations of the fully nonlinear CDC problem. The resulting convective patterns compare favorably with recent experimental results found in microemulsion systems.

A comparison of the effect of convection against diffusion in hemodynamics and cytokines clearance in an experimental model of septic shock.

PubMed

Herrera-Gutiérrez, Manuel E; Seller-Pérez, Gemma; Arias-Verdú, Dolores; Granados, Maria M; Dominguez, Juan M; Navarrete, Rocío; Morgaz, Juán; Gómez-Villamandos, Rafael

2012-10-01

Replacement therapies based on the use of convection have value for the removal of inflammatory mediators. Such therapies have been proposed for the management of septic shock, but diffusion has not proved useful in this scenario, unless high-flow membranes are used. The exact role of diffusion in these cases remains to be clarified because continuous replacement therapies are usually delivered with low-flow membranes and mixed convection-diffusion modalities. However, studies specifically addressing this problem have not been performed. Our aim was to define the efficacy of hemofiltration (convection) and hemodialysis (diffusion) in cytokine clearance and hemodynamic improvement in an experimental model of septic shock. Shock was induced in 15 beagle dogs (weight 10-15 kg) by infusion of 1 mg/kg of ultrapure Escherichia coli lipopolysaccharide diluted in 20 mL saline for 10 minutes. Five animals were followed without interventions (controls), five animals were treated with convection (100 mL kg h) for 6 hours, and five animals were treated with diffusion (100 mL kg h) for 6 hours. All subjects in the control group died during the study, whereas all treated subjects survived. Mean arterial pressure, cardiac output, systolic variability volume, systemic vascular resistances, dPMax, and pulmonary compliance improved in treated subjects. However, the differences in mean arterial pressure and cardiac output were significant only in the convection group and not in the diffusion-treated group.Tumor necrosis factor α rose equally in all groups and decreased only in treated subjects. Interleukin 6 rose in the three groups but decreased only in the convection group and remained unchanged in the control and diffusion groups. Convection and diffusion improved survival and hemodynamic parameters in a septic shock model. Improvement was more pronounced with convection, a difference that may be explained by convective clearance of cytokines.

Similar solutions of double-diffusive dissipative layers along free surfaces

NASA Astrophysics Data System (ADS)

Napolitano, L. G.; Viviani, A.; Savino, R.

1990-10-01

Free convection due to buoyant forces (natural convection) and surface tension gradients (Marangoni convection) generated by temperature and concentration gradients is discussed together with the formation of double-diffusive boundary layers along liquid-gas interfaces. Similarity solutions for each class of free convection are derived and the resulting nonlinear two-point problems are solved numerically using the quasi-linearization method. Velocity, temperature, concentration profiles, interfacial velocity, heat and mass transfer bulk coefficients for various Prandtl and Schmidt numbers, and different values of the similarity parameters are determined. The convective flows are of particular interest because they are considered to influence the processes of crystal growth, both on earth and in a microgravity environment.

ULTRA-SHARP solution of the Smith-Hutton problem

NASA Technical Reports Server (NTRS)

Leonard, B. P.; Mokhtari, Simin

1992-01-01

Highly convective scalar transport involving near-discontinuities and strong streamline curvature was addressed in a paper by Smith and Hutton in 1982, comparing several different convection schemes applied to a specially devised test problem. First order methods showed significant artificial diffusion, whereas higher order methods gave less smearing but had a tendency to overshoot and oscillate. Perhaps because unphysical oscillations are more obvious than unphysical smearing, the intervening period has seen a rise in popularity of low order artificially diffusive schemes, especially in the numerical heat transfer industry. The present paper describes an alternate strategy of using non-artificially diffusive high order methods, while maintaining strictly monotonic transitions through the use of simple flux limited constraints. Limited third order upwinding is usually found to be the most cost effective basic convection scheme. Tighter resolution of discontinuities can be obtained at little additional cost by using automatic adaptive stencil expansion to higher order in local regions, as needed.

Benchmarking FEniCS for mantle convection simulations

NASA Astrophysics Data System (ADS)

Vynnytska, L.; Rognes, M. E.; Clark, S. R.

2013-01-01

This paper evaluates the usability of the FEniCS Project for mantle convection simulations by numerical comparison to three established benchmarks. The benchmark problems all concern convection processes in an incompressible fluid induced by temperature or composition variations, and cover three cases: (i) steady-state convection with depth- and temperature-dependent viscosity, (ii) time-dependent convection with constant viscosity and internal heating, and (iii) a Rayleigh-Taylor instability. These problems are modeled by the Stokes equations for the fluid and advection-diffusion equations for the temperature and composition. The FEniCS Project provides a novel platform for the automated solution of differential equations by finite element methods. In particular, it offers a significant flexibility with regard to modeling and numerical discretization choices; we have here used a discontinuous Galerkin method for the numerical solution of the advection-diffusion equations. Our numerical results are in agreement with the benchmarks, and demonstrate the applicability of both the discontinuous Galerkin method and FEniCS for such applications.

On the stability of the Atlantic meridional overturning circulation

PubMed Central

Hofmann, Matthias; Rahmstorf, Stefan

2009-01-01

One of the most important large-scale ocean current systems for Earth's climate is the Atlantic meridional overturning circulation (AMOC). Here we review its stability properties and present new model simulations to study the AMOC's hysteresis response to freshwater perturbations. We employ seven different versions of an Ocean General Circulation Model by using a highly accurate tracer advection scheme, which minimizes the problem of numerical diffusion. We find that a characteristic freshwater hysteresis also exists in the predominantly wind-driven, low-diffusion limit of the AMOC. However, the shape of the hysteresis changes, indicating that a convective instability rather than the advective Stommel feedback plays a dominant role. We show that model errors in the mean climate can make the hysteresis disappear, and we investigate how model innovations over the past two decades, like new parameterizations and mixing schemes, affect the AMOC stability. Finally, we discuss evidence that current climate models systematically overestimate the stability of the AMOC. PMID:19897722

Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations

NASA Technical Reports Server (NTRS)

Kennedy, Christopher A.; Carpenter, Mark H.

2001-01-01

Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one-dimensional convection-diffusion-reaction (CDR) equations. First, accuracy, stability, conservation, and dense output are considered for the general case when N different Runge-Kutta methods are grouped into a single composite method. Then, implicit-explicit, N = 2, additive Runge-Kutta ARK2 methods from third- to fifth-order are presented that allow for integration of stiff terms by an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method while the nonstiff terms are integrated with a traditional explicit Runge-Kutta method (ERK). Coupling error terms are of equal order to those of the elemental methods. Derived ARK2 methods have vanishing stability functions for very large values of the stiff scaled eigenvalue, z(exp [I]) goes to infinity, and retain high stability efficiency in the absence of stiffness, z(exp [I]) goes to zero. Extrapolation-type stage-value predictors are provided based on dense-output formulae. Optimized methods minimize both leading order ARK2 error terms and Butcher coefficient magnitudes as well as maximize conservation properties. Numerical tests of the new schemes on a CDR problem show negligible stiffness leakage and near classical order convergence rates. However, tests on three simple singular-perturbation problems reveal generally predictable order reduction. Error control is best managed with a PID-controller. While results for the fifth-order method are disappointing, both the new third- and fourth-order methods are at least as efficient as existing ARK2 methods while offering error control and stage-value predictors.

The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

NASA Technical Reports Server (NTRS)

Cockburn, Bernardo; Shu, Chi-Wang

1997-01-01

In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L(sup 2)-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.

Flow of nanofluid past a Riga plate

NASA Astrophysics Data System (ADS)

Ahmad, Adeel; Asghar, Saleem; Afzal, Sumaira

2016-03-01

This paper studies the mixed convection boundary layer flow of a nanofluid past a vertical Riga plate in the presence of strong suction. The mathematical model incorporates the Brownian motion and thermophoresis effects due to nanofluid and the Grinberg-term for the wall parallel Lorentz force due to Riga plate. The analytical solution of the problem is presented using the perturbation method for small Brownian and thermophoresis diffusion parameters. The numerical solution is also presented to ensure the reliability of the asymptotic method. The comparison of the two solutions shows an excellent agreement. The correlation expressions for skin friction, Nusselt number and Sherwood number are developed by performing linear regression on the obtained numerical data. The effects of nanofluid and the Lorentz force due to Riga plate, on the skin friction are discussed.

Properties of convective oxygen and silicon burning shells in supernova progenitors

NASA Astrophysics Data System (ADS)

Collins, Christine; Müller, Bernhard; Heger, Alexander

2018-01-01

Recent 3D simulations have suggested that convective seed perturbations from shell burning can play an important role in triggering neutrino-driven supernova explosions. Since isolated simulations cannot determine whether this perturbation-aided mechanism is of general relevance across the progenitor mass range, we here investigate the pertinent properties of convective oxygen and silicon burning shells in a broad range of pre-supernova stellar evolution models. We find that conditions for perturbation-aided explosions are most favourable in the extended oxygen shells of progenitors between about 16 and 26 solar masses, which exhibit large-scale convective overturn with high convective Mach numbers. Although the highest convective Mach numbers of up to 0.3 are reached in the oxygen shells of low-mass progenitors, convection is typically dominated by small-scale modes in these shells, which implies a more modest role of initial perturbations in the explosion mechanism. Convective silicon burning rarely provides the high Mach numbers and large-scale perturbations required for perturbation-aided explosions. We also find that about 40 per cent of progenitors between 16 and 26 solar masses exhibit simultaneous oxygen and neon burning in the same convection zone as a result of a shell merger shortly before collapse.

A Comparison of Some Difference Schemes for a Parabolic Problem of Zero-Coupon Bond Pricing

NASA Astrophysics Data System (ADS)

Chernogorova, Tatiana; Vulkov, Lubin

2009-11-01

This paper describes a comparison of some numerical methods for solving a convection-diffusion equation subjected by dynamical boundary conditions which arises in the zero-coupon bond pricing. The one-dimensional convection-diffusion equation is solved by using difference schemes with weights including standard difference schemes as the monotone Samarskii's scheme, FTCS and Crank-Nicolson methods. The schemes are free of spurious oscillations and satisfy the positivity and maximum principle as demanded for the financial and diffusive solution. Numerical results are compared with analytical solutions.

The numerical study and comparison of radial basis functions in applications of the dual reciprocity boundary element method to convection-diffusion problems

NASA Astrophysics Data System (ADS)

Chanthawara, Krittidej; Kaennakham, Sayan; Toutip, Wattana

2016-02-01

The methodology of Dual Reciprocity Boundary Element Method (DRBEM) is applied to the convection-diffusion problems and investigating its performance is our first objective of the work. Seven types of Radial Basis Functions (RBF); Linear, Thin-plate Spline, Cubic, Compactly Supported, Inverse Multiquadric, Quadratic, and that proposed by [12], were closely investigated in order to numerically compare their effectiveness drawbacks etc. and this is taken as our second objective. A sufficient number of simulations were performed covering as many aspects as possible. Varidated against both exacts and other numerical works, the final results imply strongly that the Thin-Plate Spline and Linear type of RBF are superior to others in terms of both solutions' quality and CPU-time spent while the Inverse Multiquadric seems to poorly yield the results. It is also found that DRBEM can perform relatively well at moderate level of convective force and as anticipated becomes unstable when the problem becomes more convective-dominated, as normally found in all classical mesh-dependence methods.

Non-oscillatory and non-diffusive solution of convection problems by the iteratively reweighted least-squares finite element method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1993-01-01

A comparative description is presented for the least-squares FEM (LSFEM) for 2D steady-state pure convection problems. In addition to exhibiting better control of the streamline derivative than the streamline upwinding Petrov-Galerkin method, numerical convergence rates are obtained which show the LSFEM to be virtually optimal. The LSFEM is used as a framework for an iteratively reweighted LSFEM yielding nonoscillatory and nondiffusive solutions for problems with contact discontinuities; this method is shown to convect contact discontinuities without error when using triangular and bilinear elements.

Onset of the convection in a supercritical fluid.

PubMed

Meyer, H

2006-01-01

A model is proposed that leads to the scaled relation tp/tau D=Ftp(Ra-Rac) for the development of convection in a pure fluid in a Rayleigh-Bénard cell after the start of the heat current at t=0. Here tp is the time of the first maximum of the temperature drop DeltaT(t) across the fluid layer, the signature of rapidly growing convection, tau D is the diffusion relaxation time, and Rac is the critical Rayleigh number. Such a relation was first obtained empirically from experimental data. Because of the unknown perturbations in the cell that lead to convection development beyond the point of the fluid instability, the model determines tp/tau D within a multiplicative factor Psi square root Rac(HBL), the only fit parameter product. Here Rac(HBL), of the order 10(3), is the critical Rayleigh number of the hot boundary layer and Psi is a fit parameter. There is then good agreement over more than four decades of Ra-Rac between the model and the experiments on supercritical 3He at various heat currents and temperatures. The value of the parameter Psi, which phenomenologically represents the effectiveness of the perturbations, is discussed in connection with predictions by El Khouri and Carlès of the fluid instability onset time.

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

A numerical scheme for singularly perturbed reaction-diffusion problems with a negative shift via numerov method

NASA Astrophysics Data System (ADS)

Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.

2017-11-01

In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.

Maximum Principles and Application to the Analysis of An Explicit Time Marching Algorithm

NASA Technical Reports Server (NTRS)

LeTallec, Patrick; Tidriri, Moulay D.

1996-01-01

In this paper we develop local and global estimates for the solution of convection-diffusion problems. We then study the convergence properties of a Time Marching Algorithm solving Advection-Diffusion problems on two domains using incompatible discretizations. This study is based on a De-Giorgi-Nash maximum principle.

Double-diffusive boundary layers along vertical free surfaces

NASA Astrophysics Data System (ADS)

Napolitano, L. G.; Viviani, A.; Savino, R.

1992-05-01

This paper deals with double-diffusive (or thermosolutal) combined free convection, i.e., free convection due to buoyant forces (natural convection) and surface tension gradients (Marangoni convection), which are generated by volume differences and surface gradients of temperature and solute concentration. Attention is focused on boundary layers that form along a vertical liquid-gas interface, when the appropriately defined nondimensional characteristic transport numbers are large enough, in problems of thermosolutal natural and Marangoni convection, such as buoyancy and surface tension driven flows in differentially heated open cavities and liquid bridges. Classes of similar solutions are derived for each class of convection on the basis of a rigorous order of magnitude analysis. Velocity, temperature and concentration profiles are reported in the similarity plane; flow and transport properties at the liquid-gas interface (interfacial velocity, heat and mass transfer bulk coefficients) are obtained for a wide range of Prandtl and Schmidt numbers and different values of the similarity parameter.

Numerical simulation of electrophoresis separation processes

NASA Technical Reports Server (NTRS)

Ganjoo, D. K.; Tezduyar, T. E.

1986-01-01

A new Petrov-Galerkin finite element formulation has been proposed for transient convection-diffusion problems. Most Petrov-Galerkin formulations take into account the spatial discretization, and the weighting functions so developed give satisfactory solutions for steady state problems. Though these schemes can be used for transient problems, there is scope for improvement. The schemes proposed here, which consider temporal as well as spatial discretization, provide improved solutions. Electrophoresis, which involves the motion of charged entities under the influence of an applied electric field, is governed by equations similiar to those encountered in fluid flow problems, i.e., transient convection-diffusion equations. Test problems are solved in electrophoresis and fluid flow. The results obtained are satisfactory. It is also expected that these schemes, suitably adapted, will improve the numerical solutions of the compressible Euler and the Navier-Stokes equations.

Topology optimisation for natural convection problems

NASA Astrophysics Data System (ADS)

Alexandersen, Joe; Aage, Niels; Andreasen, Casper Schousboe; Sigmund, Ole

2014-12-01

This paper demonstrates the application of the density-based topology optimisation approach for the design of heat sinks and micropumps based on natural convection effects. The problems are modelled under the assumptions of steady-state laminar flow using the incompressible Navier-Stokes equations coupled to the convection-diffusion equation through the Boussinesq approximation. In order to facilitate topology optimisation, the Brinkman approach is taken to penalise velocities inside the solid domain and the effective thermal conductivity is interpolated in order to accommodate differences in thermal conductivity of the solid and fluid phases. The governing equations are discretised using stabilised finite elements and topology optimisation is performed for two different problems using discrete adjoint sensitivity analysis. The study shows that topology optimisation is a viable approach for designing heat sink geometries cooled by natural convection and micropumps powered by natural convection.

Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization

NASA Astrophysics Data System (ADS)

Christensen, H. M.; Moroz, I.; Palmer, T.

2015-12-01

It is now acknowledged that representing model uncertainty in atmospheric simulators is essential for the production of reliable probabilistic ensemble forecasts, and a number of different techniques have been proposed for this purpose. Stochastic convection parameterization schemes use random numbers to represent the difference between a deterministic parameterization scheme and the true atmosphere, accounting for the unresolved sub grid-scale variability associated with convective clouds. An alternative approach varies the values of poorly constrained physical parameters in the model to represent the uncertainty in these parameters. This study presents new perturbed parameter schemes for use in the European Centre for Medium Range Weather Forecasts (ECMWF) convection scheme. Two types of scheme are developed and implemented. Both schemes represent the joint uncertainty in four of the parameters in the convection parametrisation scheme, which was estimated using the Ensemble Prediction and Parameter Estimation System (EPPES). The first scheme developed is a fixed perturbed parameter scheme, where the values of uncertain parameters are changed between ensemble members, but held constant over the duration of the forecast. The second is a stochastically varying perturbed parameter scheme. The performance of these schemes was compared to the ECMWF operational stochastic scheme, Stochastically Perturbed Parametrisation Tendencies (SPPT), and to a model which does not represent uncertainty in convection. The skill of probabilistic forecasts made using the different models was evaluated. While the perturbed parameter schemes improve on the stochastic parametrisation in some regards, the SPPT scheme outperforms the perturbed parameter approaches when considering forecast variables that are particularly sensitive to convection. Overall, SPPT schemes are the most skilful representations of model uncertainty due to convection parametrisation. Reference: H. M. Christensen, I. M. Moroz, and T. N. Palmer, 2015: Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization. J. Atmos. Sci., 72, 2525-2544.

Numerical Study of g-Jitter Induced Double-Diffusive Convection

NASA Technical Reports Server (NTRS)

Shu, Y.; Li, B. Q.; deGroh, Henry C.

2001-01-01

A finite element study is presented of double-diffusive convection driven by g-jitter in a microgravity environment. Mathematical formulations are presented and extensive simulations are carried out for g-jitter induced fluid flow, temperature distribution, and solutal transport in an alloy system under consideration for space flights. Computations include the use of idealized single-frequency and multi-frequency g-jitter as well as the real g-jitter data taken during an actual Space Shuttle fight. Little correlation is seen between these velocity components for the g-jitter components studied. The temperature field is basically undisturbed by convection because of a small Pr number for the fluid. The disturbance of the concentration field, however, is pronounced, and the local variation of the concentration follows the velocity oscillation in time. It is found that although the concentration field varies in both position and time, the local concentration gradient remains approximately constant in time. Numerical study further indicates that with an increase in g-jitter force (or amplitude), the nonlinear convective effects become much more obvious, which in turn drastically change the concentration fields. The simulated results computed using the g-jitter data taken during space flights show that both the velocity and concentration become random, following approximately the same pattern as the g-jitter perturbations.

Entropy generation in a mixed convection Poiseulle flow of molybdenum disulphide Jeffrey nanofluid

NASA Astrophysics Data System (ADS)

Gul, Aaiza; Khan, Ilyas; Makhanov, Stanislav S.

2018-06-01

Entropy analysis in a mixed convection Poiseulle flow of a Molybdenum Disulphide Jeffrey Nanofluid (MDJN) is presented. Mixed convection is caused due to buoyancy force and external pressure gradient. The problem is formulated in terms of a boundary value problem for a system of partial differential equations. An analytical solution for the velocity and the temperature is obtained using the perturbation technique. Entropy generation has been derived as a function of the velocity and temperature gradients. The solutions are displayed graphically and the relevant importance of the input parameters is discussed. A Jeffrey nanofluid (JN) has been compared with a second grade nanofluid (SGN) and Newtonian nanofluid (NN). It is found that the entropy generation decreases when the temperature increases whereas increasing the Brickman number increases entropy generation.

Analysis of models for two solution crystal growth problems

NASA Technical Reports Server (NTRS)

Fehribach, Joseph D.; Rosenberger, Franz

1989-01-01

Two diffusive solution crystal growth models are considered which are characterized by two phases separated by an interface, a lack of convective mixing in either phase, and the presence of diffusion components differing widely in diffusivity. The first model describes precipitant-driven solution crystal growth and the second model describes a hanging drop evaporation problem. It is shown that for certain proteins sharp concentration gradients may develop in the drop during evaporation, while under the same conditions the concentrations of other proteins remain uniform.

Influence of diffusion and convective transport on dendritic growth in dilute alloys

NASA Technical Reports Server (NTRS)

Glicksman, M. E.; Singh, N. B.; Chopra, M.

1982-01-01

Experimentation has been carried out in which the kinetics and morphology of dendritic growth were measured as a function of thermal supercooling, solute concentration, and spatial orientation of the dendritic growth axis. The crystal growth system studied is succinonitrile, NC(CH2)2CN, with additions of argon (up to 0.1 mole percent). This system is especially useful as a model for alloy studies because kinetic data are available for high purity (7-9's) succinonitrile. The influence of the solute, at fixed thermal supercooling, is to increase the growth velocity and correspondingly decrease intrinsic crystal dimensions. Morphological measurements are described in detail relating tip size, perturbation wavelength, supercooling, and solute concentration. The analysis of these effects based on morphological stability theory is also discussed, and experiments permitting the separation of convective and diffusive heat transport during crystal growth of succinonitrile are described. The studies underscore the importance of gravitationally-induced buoyancy effects on crystal growth.

Unsteady, one-dimensional gas dynamics computations using a TVD type sequential solver

NASA Technical Reports Server (NTRS)

Thakur, Siddharth; Shyy, Wei

1992-01-01

The efficacy of high resolution convection schemes to resolve sharp gradient in unsteady, 1D flows is examined using the TVD concept based on a sequential solution algorithm. Two unsteady flow problems are considered which include the problem involving the interaction of the various waves in a shock tube with closed reflecting ends and the problem involving the unsteady gas dynamics in a tube with closed ends subject to an initial pressure perturbation. It is concluded that high accuracy convection schemes in a sequential solution framework are capable of resolving discontinuities in unsteady flows involving complex gas dynamics. However, a sufficient amount of dissipation is required to suppress oscillations near discontinuities in the sequential approach, which leads to smearing of the solution profiles.

A cost-effective strategy for nonoscillatory convection without clipping

NASA Technical Reports Server (NTRS)

Leonard, B. P.; Niknafs, H. S.

1990-01-01

Clipping of narrow extrema and distortion of smooth profiles is a well known problem associated with so-called high resolution nonoscillatory convection schemes. A strategy is presented for accurately simulating highly convective flows containing discontinuities such as density fronts or shock waves, without distorting smooth profiles or clipping narrow local extrema. The convection algorithm is based on non-artificially diffusive third-order upwinding in smooth regions, with automatic adaptive stencil expansion to (in principle, arbitrarily) higher order upwinding locally, in regions of rapidly changing gradients. This is highly cost effective because the wider stencil is used only where needed-in isolated narrow regions. A recently developed universal limiter assures sharp monotonic resolution of discontinuities without introducing artificial diffusion or numerical compression. An adaptive discriminator is constructed to distinguish between spurious overshoots and physical peaks; this automatically relaxes the limiter near local turning points, thereby avoiding loss of resolution in narrow extrema. Examples are given for one-dimensional pure convection of scalar profiles at constant velocity.

Residual fields from extinct dynamos

NASA Astrophysics Data System (ADS)

Parker, E. N.

The generation of magnetic fields in convective zones of declining vigor and/or thickness is considered, the goal being to explain the magnetic fields observed in A-stars. The investigation is restricted to kinematical dynamos in order to show some of the many possibilities, which depend on the assumed conditions of decline of the convection. The examples illustrate the quantitative detail required to describe the convection in order to extract any firm conclusions concerning specific stars. The first example treats the basic problem of diffusion from a layer of declining thickness. The second has a buoyant rise added to the field in the layer. The third deals with plane dynamo waves in a region with declining eddy diffusivity, dynamo coefficient, and large-scale shear. It is noted that the dynamo number may increase or decrease with declining convection, with an increase expected if the large-scale shear does not decline as rapidly as the eddy diffusivity. It is shown that one of the components of the field may increase without bound even when the dynamo number declines to zero.

Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems

NASA Astrophysics Data System (ADS)

Ge, Yongbin; Cao, Fujun

2011-05-01

In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection-diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33-53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature.

Non-local transport in turbulent MHD convection

NASA Technical Reports Server (NTRS)

Miesch, Mark; Brandenburg, Axel; Zweibel, Ellen; Toomre, Juri

1995-01-01

The nonlocal non-diffusive transport of passive scalars in turbulent magnetohydrodynamic (MHD) convection is investigated using transilient matrices. These matrices describe the probability that a tracer particle beginning at one position in a flow will be advected to another position after some time. A method for the calculation of these matrices from simulation data which involves following the trajectories of passive tracer particles and calculating their transport statistics, is presented. The method is applied to study the transport in several simulations of turbulent, rotating, three dimensional compressible, penetrative MDH convection. Transport coefficients and other diagnostics are used to quantify the transport, which is found to resemble advection more closely than diffusion. Some of the results are found to have direct relevance to other physical problems, such as the light element depletion in sun-type stars. The large kurtosis found for downward moving particles at the base of the convection zone implies several extreme events.

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Multiple and exact soliton solutions of the perturbed Korteweg-de Vries equation of long surface waves in a convective fluid via Painlevé analysis, factorization, and simplest equation methods.

PubMed

Selima, Ehab S; Yao, Xiaohua; Wazwaz, Abdul-Majid

2017-06-01

In this research, the surface waves of a horizontal fluid layer open to air under gravity field and vertical temperature gradient effects are studied. The governing equations of this model are reformulated and converted to a nonlinear evolution equation, the perturbed Korteweg-de Vries (pKdV) equation. We investigate the latter equation, which includes dispersion, diffusion, and instability effects, in order to examine the evolution of long surface waves in a convective fluid. Dispersion relation of the pKdV equation and its properties are discussed. The Painlevé analysis is applied not only to check the integrability of the pKdV equation but also to establish the Bäcklund transformation form. In addition, traveling wave solutions and a general form of the multiple-soliton solutions of the pKdV equation are obtained via Bäcklund transformation, the simplest equation method using Bernoulli, Riccati, and Burgers' equations as simplest equations, and the factorization method.

Comparison of numerical simulation and experimental data for steam-in-place sterilization

NASA Technical Reports Server (NTRS)

Young, Jack H.; Lasher, William C.

1993-01-01

A complex problem involving convective flow of a binary mixture containing a condensable vapor and noncondensable gas in a partially enclosed chamber was modelled and results compared to transient experimental values. The finite element model successfully predicted transport processes in dead-ended tubes with inside diameters of 0.4 to 1.0 cm. When buoyancy driven convective flow was dominant, temperature and mixture compositions agreed with experimental data. Data from 0.4 cm tubes indicate diffusion to be the primary air removal method in small diameter tubes and the diffusivity value in the model to be too large.

Moist, Double-diffusive convection

NASA Astrophysics Data System (ADS)

Oishi, Jeffrey; Burns, Keaton; Brown, Ben; Lecoanet, Daniel; Vasil, Geoffrey

2017-11-01

Double-diffusive convection occurs when the competition between stabilizing and a destabilizing buoyancy source is mediated by a difference in the diffusivity of each source. Such convection is important in a wide variety of astrophysical and geophysical flows. However, in giant planets, double-diffusive convection occurs in regions where condensation of important components of the atmosphere occurs. Here, we present preliminary calculations of moist, double-diffusive convection using the Dedalus pseudospectral framework. Using a simple model for phase change, we verify growth rates for moist double diffusive convection from linear calculations and report on preliminary relationships between the ability to form liquid phase and the resulting Nusselt number in nonlinear simulations.

Numerical modeling of HgCdTe solidification: Effects of phase diagram, double-diffusion convection and microgravity level

NASA Technical Reports Server (NTRS)

Bune, Andris V.; Gillies, Donald C.; Lehozky, Sandor L.

1997-01-01

A numerical model of HgCdTe solidification was implemented using finite the element code FIDAP. Model verification was done using both experimental data and numerical test problems. The model was used to evaluate possible effects of double-diffusion convection in molten material, and microgravity level on concentration distribution in the solidified HgCdTe. Particular attention was paid to incorporation of HgCdTe phase diagram. It was found, that below a critical microgravity amplitude, the maximum convective velocity in the melt appears virtually independent on the microgravity vector orientation. Good agreement between predicted interface shape and an interface obtained experimentally by quenching was achieved. The results of numerical modeling are presented in the form of video film.

From convection rolls to finger convection in double-diffusive turbulence

NASA Astrophysics Data System (ADS)

Yang, Yantao; Verzicco, Roberto; Lohse, Detlef

2015-11-01

The double diffusive convection (DDC), where the fluid density depends on two scalar components with very different molecular diffusivities, is frequently encountered in oceanography, astrophysics, and electrochemistry. In this talk we report a systematic study of vertically bounded DDC for various control parameters. The flow is driven by an unstable salinity difference between two plates and stabilized by a temperature difference. As the relative strength of temperature difference becomes stronger, the flow transits from a state with large-scale convection rolls, which is similar to the Rayleigh-Bénard (RB) flow, to a state with well-organised salt fingers. When the temperature difference increases further, the flow breaks down to a purely conductive state. During this transit the velocity decreases monotonically. Counterintuitively, the salinity transfer can be enhanced when a stabilising temperature field is applied to the system. This happens when convection rolls are replaced by salt fingers. In addition, we show that the Grossmann-Lohse theory originally developed for RB flow can be directly applied to the current problem and accurately predicts the salinity transfer rate for a wide range of control parameters. Supported by Stichting FOM and the National Computing Facilities (NCF), both sponsored by NWO. The simulations were conducted on the Dutch supercomputer Cartesius at SURFsara.

An extended laser flash technique for thermal diffusivity measurement of high-temperature materials

NASA Technical Reports Server (NTRS)

Shen, F.; Khodadadi, J. M.

1993-01-01

Knowledge of thermal diffusivity data for high-temperature materials (solids and liquids) is very important in analyzing a number of processes, among them solidification, crystal growth, and welding. However, reliable thermal diffusivity versus temperature data, particularly those for high-temperature liquids, are still far from complete. The main measurement difficulties are due to the presence of convection and the requirement for a container. Fortunately, the availability of levitation techniques has made it possible to solve the containment problem. Based on the feasibility of the levitation technology, a new laser flash technique which is applicable to both levitated liquid and solid samples is being developed. At this point, the analysis for solid samples is near completion and highlights of the technique are presented here. The levitated solid sample which is assumed to be a sphere is subjected to a very short burst of high power radiant energy. The temperature of the irradiated surface area is elevated and a transient heat transfer process takes place within the sample. This containerless process is a two-dimensional unsteady heat conduction problem. Due to the nonlinearity of the radiative plus convective boundary condition, an analytic solution cannot be obtained. Two options are available at this point. Firstly, the radiation boundary condition can be linearized, which then accommodates a closed-form analytic solution. Comparison of the analytic curves for the temperature rise at different points to the experimentally-measured values will then provide the thermal diffusivity values. Secondly, one may set up an inverse conduction problem whereby experimentally obtained surface temperature history is used as the boundary conditions. The thermal diffusivity can then be elevated by minimizing the difference between the real heat flux boundary condition (radiation plus convection) and the measurements. Status of an experimental study directed at measuring the thermal diffusivity of high-temperature solid samples of pure Nickel and Inconel 718 superalloys are presented. Preliminary measurements showing surface temperature histories are discussed.

Venus ionosphere: photochemical and thermal diffusion control of ion composition.

PubMed

Bauer, S J; Donahue, T M; Hartle, R E; Taylor, H A

1979-07-06

The major photochemical sources and sinks for ten of the ions measured by the ion mass spectrometer on the Pioneer Venus bus and orbiter spacecraft that are consistent with the neutral gas composition measured on the same spacecraft have been identified. The neutral gas temperature (Tn) as a function of solar zenith angle (chi) derived from measured ion distributions in photochemical equilibrium is given by Tn (K) = 323 cos(1/5)chi. Above 200 kilometers, the altitude behavior of ions is generally controlled by plasma diffusion, with important modifications for minor ions due to thermal diffusion resulting from the observed gradients of plasma temperatures. The dayside equilibrium distributions of ions are sometimes perturbed by plasma convection, while lateral transport of ions from the dayside seems to be a major source of the nightside ionosphere.

Perturbative momentum transport in MAST L-mode plasmas

DOE PAGES

Guttenfelder, W.; Field, A. R.; Lupelli, I.; ...

2017-03-28

Non-axisymmetric magnetic fields are used to perturbatively probe momentum transport physics in MAST L-mode plasmas. The low beta L-mode target was chosen to complement previous experiments conducted in high beta NSTX H-mode plasmas (beta N = 3.5-4.6) where an inward momentum pinch was measured. In those cases quasi-linear gyrokinetic simulations of unstable ballooning micro-instabilities predict weak or outward momentum convection, in contrast to the measurements. The weak pinch was predicted to be due to both electromagnetic effects at high beta and low aspect ratio minimizing the symmetry-breaking of the instabilities responsible for momentum transport. In an attempt to lessen thesemore » electromagnetic effects at low aspect ratio, perturbative experiments were run in MAST L-mode discharges at lower beta (beta N = 2). The perturbative transport analysis used the time-dependent response following the termination of applied 3D fields that briefly brake the plasma rotation ( similar to the NSTX H-mode experiments). Assuming time-invariant diffusive (chi(phi))and convective (V-phi) transport coefficients, an inward pinch is inferred with magnitudes, (RV phi/chi(phi)) = (-1)-(-9), similar to those found in NSTX H-modes and in conventional tokamaks. However, if experimental uncertainties due to non-stationary conditions during and after the applied 3D field are considered, a weak pinch or even outward convection is inferred, ( RV phi/chi(phi)) = (-1)-(+5). Linear gyrokinetic simulations indicate that for these lower beta L-modes, the predicted momentum pinch is predicted to be relatively small, ( RV phi/chi(phi))(sim) approximate to -1. While this falls within the experimentally inferred range, the uncertainties are practically too large to quantitatively validate the predictions. Challenges and implications for this particular experimental technique are discussed, as well as additional possible physical mechanisms that may be important in understanding momentum transport in these low aspect ratio plasmas.« less

Perturbative momentum transport in MAST L-mode plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guttenfelder, W.; Field, A. R.; Lupelli, I.

Non-axisymmetric magnetic fields are used to perturbatively probe momentum transport physics in MAST L-mode plasmas. The low beta L-mode target was chosen to complement previous experiments conducted in high beta NSTX H-mode plasmas (beta N = 3.5-4.6) where an inward momentum pinch was measured. In those cases quasi-linear gyrokinetic simulations of unstable ballooning micro-instabilities predict weak or outward momentum convection, in contrast to the measurements. The weak pinch was predicted to be due to both electromagnetic effects at high beta and low aspect ratio minimizing the symmetry-breaking of the instabilities responsible for momentum transport. In an attempt to lessen thesemore » electromagnetic effects at low aspect ratio, perturbative experiments were run in MAST L-mode discharges at lower beta (beta N = 2). The perturbative transport analysis used the time-dependent response following the termination of applied 3D fields that briefly brake the plasma rotation ( similar to the NSTX H-mode experiments). Assuming time-invariant diffusive (chi(phi))and convective (V-phi) transport coefficients, an inward pinch is inferred with magnitudes, (RV phi/chi(phi)) = (-1)-(-9), similar to those found in NSTX H-modes and in conventional tokamaks. However, if experimental uncertainties due to non-stationary conditions during and after the applied 3D field are considered, a weak pinch or even outward convection is inferred, ( RV phi/chi(phi)) = (-1)-(+5). Linear gyrokinetic simulations indicate that for these lower beta L-modes, the predicted momentum pinch is predicted to be relatively small, ( RV phi/chi(phi))(sim) approximate to -1. While this falls within the experimentally inferred range, the uncertainties are practically too large to quantitatively validate the predictions. Challenges and implications for this particular experimental technique are discussed, as well as additional possible physical mechanisms that may be important in understanding momentum transport in these low aspect ratio plasmas.« less

An optimal analysis for Darcy-Forchheimer 3D flow of Carreau nanofluid with convectively heated surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2018-06-01

Darcy-Forchheimer three dimensional flow of Carreau nanoliquid induced by a linearly stretchable surface with convective boundary condition has been analyzed. Buongiorno model has been employed to elaborate thermophoresis and Brownian diffusion effects. Zero nanoparticles mass flux and convective surface conditions are implemented at the boundary. The governing problems are nonlinear. Optimal homotopic procedure has been used to tackle the governing mathematical system. Graphical results clearly depict the outcome of temperature and concentration fields. Surface drag coefficients and local Nusselt number are also plotted and discussed.

Existence, uniqueness and regularity of a time-periodic probability density distribution arising in a sedimentation-diffusion problem

NASA Technical Reports Server (NTRS)

Nitsche, Ludwig C.; Nitsche, Johannes M.; Brenner, Howard

1988-01-01

The sedimentation and diffusion of a nonneutrally buoyant Brownian particle in vertical fluid-filled cylinder of finite length which is instantaneously inverted at regular intervals are investigated analytically. A one-dimensional convective-diffusive equation is derived to describe the temporal and spatial evolution of the probability density; a periodicity condition is formulated; the applicability of Fredholm theory is established; and the parameter-space regions are determined within which the existence and uniqueness of solutions are guaranteed. Numerical results for sample problems are presented graphically and briefly characterized.

Numerical analysis of mixing by sharp-edge-based acoustofluidic micromixer

NASA Astrophysics Data System (ADS)

Nama, Nitesh; Huang, Po-Hsun; Jun Huang, Tony; Costanzo, Francesco

2015-11-01

Recently, acoustically oscillated sharp-edges have been employed to realize rapid and homogeneous mixing at microscales (Huang, Lab on a Chip, 13, 2013). Here, we present a numerical model, qualitatively validated by experimental results, to analyze the acoustic mixing inside a sharp-edge-based micromixer. We extend our previous numerical model (Nama, Lab on a Chip, 14, 2014) to combine the Generalized Lagrangian Mean (GLM) theory with the convection-diffusion equation, while also allowing for the presence of a background flow as observed in a typical sharp-edge-based micromixer. We employ a perturbation approach to divide the flow variables into zeroth-, first- and second-order fields which are successively solved to obtain the Lagrangian mean velocity. The Langrangian mean velocity and the background flow velocity are further employed with the convection-diffusion equation to obtain the concentration profile. We characterize the effects of various operational and geometrical parameters to suggest potential design changes for improving the mixing performance of the sharp-edge-based micromixer. Lastly, we investigate the possibility of generation of a spatio-temporally controllable concentration gradient by placing sharp-edge structures inside the microchannel.

Influence of surface wettability on transport mechanisms governing water droplet evaporation.

PubMed

Pan, Zhenhai; Weibel, Justin A; Garimella, Suresh V

2014-08-19

Prediction and manipulation of the evaporation of small droplets is a fundamental problem with importance in a variety of microfluidic, microfabrication, and biomedical applications. A vapor-diffusion-based model has been widely employed to predict the interfacial evaporation rate; however, its scope of applicability is limited due to incorporation of a number of simplifying assumptions of the physical behavior. Two key transport mechanisms besides vapor diffusion-evaporative cooling and natural convection in the surrounding gas-are investigated here as a function of the substrate wettability using an augmented droplet evaporation model. Three regimes are distinguished by the instantaneous contact angle (CA). In Regime I (CA ≲ 60°), the flat droplet shape results in a small thermal resistance between the liquid-vapor interface and substrate, which mitigates the effect of evaporative cooling; upward gas-phase natural convection enhances evaporation. In Regime II (60 ≲ CA ≲ 90°), evaporative cooling at the interface suppresses evaporation with increasing contact angle and counterbalances the gas-phase convection enhancement. Because effects of the evaporative cooling and gas-phase convection mechanisms largely neutralize each other, the vapor-diffusion-based model can predict the overall evaporation rates in this regime. In Regime III (CA ≳ 90°), evaporative cooling suppresses the evaporation rate significantly and reverses entirely the direction of natural convection induced by vapor concentration gradients in the gas phase. Delineation of these counteracting mechanisms reconciles previous debate (founded on single-surface experiments or models that consider only a subset of the governing transport mechanisms) regarding the applicability of the classic vapor-diffusion model. The vapor diffusion-based model cannot predict the local evaporation flux along the interface for high contact angle (CA ≥ 90°) when evaporative cooling is strong and the temperature gradient along the interface determines the peak local evaporation flux.

Transport mechanisms of contaminants released from fine sediment in rivers

NASA Astrophysics Data System (ADS)

Cheng, Pengda; Zhu, Hongwei; Zhong, Baochang; Wang, Daozeng

2015-12-01

Contaminants released from sediment into rivers are one of the main problems to study in environmental hydrodynamics. For contaminants released into the overlying water under different hydrodynamic conditions, the mechanical mechanisms involved can be roughly divided into convective diffusion, molecular diffusion, and adsorption/desorption. Because of the obvious environmental influence of fine sediment (D_{90}= 0.06 mm), non-cohesive fine sediment, and cohesive fine sediment are researched in this paper, and phosphorus is chosen for a typical adsorption of a contaminant. Through theoretical analysis of the contaminant release process, according to different hydraulic conditions, the contaminant release coupling mathematical model can be established by the N-S equation, the Darcy equation, the solute transport equation, and the adsorption/desorption equation. Then, the experiments are completed in an open water flume. The simulation results and experimental results show that convective diffusion dominates the contaminant release both in non-cohesive and cohesive fine sediment after their suspension, and that they contribute more than 90 % of the total release. Molecular diffusion and desorption have more of a contribution for contaminant release from unsuspended sediment. In unsuspension sediment, convective diffusion is about 10-50 times larger than molecular diffusion during the initial stages under high velocity; it is close to molecular diffusion in the later stages. Convective diffusion is about 6 times larger than molecular diffusion during the initial stages under low velocity, it is about a quarter of molecular diffusion in later stages, and has a similar level with desorption/adsorption. In unsuspended sediment, a seepage boundary layer exists below the water-sediment interface, and various release mechanisms in that layer mostly dominate the contaminant release process. In non-cohesive fine sediment, the depth of that layer increases linearly with shear stress. In cohesive fine sediment, the range seepage boundary is different from that in non-cohesive sediment, and that phenomenon is more obvious under a lower shear stress.

Parametric modulation of thermomagnetic convection in magnetic fluids.

PubMed

Engler, H; Odenbach, S

2008-05-21

Previous theoretical investigations on thermal flow in a horizontal fluid layer have shown that the critical temperature difference, where heat transfer changes from diffusion to convective flow, depends on the frequency of a time-modulated driving force. The driving force of thermal convection is the buoyancy force resulting from the interaction of gravity and the density gradient provided by a temperature difference in the vertical direction of a horizontal fluid layer. An experimental investigation of such phenomena fails because of technical problems arising if buoyancy is to be changed by altering the temperature difference or gravitational acceleration. The possibility of influencing convective flow in a horizontal magnetic fluid layer by magnetic forces might provide us with a means to solve the problem of a time-modulated magnetic driving force. An experimental setup to investigate the dependence of the critical temperature difference on the frequency of the driving force has been designed and implemented. First results show that the time modulation of the driving force has significant influence on the strength of the convective flow. In particular a pronounced minimum in the strength of convection has been found for a particular frequency.

Nonequilibrium scheme for computing the flux of the convection-diffusion equation in the framework of the lattice Boltzmann method.

PubMed

Chai, Zhenhua; Zhao, T S

2014-07-01

In this paper, we propose a local nonequilibrium scheme for computing the flux of the convection-diffusion equation with a source term in the framework of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Both the Chapman-Enskog analysis and the numerical results show that, at the diffusive scaling, the present nonequilibrium scheme has a second-order convergence rate in space. A comparison between the nonequilibrium scheme and the conventional second-order central-difference scheme indicates that, although both schemes have a second-order convergence rate in space, the present nonequilibrium scheme is more accurate than the central-difference scheme. In addition, the flux computation rendered by the present scheme also preserves the parallel computation feature of the LBM, making the scheme more efficient than conventional finite-difference schemes in the study of large-scale problems. Finally, a comparison between the single-relaxation-time model and the MRT model is also conducted, and the results show that the MRT model is more accurate than the single-relaxation-time model, both in solving the convection-diffusion equation and in computing the flux.

Linear and nonlinear pattern selection in Rayleigh-Benard stability problems

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

1993-01-01

A new algorithm is introduced to compute finite-amplitude states using primitive variables for Rayleigh-Benard convection on relatively coarse meshes. The algorithm is based on a finite-difference matrix-splitting approach that separates all physical and dimensional effects into one-dimensional subsets. The nonlinear pattern selection process for steady convection in an air-filled square cavity with insulated side walls is investigated for Rayleigh numbers up to 20,000. The internalization of disturbances that evolve into coherent patterns is investigated and transient solutions from linear perturbation theory are compared with and contrasted to the full numerical simulations.

Influence of non steady gravity on natural convection during micro-gravity solidification of semiconductors. I - Time scale analysis. II - Implications for crystal growth experiments

NASA Technical Reports Server (NTRS)

Griffin, P. R.; Motakef, S.

1989-01-01

Consideration is given to the influence of temporal variations in the magnitude of gravity on natural convection during unidirectional solidification of semiconductors. It is shown that the response time to step changes in g at low Rayleigh numbers is controlled by the momentum diffusive time scale. At higher Rayleigh numbers, the response time to increases in g is reduced because of inertial effects. The degree of perturbation of flow fields by transients in the gravitational acceleration on the Space Shuttle and the Space Station is determined. The analysis is used to derive the requirements for crystal growth experiments conducted on low duration low-g vehicles. Also, the effectiveness of sounding rockets and KC-135 aircraft for microgravity experiments is examined.

Origin of the pre-tropical storm Debby (2006) African easterly wave-mesoscale convective system

NASA Astrophysics Data System (ADS)

Lin, Yuh-Lang; Liu, Liping; Tang, Guoqing; Spinks, James; Jones, Wilson

2013-05-01

The origins of the pre-Debby (2006) mesoscale convective system (MCS) and African easterly wave (AEW) and their precursors were traced back to the southwest Arabian Peninsula, Asir Mountains (AS), and Ethiopian Highlands (EH) in the vicinity of the ITCZ using satellite imagery, GFS analysis data and ARW model. The sources of the convective cloud clusters and vorticity perturbations were attributed to the cyclonic convergence of northeasterly Shamal wind and the Somali jet, especially when the Mediterranean High shifted toward east and the Indian Ocean high strengthened and its associated Somali jet penetrated farther to the north. The cyclonic vorticity perturbations were strengthened by the vorticity stretching associated with convective cloud clusters in the genesis region—southwest Arabian Peninsula. A conceptual model was proposed to explain the genesis of convective cloud clusters and cyclonic vorticity perturbations preceding the pre-Debby (2006) AEW-MCS system.

Magnetic resonance electrical impedance tomography (MREIT) based on the solution of the convection equation using FEM with stabilization.

PubMed

Oran, Omer Faruk; Ider, Yusuf Ziya

2012-08-21

Most algorithms for magnetic resonance electrical impedance tomography (MREIT) concentrate on reconstructing the internal conductivity distribution of a conductive object from the Laplacian of only one component of the magnetic flux density (∇²B(z)) generated by the internal current distribution. In this study, a new algorithm is proposed to solve this ∇²B(z)-based MREIT problem which is mathematically formulated as the steady-state scalar pure convection equation. Numerical methods developed for the solution of the more general convection-diffusion equation are utilized. It is known that the solution of the pure convection equation is numerically unstable if sharp variations of the field variable (in this case conductivity) exist or if there are inconsistent boundary conditions. Various stabilization techniques, based on introducing artificial diffusion, are developed to handle such cases and in this study the streamline upwind Petrov-Galerkin (SUPG) stabilization method is incorporated into the Galerkin weighted residual finite element method (FEM) to numerically solve the MREIT problem. The proposed algorithm is tested with simulated and also experimental data from phantoms. Successful conductivity reconstructions are obtained by solving the related convection equation using the Galerkin weighted residual FEM when there are no sharp variations in the actual conductivity distribution. However, when there is noise in the magnetic flux density data or when there are sharp variations in conductivity, it is found that SUPG stabilization is beneficial.

Boundary condition at a two-phase interface in the lattice Boltzmann method for the convection-diffusion equation.

PubMed

Yoshida, Hiroaki; Kobayashi, Takayuki; Hayashi, Hidemitsu; Kinjo, Tomoyuki; Washizu, Hitoshi; Fukuzawa, Kenji

2014-07-01

A boundary scheme in the lattice Boltzmann method (LBM) for the convection-diffusion equation, which correctly realizes the internal boundary condition at the interface between two phases with different transport properties, is presented. The difficulty in satisfying the continuity of flux at the interface in a transient analysis, which is inherent in the conventional LBM, is overcome by modifying the collision operator and the streaming process of the LBM. An asymptotic analysis of the scheme is carried out in order to clarify the role played by the adjustable parameters involved in the scheme. As a result, the internal boundary condition is shown to be satisfied with second-order accuracy with respect to the lattice interval, if we assign appropriate values to the adjustable parameters. In addition, two specific problems are numerically analyzed, and comparison with the analytical solutions of the problems numerically validates the proposed scheme.

Wind effect on the Atlantic meridional overturning circulation via sea ice and vertical diffusion

NASA Astrophysics Data System (ADS)

Yang, Haijun; Wang, Kun; Dai, Haijin; Wang, Yuxing; Li, Qing

2016-06-01

Effects of wind and fresh water on the Atlantic meridional overturning circulation (AMOC) are investigated using a fully coupled climate model. The AMOC can change significantly when perturbed by either wind stress or freshwater flux in the North Atlantic. This study focuses on wind stress effect. Our model results show that the wind forcing is crucial in maintaining the AMOC. Reducing wind forcing over the ocean can cause immediately weakening of the vertical salinity diffusion and convection in the mid-high latitudes Atlantic, resulting in an enhancement of vertical salinity stratification that restrains the deep water formation there, triggering a slowdown of the thermohaline circulation. As the thermohaline circulation weakens, the sea ice expands southward and melts, providing the upper ocean with fresh water that weakens the thermohaline circulation further. The wind perturbation experiments suggest a positive feedback between sea-ice and thermohaline circulation strength, which can eventually result in a complete shutdown of the AMOC. This study also suggests that sea-ice variability may be also important to the natural AMOC variability on decadal and longer timescales.

Active control of convection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bau, H.H.

Using stability theory, numerical simulations, and in some instances experiments, it is demonstrated that the critical Rayleigh number for the bifurcation (1) from the no-motion (conduction) state to the motion state and (2) from time-independent convection to time-dependent, oscillatory convection in the thermal convection loop and Rayleigh-Benard problems can be significantly increased or decreased. This is accomplished through the use of a feedback controller effectuating small perturbations in the boundary data. The controller consists of sensors which detect deviations in the fluid`s temperature from the motionless, conductive values and then direct actuators to respond to these deviations in such amore » way as to suppress the naturally occurring flow instabilities. Actuators which modify the boundary`s temperature/heat flux are considered. The feedback controller can also be used to control flow patterns and generate complex dynamic behavior at relatively low Rayleigh numbers.« less

Core heat convection in NSTX-U via modification of electron orbits by high frequency Alfvén eigenmodes

NASA Astrophysics Data System (ADS)

Crocker, N. A.; Tritz, K.; White, R. B.; Fredrickson, E. D.; Gorelenkov, N. N.; NSTX-U Team

2015-11-01

New simulation results demonstrate that high frequency compressional (CAE) and global (GAE) Alfvén eigenmodes cause radial convection of electrons, with implications for particle and energy confinement, as well as electric field formation in NSTX-U. Simulations of electron orbits in the presence of multiple experimentally determined CAEs and GAEs, using the gyro-center code ORBIT, have revealed substantial convective transport, in addition to the expected diffusion via orbit stochastization. These results advance understanding of anomalous core energy transport expected in high performance, beam-heated NSTX-U plasmas. The simulations make use of experimentally determined density perturbation (δn) amplitudes and mode structures obtained by inverting measurements from 16 a channel reflectometer array using a synthetic diagnostic. Combined with experimentally determined mode polarizations (i.e. CAE or GAE), the δn are used to estimate the ExB displacements for use in ORBIT. Preliminary comparison of the simulation results with transport modeling by TRANSP indicate that the convection is currently underestimated. Supported by US DOE Contracts DE-SC0011810, DE-FG02-99ER54527 & DE-AC02-09CH11466.

Modeling Postconvective Submesoscale Coherent Vortices in the Northwestern Mediterranean Sea

NASA Astrophysics Data System (ADS)

Damien, P.; Bosse, A.; Testor, P.; Marsaleix, P.; Estournel, C.

2017-12-01

For the first time, the formation of submesoscale coherent vortices (SCVs) during intermediate and deep convection events is documented in a realistic high-resolution (1 km) numerical simulation of the oceanic circulation in the northwestern Mediterranean Sea. Winter intermediate and deep convection leads to the formation of anticyclonic and cyclonic eddies with lifetimes exceeding 1 year. By focusing on three typical eddies, the main characteristics of such vortices are discussed. The anticyclonic eddies are typical of SCVs observed in deep convection areas so far. They are characterized by a small radius (˜6.5 km) and orbital peak velocities of about 7 cm/s located at great depth (˜1500 m) or intermediate depth (˜500 m). The cyclonic vortices show very similar characteristics, such as a high Rossby number (˜0.4), but with surface-intensified structures. The long lifetimes of both anticyclonic and cyclonic eddies reflect very slow diffusive processes between their core and their surroundings and a strong resistance to external perturbations. These long-lived eddies are found to participate in the spreading of a significant portion (from 15 to 35%) of the convected waters in the Gulf of Lions and contribute to the ventilation of the deep basin.

Simulating the swelling and deformation behaviour in soft tissues using a convective thermal analogy

PubMed Central

Wu, John Z; Herzog, Walter

2002-01-01

Background It is generally accepted that cartilage adaptation and degeneration are mechanically mediated. Investigating the swelling behaviour of cartilage is important because the stress and strain state of cartilage is associated with the swelling and deformation behaviour. It is well accepted that the swelling of soft tissues is associated with mechanical, chemical, and electrical events. Method The purpose of the present study was to implement the triphasic theory into a commercial finite element tool (ABAQUS) to solve practical problems in cartilage mechanics. Because of the mathematical identity between thermal and mass diffusion processes, the triphasic model was transferred into a convective thermal diffusion process in the commercial finite element software. The problem was solved using an iterative procedure. Results The proposed approach was validated using the one-dimensional numerical solutions and the experimental results of confined compression of articular cartilage described in the literature. The time-history of the force response of a cartilage specimen in confined compression, which was subjected to swelling caused by a sudden change of saline concentration, was predicted using the proposed approach and compared with the published experimental data. Conclusion The advantage of the proposed thermal analogy technique over previous studies is that it accounts for the convective diffusion of ion concentrations and the Donnan osmotic pressure in the interstitial fluid. PMID:12685940

Unsteady Oxygen Transfer in Space-Filling Models of the Pulmonary Acinus

NASA Astrophysics Data System (ADS)

Hofemeier, Philipp; Shachar-Berman, Lihi; Filoche, Marcel; Sznitman, Josue

2014-11-01

Diffusional screening in the pulmonary acinus is a well-known physical phenomenon that results from the depletion of fresh oxygen in proximal acinar generations diffusing through the alveolar wall membranes and effectively creating a gradient in the oxygen partial pressure along the acinar airways. Until present, most studies have focused on steady-state oxygen diffusion in generic sub-acinar structures and discarded convective oxygen transport due to low Peclet numbers in this region. Such studies, however, fall typically short in capturing the complex morphology of acinar airways as well as the oscillatory nature of convecive acinar breathing. Here, we revisit this problem and solve the convective-diffusive transport equations in breathing 3D acinar structures, underlining the significance of convective flows in proximal acinar generations as well as recirculating alveolar flow patterns. In particular, to assess diffusional screening, we monitor time-dependent efficiencies of the acinus under cyclic breathing motion. Our study emphasizes the necessity of capturing both a dynamically breathing and anatomically-realistic model of the sub-acinus to characterize unsteady oxygen transport across the acinar walls.

Impacts of a Fire Smoke Plume on Deep Convective Clouds Observed during DC3

NASA Astrophysics Data System (ADS)

Takeishi, A.; Storelvmo, T.; Zagar, M.

2014-12-01

While the ability of aerosols to act as cloud condensation nuclei (CCN) and ice nuclei (IN) is well recognized, the effects of changing aerosol number concentrations on convective clouds have only been studied extensively in recent years. As deep convective clouds can produce heavy precipitation and may sometimes bring severe damages, especially in the tropics, we need to understand the changes in the convective systems that could stem from aerosol perturbations. By perturbing convective clouds, it has also been proposed that aerosols can affect large-scale climate. According to the convective invigoration mechanism, an increase in the aerosol concentration could lead to a larger amount of rainfall and higher vertical velocities in convective clouds, due to an increase in the latent heat release aloft. With some of the satellite observations supporting this mechanism, it is necessary to understand how sensitive the model simulations actually are to aerosol perturbations. This study uses the Weather Research and Forecasting (WRF) model as a cloud-resolving model to reproduce deep convective clouds observed during the Deep Convective Clouds and Chemistry (DC3) field campaign. The convective cloud of our interest was observed in northeastern Colorado on June 22nd in 2012, with a plume of forest fire smoke flowing into its core. Compared to other convective cells observed in the same area on different days, our aircraft data analysis shows that the convective cloud in question included more organic aerosols and more CCN. These indicate the influence of the biomass burning. We compare the results from simulations with different microphysics schemes and different cloud or ice number concentrations. These sensitivity tests tell us how different the amount and the pattern of precipitation would have been if the aerosol concentration had been higher or lower on that day. Both the sensitivity to aerosol perturbation and the reproducibility of the storm are shown to highly depend on the choice of the microphysics scheme.

Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection-diffusion problems: Insights into spectral vanishing viscosity

NASA Astrophysics Data System (ADS)

Moura, R. C.; Sherwin, S. J.; Peiró, J.

2016-02-01

This study addresses linear dispersion-diffusion analysis for the spectral/hp continuous Galerkin (CG) formulation in one dimension. First, numerical dispersion and diffusion curves are obtained for the advection-diffusion problem and the role of multiple eigencurves peculiar to spectral/hp methods is discussed. From the eigencurves' behaviour, we observe that CG might feature potentially undesirable non-smooth dispersion/diffusion characteristics for under-resolved simulations of problems strongly dominated by either convection or diffusion. Subsequently, the linear advection equation augmented with spectral vanishing viscosity (SVV) is analysed. Dispersion and diffusion characteristics of CG with SVV-based stabilization are verified to display similar non-smooth features in flow regions where convection is much stronger than dissipation or vice-versa, owing to a dependency of the standard SVV operator on a local Péclet number. First a modification is proposed to the traditional SVV scaling that enforces a globally constant Péclet number so as to avoid the previous issues. In addition, a new SVV kernel function is suggested and shown to provide a more regular behaviour for the eigencurves along with a consistent increase in resolution power for higher-order discretizations, as measured by the extent of the wavenumber range where numerical errors are negligible. The dissipation characteristics of CG with the SVV modifications suggested are then verified to be broadly equivalent to those obtained through upwinding in the discontinuous Galerkin (DG) scheme. Nevertheless, for the kernel function proposed, the full upwind DG scheme is found to have a slightly higher resolution power for the same dissipation levels. These results show that improved CG-SVV characteristics can be pursued via different kernel functions with the aid of optimization algorithms.

Effective diffusion coefficient including the Marangoni effect

NASA Astrophysics Data System (ADS)

Kitahata, Hiroyuki; Yoshinaga, Natsuhiko

2018-04-01

Surface-active molecules supplied from a particle fixed at the water surface create a spatial gradient of the molecule concentration, resulting in Marangoni convection. Convective flow transports the molecules far from the particle, enhancing diffusion. We analytically derive the effective diffusion coefficient associated with the Marangoni convection rolls. The resulting estimated effective diffusion coefficient is consistent with our numerical results and the apparent diffusion coefficient measured in experiments.

Adaptive Discontinuous Galerkin Methods in Multiwavelets Bases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Archibald, Richard K; Fann, George I; Shelton Jr, William Allison

2011-01-01

We use a multiwavelet basis with the Discontinuous Galerkin (DG) method to produce a multi-scale DG method. We apply this Multiwavelet DG method to convection and convection-diffusion problems in multiple dimensions. Merging the DG method with multiwavelets allows the adaptivity in the DG method to be resolved through manipulation of multiwavelet coefficients rather than grid manipulation. Additionally, the Multiwavelet DG method is tested on non-linear equations in one dimension and on the cubed sphere.

The impact of vorticity waves on the shock dynamics in core-collapse supernovae

NASA Astrophysics Data System (ADS)

Huete, César; Abdikamalov, Ernazar; Radice, David

2018-04-01

Convective perturbations arising from nuclear shell burning can play an important role in propelling neutrino-driven core-collapse supernova explosions. In this work, we analyse the impact of vorticity waves on the shock dynamics, and subsequently on the post-shock flow, using the solution of the linear hydrodynamics equations. As a result of the interaction with the shock wave, vorticity waves increase their kinetic energy, and a new set of entropic and acoustic waves is deposited in the post-shock region. These perturbations interact with the neutrino-driven turbulent convection that develops in that region. Although both vorticity and acoustic waves inject non-radial motion into the gain region, the contribution of the acoustic waves is found to be negligibly small in comparison to that of the vorticity waves. On the other hand, entropy waves become buoyant and trigger more convection. Using the concept of critical neutrino luminosity, we assess the impact of these modes on the explosion conditions. While the direct injection of non-radial motion reduces the critical neutrino luminosity by ˜ 12 per cent for typical problem parameters, the buoyancy-driven convection triggered by entropy waves reduces the critical luminosity by ˜ 17-24 per cent, which approximately agrees with the results of three-dimensional neutrino-hydrodynamics simulations. Finally, we discuss the limits of validity of the assumptions employed.

Convection-Diffusion Layer in an "Open Space" for Local Surface Treatment and Microfabrication using a Four-Aperture Microchemical Pen.

PubMed

Mao, Sifeng; Zhang, Yong; Zhang, Weifei; Zeng, Hulie; Nakajima, Hizuru; Lin, Jin-Ming; Uchiyama, Katsumi

2017-09-06

A four-aperture microchemical pen was used to produce a stable convection-diffusion layer in an "open space" for microreactions and microfabrication. The process represents a new method for microreactions and microfabrication in a convection-diffusion layer. To prove the concept of a convection-diffusion layer in an "open space", bovine serum albumin was labeled with 4-fluoro-7-nitro-2,1,3-benzoxadiazole to confirm that the small convection-diffusion layer was effective for local surface treatment. To demonstrate the potential for microfabrication, silver patterns were fabricated on a glass surface with a convection-diffusion layer by using the silver-mirror reaction. The widths of each silver pattern could be easily controlled from 10 to 60 μm. Patterned silver lines with uniform widths or gradient widths were prepared. This is the first proof of concept study of a convection-diffusion layer in an "open space" used in local surface treatment and microfabrication on a surface. The microchemical pen represents a potential method for the region-selective microtreatment of tissues, cells, and other biological interfaces. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization

NASA Astrophysics Data System (ADS)

Burman, Erik; Hansbo, Peter; Larson, Mats G.

2018-03-01

Tikhonov regularization is one of the most commonly used methods for the regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably weighted least squares terms of the control variable, or derivatives thereof, to the Lagrangian determining the optimality system. In this note we show that the stabilization methods for discretely ill-posed problems developed in the setting of convection-dominated convection-diffusion problems, can be highly suitable for stabilizing optimal control problems, and that Tikhonov regularization will lead to less accurate discrete solutions. We consider some inverse problems for Poisson’s equation as an illustration and derive new error estimates both for the reconstruction of the solution from the measured data and reconstruction of the source term from the measured data. These estimates include both the effect of the discretization error and error in the measurements.

On inter-tidal transport equation

USGS Publications Warehouse

Cheng, Ralph T.; Feng, Shizuo; Pangen, Xi

1989-01-01

The transports of solutes, sediments, nutrients, and other tracers are fundamental to the interactive physical, chemical, and biological processes in estuaries. The characteristic time scales for most estuarine biological and chemical processes are on the order of several tidal cycles or longer. To address the long-term transport mechanism meaningfully, the formulation of an inter-tidal conservation equation is the main subject of this paper. The commonly used inter-tidal conservation equation takes the form of a convection-dispersion equation in which the convection is represented by the Eulerian residual current, and the dispersion terms are due to the introduction of a Fickian hypothesis, unfortunately, the physical significance of this equation is not clear, and the introduction of a Fickian hypothesis is at best an ad hoc approximation. Some recent research results on the Lagrangian residual current suggest that the long-term transport problem is more closely related to the Lagrangian residual current than to the Eulerian residual current. With the aid of additional insight of residual current, the inter-tidal transport equation has been reformulated in this paper using a small perturbation method for a weakly nonlinear tidal system. When tidal flows can be represented by an M2 system, the new intertidal transport equation also takes the form of a convective-dispersion equation without the introduction of a Fickian hypothesis. The convective velocity turns out to be the first order Lagrangian residual current (the sum of the Eulerian residual current and the Stokes’ drift), and the correlation terms take the form of convection with the Stokes’ drift as the convective velocity. The remaining dispersion terms are perturbations of lower order solution to higher order solutions due to shear effect and turbulent mixing.

Self-aggregation of clouds in conditionally unstable moist convection

PubMed Central

Pauluis, Olivier; Schumacher, Jörg

2011-01-01

The behavior of moist Rayleigh–Bénard convection is investigated using a Boussinesq model with a simplified thermodynamics for phase transitions. This idealized configuration makes the problem accessible to high-resolution three-dimensional direct numerical simulations without small-scale parameterizations of the turbulence for extended layers with aspect ratios up to 64. Our study is focused on the frequently observed conditionally unstable environment that is stably stratified for unsaturated air, but is unstable for cloudy air. We find that no sharp threshold for the transition to convective turbulence exists, a situation similar to wall-bounded shear flows. Rather, the transition depends on the amplitude of the initial perturbation of the quiescent equilibrium and on the aspect ratio of the convective domain. In contrast to the classical dry Rayleigh–Bénard case, convection is highly asymmetric with respect to the vertical direction. Moist upwelling air inside turbulent cloud aggregates is surrounded by ambient regions of slowly descending unsaturated air. It is also found that conditionally unstable moist convection is inefficient at transporting energy. Our study suggests that there is an upper bound on the Nusselt number in moist convection that is lower than that of the classical dry case. PMID:21768333

CONDIF - A modified central-difference scheme for convective flows

NASA Technical Reports Server (NTRS)

Runchal, Akshai K.

1987-01-01

The paper presents a method, called CONDIF, which modifies the CDS (central-difference scheme) by introducing a controlled amount of numerical diffusion based on the local gradients. The numerical diffusion can be adjusted to be negligibly low for most problems. CONDIF results are significantly more accurate than those obtained from the hybrid scheme when the Peclet number is very high and the flow is at large angles to the grid.

Simulation of Deep Convective Clouds with the Dynamic Reconstruction Turbulence Closure

NASA Astrophysics Data System (ADS)

Shi, X.; Chow, F. K.; Street, R. L.; Bryan, G. H.

2017-12-01

The terra incognita (TI), or gray zone, in simulations is a range of grid spacing comparable to the most energetic eddy diameter. Spacing in mesoscale and simulations is much larger than the eddies, and turbulence is parameterized with one-dimensional vertical-mixing. Large eddy simulations (LES) have grid spacing much smaller than the energetic eddies, and use three-dimensional models of turbulence. Studies of convective weather use convection-permitting resolutions, which are in the TI. Neither mesoscale-turbulence nor LES models are designed for the TI, so TI turbulence parameterization needs to be discussed. Here, the effects of sub-filter scale (SFS) closure schemes on the simulation of deep tropical convection are evaluated by comparing three closures, i.e. Smagorinsky model, Deardorff-type TKE model and the dynamic reconstruction model (DRM), which partitions SFS turbulence into resolvable sub-filter scales (RSFS) and unresolved sub-grid scales (SGS). The RSFS are reconstructed, and the SGS are modeled with a dynamic eddy viscosity/diffusivity model. The RSFS stresses/fluxes allow backscatter of energy/variance via counter-gradient stresses/fluxes. In high-resolution (100m) simulations of tropical convection use of these turbulence models did not lead to significant differences in cloud water/ice distribution, precipitation flux, or vertical fluxes of momentum and heat. When model resolutions are coarsened, the Smagorinsky and TKE models overestimate cloud ice and produces large-amplitude downward heat flux in the middle troposphere (not found in the high-resolution simulations). This error is a result of unrealistically large eddy diffusivities, i.e., the eddy diffusivity of the DRM is on the order of 1 for the coarse resolution simulations, the eddy diffusivity of the Smagorinsky and TKE model is on the order of 100. Splitting the eddy viscosity/diffusivity scalars into vertical and horizontal components by using different length scales and strain rate components helps to reduce the errors, but does not completely remedy the problem. In contrast, the coarse resolution simulations using the DRM produce results that are more consistent with the high-resolution results, suggesting that the DRM is a more appropriate turbulence model for simulating convection in the TI.

Variable mass diffusion effects on free convection flow past an impulsively started infinite vertical plate

NASA Astrophysics Data System (ADS)

Rushi Kumar, B.; Jayakar, R.; Vijay Kumar, A. G.

2017-11-01

An exact analysis of the problem of free convection flow of a viscous incompressible chemically reacting fluid past an infinite vertical plate with the flow due to impulsive motion of the plate with Newtonian heating in the presence of thermal radiation and variable mass diffusion is performed. The resulting governing equations were tackled by Laplace transform technique. Finally the effects of pertinent flow parameters such as the radiation parameter, chemical reaction parameter, buoyancy ratio parameter, thermal Grashof number, Schmidt number, Prandtl number and time on the velocity, temperature, concentration and skin friction for both aiding and opposing flows were examined in detail when Pr=0.71(conducting air) and Pr=7.0(water).

New variational bounds on convective transport. II. Computations and implications

NASA Astrophysics Data System (ADS)

Souza, Andre; Tobasco, Ian; Doering, Charles R.

2016-11-01

We study the maximal rate of scalar transport between parallel walls separated by distance h, by an incompressible fluid with scalar diffusion coefficient κ. Given velocity vector field u with intensity measured by the Péclet number Pe =h2 < | ∇ u |2 >1/2 / κ (where < . > is space-time average) the challenge is to determine the largest enhancement of wall-to-wall scalar flux over purely diffusive transport, i.e., the Nusselt number Nu . Variational formulations of the problem are studied numerically and optimizing flow fields are computed over a range of Pe . Implications of this optimal wall-to-wall transport problem for the classical problem of Rayleigh-Bénard convection are discussed: the maximal scaling Nu Pe 2 / 3 corresponds, via the identity Pe2 = Ra (Nu - 1) where Ra is the usual Rayleigh number, to Nu Ra 1 / 2 as Ra -> ∞ . Supported in part by National Science Foundation Graduate Research Fellowship DGE-0813964, awards OISE-0967140, PHY-1205219, DMS-1311833, and DMS-1515161, and the John Simon Guggenheim Memorial Foundation.

Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection.

PubMed

Sabelnikov, V A; Lipatnikov, A N

2014-09-01

The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.

Role of gravity in preparative electrophoresis

NASA Technical Reports Server (NTRS)

Bier, M.

1975-01-01

The fundamental formulas of electrophoresis are derived microscopically and applied to the problem of isotachophoresis. A simple physical model of the isotachophoresis front is proposed. The front motion and structure are studied in the simplified case without convection, diffusion and non-electric external forces.

Convective mass transfer around a dissolving bubble

NASA Astrophysics Data System (ADS)

Duplat, Jerome; Grandemange, Mathieu; Poulain, Cedric

2017-11-01

Heat or mass transfer around an evaporating drop or condensing vapor bubble is a complex issue due to the interplay between the substrate properties, diffusion- and convection-driven mass transfer, and Marangoni effects, to mention but a few. In order to disentangle these mechanisms, we focus here mainly on the convective mass transfer contribution in an isothermal mass transfer problem. For this, we study the case of a millimetric carbon dioxide bubble which is suspended under a substrate and dissolved into pure liquid water. The high solubility of CO2 in water makes the liquid denser and promotes a buoyant-driven flow at a high (solutal) Rayleigh number (Ra˜104 ). The alteration of p H allows the concentration field in the liquid to be imaged by laser fluorescence enabling us to measure both the global mass flux (bubble volume, contact angle) and local mass flux around the bubble along time. After a short period of mass diffusion, where the boundary layer thickens like the square root of time, convection starts and the CO2 is carried by a plume falling at constant velocity. The boundary layer thickness then reaches a plateau which depends on the bubble cross section. Meanwhile the plume velocity scales like (dV /d t )1 /2 with V being the volume of the bubble. As for the rate of volume loss, we recover a constant mass flux in the diffusion-driven regime followed by a decrease in the volume V like V2 /3 after convection has started. We present a model which agrees well with the bubble dynamics and discuss our results in the context of droplet evaporation, as well as high Rayleigh convection.

REVIEWS OF TOPICAL PROBLEMS: Free convection in geophysical processes

NASA Astrophysics Data System (ADS)

Alekseev, V. V.; Gusev, A. M.

1983-10-01

A highly significant geophysical process, free convection, is examined. Thermal convection often controls the dynamical behavior in several of the earth's envelopes: the atmosphere, ocean, and mantle. Section 2 sets forth the thermohydrodynamic equations that describe convection in a compressible or incompressible fluid, thermochemical convection, and convection in the presence of thermal diffusion. Section 3 reviews the mechanisms for the origin of the global atmospheric and oceanic circulation. Interlatitudinal convection and jet streams are discussed, as well as monsoon circulation and the mean meridional circulation of ocean waters due to the temperature and salinity gradients. Also described are the hypotheses for convective motion in the mantle and the thermal-wave (moving flame) mechanism for inducing global circulation (the atmospheres of Venus and Mars provide illustrations). Eddy formation by convection in a centrifugal force field is considered. Section 4 deals with medium- and small-scale convective processes, including hurricane systems with phase transitions, cellular cloud structure, and convection penetrating into the ocean, with its stepped vertical temperature and salinity microstructure. Self-oscillatory processes involving convection in fresh-water basins are discussed, including effects due to the anomalous (p,T) relation for water.

Inhibition of ordinary and diffusive convection in the water condensation zone of the ice giants and implications for their thermal evolution

NASA Astrophysics Data System (ADS)

Friedson, A. James; Gonzales, Erica J.

2017-11-01

We explore the conditions under which ordinary and double-diffusive thermal convection may be inhibited by water condensation in the hydrogen atmospheres of the ice giants and examine the consequences. The saturation of vapor in the condensation layer induces a vertical gradient in the mean molecular weight that stabilizes the layer against convective instability when the abundance of vapor exceeds a critical value. In this instance, the layer temperature gradient can become superadiabatic and heat must be transported vertically by another mechanism. On Uranus and Neptune, water is inferred to be sufficiently abundant for inhibition of ordinary convection to take place in their respective condensation zones. We find that suppression of double-diffusive convection is sensitive to the ratio of the sedimentation time scale of the condensates to the buoyancy period in the condensation layer. In the limit of rapid sedimentation, the layer is found to be stable to diffusive convection. In the opposite limit, diffusive convection can occur. However, if the fluid remains saturated, then layered convection is generally suppressed and the motion is restricted in form to weak, homogeneous, oscillatory turbulence. This form of diffusive convection is a relatively inefficient mechanism for transporting heat, characterized by low Nusselt numbers. When both ordinary and layered convection are suppressed, the condensation zone acts effectively as a thermal insulator, with the heat flux transported across it only slightly greater than the small value that can be supported by radiative diffusion. This may allow a large superadiabatic temperature gradient to develop in the layer over time. Once the layer has formed, however, it is vulnerable to persistent erosion by entrainment of fluid into the overlying convective envelope of the cooling planet, potentially leading to its collapse. We discuss the implications of our results for thermal evolution models of the ice giants, for understanding Uranus' anomalously low intrinsic luminosity, and for inducing episodes of intense convection in the atmospheres of Saturn, Uranus, and Neptune.

Cross-diffusive effects on the onset of double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above

NASA Astrophysics Data System (ADS)

Rajib, Basu; C. Layek, G.

2013-05-01

Double-diffusive stationary and oscillatory instabilities at the marginal state in a saturated porous horizontal fluid layer heated and salted from above are investigated theoretically under the Darcy's framework for a porous medium. The contributions of Soret and Dufour coefficients are taken into account in the analysis. Linear stability analysis shows that the critical value of the Darcy—Rayleigh number depends on cross-diffusive parameters at marginally stationary convection, while the marginal state characterized by oscillatory convection does not depend on the cross-diffusion terms even if the condition and frequency of oscillatory convection depends on the cross-diffusive parameters. The critical value of the Darcy—Rayleigh number increases with increasing value of the solutal Darcy—Rayleigh number in the absence of cross-diffusive parameters. The critical Darcy—Rayleigh number decreases with increasing Soret number, resulting in destabilization of the system, while its value increases with increasing Dufour number, resulting in stabilization of the system at the marginal state characterized by stationary convection. The analysis reveals that the Dufour and Soret parameters as well as the porosity parameter play an important role in deciding the type of instability at the onset. This analysis also indicates that the stationary convection is followed by the oscillatory convection for certain fluid mixtures. It is interesting to note that the roles of cross-diffusive parameters on the double-diffusive system heated and salted from above are reciprocal to the double-diffusive system heated and salted from below.

Effect of Marangoni Convection on Surfactant Transfer Between the Drop Connected to the Reservoir and Surrounding Liquid

NASA Astrophysics Data System (ADS)

Kostarev, K.; Denisova, M.; Shmyrov, A.

2018-03-01

The paper presents the results of comparative investigation of the interaction between the capillary and buoyant mechanisms of motion in a problem of surfactant mass transfer between an insoluble drop and surrounding fluid under different gravity conditions. The research was performed for the drop that is coupled with the reservoir filled with a source mixture through a long thin tube (needle). Visualization of the flow patterns and concentration fields has shown that surfactant diffusion from the needle at normal gravity leads to the onset of the oscillatory mode of the capillary convection in the drop. It has been found that the frequency of the Marangoni convection outbursts, the lifetime of the oscillatory flow modes and the amount of the source mixture involved in the process of mass transfer depend on the drop size and initial concentration of the surfactant. The obtained results are compared with the cases of surfactant diffusion from the isolated drop under terrestrial conditions and from the drop coupled with reservoir in microgravity. Additionally, a series of experiments were performed to investigate diffusion of a surfactant from the surrounding solution into a drop.

New Layer Thickness Parameterization of Diffusive Convection

NASA Astrophysics Data System (ADS)

Zhou, Sheng-Qi; Lu, Yuan-Zheng; Guo, Shuang-Xi; Song, Xue-Long; Qu, Ling; Cen, Xian-Rong; Fer, Ilker

2017-11-01

Double-diffusion convection is one of the most important non-mechanically driven mixing processes. Its importance has been particular recognized in oceanography, material science, geology, and planetary physics. Double-diffusion occurs in a fluid in which there are gradients of two (or more) properties with different molecular diffusivities and of opposing effects on the vertical density distribution. It has two primary modes: salt finger and diffusive convection. Recently, the importance of diffusive convection has aroused more interest due to its impact to the diapycnal mixing in the interior ocean and the ice and the ice-melting in the Arctic and Antarctic Oceans. In our recent work, we constructed a length scale of energy-containing eddy and proposed a new layer thickness parameterization of diffusive convection by using the laboratory experiment and in situ observations in the lakes and oceans. The new parameterization can well describe the laboratory convecting layer thicknesses (0.01 0.1 m) and those observed in oceans and lakes (0.1 1000 m). This work was supported by China NSF Grants (41476167,41406035 and 41176027), NSF of Guangdong Province, China (2016A030311042) and the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA11030302).

The study of flow pattern and phase-change problem in die casting process

NASA Technical Reports Server (NTRS)

Wang, T. S.; Wei, H.; Chen, Y. S.; Shang, H. M.

1996-01-01

The flow pattern and solidification phenomena in die casting process have been investigated in the first phase study. The flow pattern in filling process is predicted by using a VOF (volume of fluid) method. A good agreement with experimental observation is obtained for filling the water into a die cavity with different gate geometry and with an obstacle in the cavity. An enthalpy method has been applied to solve the solidification problem. By treating the latent heat implicitly into the enthalpy instead of explicitly into the source term, the CPU time can be reduced at least 20 times. The effect of material properties on solidification fronts is tested. It concludes that the dependence of properties on temperature is significant. The influence of the natural convection over the diffusion has also been studied. The result shows that the liquid metal solidification phenomena is diffusion dominant, and the natural convection can affect the shape of the interface. In the second phase study, the filling and solidification processes will be considered simultaneously.

Salinity transfer in double diffusive convection bounded by two parallel plates

NASA Astrophysics Data System (ADS)

Yang, Yantao; van der Poel, Erwin P.; Ostilla-Monico, Rodolfo; Sun, Chao; Verzicco, Roberto; Grossmann, Siegfried; Lohse, Detlef

2014-11-01

The double diffusive convection (DDC) is the convection flow with the fluid density affected by two different components. In this study we numerically investigate DDC between two parallel plates with no-slip boundary conditions. The top plate has higher salinity and temperature than the lower one. Thus the flow is driven by the salinity difference and stabilised by the temperature difference. Our simulations are compared with the experiments by Hage and Tilgner (Phys. Fluids 22, 076603 (2010)) for several sets of parameters. Reasonable agreement is achieved for the salinity flux and its dependence on the salinity Rayleigh number. For all parameters considered, salt fingers emerge and extend through the entire domain height. The thermal Rayleigh number shows minor influence on the salinity flux although it does affect the Reynolds number. We apply the Grossmann-Lohse theory for Rayleigh-Bénard flow to the current problem without introducing any new coefficients. The theory successfully predicts the salinity flux with respect to the scaling for both the numerical and experimental results.

Onset of natural convection in a continuously perturbed system

NASA Astrophysics Data System (ADS)

Ghorbani, Zohreh; Riaz, Amir

2017-11-01

The convective mixing triggered by gravitational instability plays an important role in CO2 sequestration in saline aquifers. The linear stability analysis and the numerical simulation concerning convective mixing in porous media requires perturbations of small amplitude to be imposed on the concentration field in the form of an initial shape function. In aquifers, however, the instability is triggered by local porosity and permeability. In this work, we consider a canonical 2D homogeneous system where perturbations arise due to spatial variation of porosity in the system. The advantage of this approach is not only the elimination of the required initial shape function, but it also serves as a more realistic approach. Using a reduced nonlinear method, we first explore the effect of harmonic variations of porosity in the transverse and streamwise direction on the onset time of convection and late time behavior. We then obtain the optimal porosity structure that minimizes the convection onset. We further examine the effect of a random porosity distribution, that is independent of the spatial mode of porosity structure, on the convection onset. Using high-order pseudospectral DNS, we explore how the random distribution differs from the modal approach in predicting the onset time.

Scaling rates of true polar wander in convecting planets and moons

NASA Astrophysics Data System (ADS)

Rose, Ian; Buffett, Bruce

2017-12-01

Mass redistribution in the convecting mantle of a planet causes perturbations in its moment of inertia tensor. Conservation of angular momentum dictates that these perturbations change the direction of the rotation vector of the planet, a process known as true polar wander (TPW). Although the existence of TPW on Earth is firmly established, its rate and magnitude over geologic time scales remain controversial. Here we present scaling analyses and numerical simulations of TPW due to mantle convection over a range of parameter space relevant to planetary interiors. For simple rotating convection, we identify a set of dimensionless parameters that fully characterize true polar wander. We use these parameters to define timescales for the growth of moment of inertia perturbations due to convection and for their relaxation due to true polar wander. These timescales, as well as the relative sizes of convective anomalies, control the rate and magnitude of TPW. This analysis also clarifies the nature of so called "inertial interchange" TPW events, and relates them to a broader class of events that enable large and often rapid TPW. We expect these events to have been more frequent in Earth's past.

Breathing pulses in singularly perturbed reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Veerman, Frits

2015-07-01

The weakly nonlinear stability of pulses in general singularly perturbed reaction-diffusion systems near a Hopf bifurcation is determined using a centre manifold expansion. A general framework to obtain leading order expressions for the (Hopf) centre manifold expansion for scale separated, localised structures is presented. Using the scale separated structure of the underlying pulse, directly calculable expressions for the Hopf normal form coefficients are obtained in terms of solutions to classical Sturm-Liouville problems. The developed theory is used to establish the existence of breathing pulses in a slowly nonlinear Gierer-Meinhardt system, and is confirmed by direct numerical simulation.

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. I. Semi-infinite slab approximations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berkel, M. van; Fellow of the Japan Society for the Promotion of Science; FOM Institute DIFFER-Dutch Institute for Fundamental Energy Research, Association EURATOM- FOM, Trilateral Euregio Cluster, PO Box 1207, 3430 BE Nieuwegein

2014-11-15

In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on semi-infinite slab approximations of the heat equation. The main result is the approximation of χ under the influence of V and τ based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate χ well in cylindrical geometry, the relationships betweenmore » heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate χ, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which χ, V, and τ can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and τ in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and τ based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated.« less

Variational fine-grained data assimilation schemes for atmospheric chemistry transport and transformation models

NASA Astrophysics Data System (ADS)

Penenko, Alexey; Penenko, Vladimir; Tsvetova, Elena

2015-04-01

The paper concerns data assimilation problem for an atmospheric chemistry transport and transformation models. Data assimilation is carried out within variation approach on a single time step of the approximated model. A control function is introduced into the model source term (emission rate) to provide flexibility to adjust to data. This function is evaluated as the minimum of the target functional combining control function norm to a misfit between measured and model-simulated analog of data. This provides a flow-dependent and physically-plausible structure of the resulting analysis and reduces the need to calculate model error covariance matrices that are sought within conventional approach to data assimilation. Extension of the atmospheric transport model with a chemical transformations module influences data assimilation algorithms performance. This influence is investigated with numerical experiments for different meteorological conditions altering convection-diffusion processes characteristics, namely strong, medium and low wind conditions. To study the impact of transformation and data assimilation, we compare results for a convection-diffusion model (without data assimilation), convection-diffusion with assimilation, convection-diffusion-reaction (without data assimilation) and convection-diffusion-reaction-assimilation models. Both high dimensionalities of the atmospheric chemistry models and a real-time mode of operation demand for computational efficiency of the algorithms. Computational issues with complicated models can be solved by using a splitting technique. As the result a model is presented as a set of relatively independent simple models equipped with a kind of coupling procedure. With regard to data assimilation two approaches can be identified. In a fine-grained approach data assimilation is carried out on the separate splitting stages [1,2] independently on shared measurement data. The same situation arises when constructing a hybrid model out of two models each having its own assimilation scheme. In integrated schemes data assimilation is carried out with respect to the split model as a whole. First approach is more efficient from computational point of view, for in some important cases it can be implemented without iterations [2]. Its shortcoming is that control functions in different part of the model are adjusted independently thus having less evident physical sense. With the aid of numerical experiments we compare the two approaches. Work has been partially supported by COST Action ES1004 STSM Grants #16817 and #21654, RFBR 14-01-31482 mol a and 14-01-00125, Programmes # 4 Presidium RAS and # 3 MSD RAS, integration projects SB RAS #8 and #35. References: [1] V. V. Penenko Variational methods of data assimilation and inverse problems for studying the atmosphere, ocean, and environment Num. Anal. and Appl., 2009 V 2 No 4, 341-351. [2] A.V. Penenko and V.V. Penenko. Direct data assimilation method for convection-diffusion models based on splitting scheme. Computational technologies, 19(4):69-83, 2014.

Multigrid techniques for the solution of the passive scalar advection-diffusion equation

NASA Technical Reports Server (NTRS)

Phillips, R. E.; Schmidt, F. W.

1985-01-01

The solution of elliptic passive scalar advection-diffusion equations is required in the analysis of many turbulent flow and convective heat transfer problems. The accuracy of the solution may be affected by the presence of regions containing large gradients of the dependent variables. The multigrid concept of local grid refinement is a method for improving the accuracy of the calculations in these problems. In combination with the multilevel acceleration techniques, an accurate and efficient computational procedure is developed. In addition, a robust implementation of the QUICK finite-difference scheme is described. Calculations of a test problem are presented to quantitatively demonstrate the advantages of the multilevel-multigrid method.

Double Diffusive Convection in Materials Processing

NASA Technical Reports Server (NTRS)

Ramachandra, Narayanan; Leslie, Fred W.

1999-01-01

A great number of crystals grown in space are plagued by convective motions which contribute to structural flaws. The character of these instabilities is not well understood but is associated with density variations in the presence of residual gravity (g-jitter). As a specific example, past HgCdTe crystal growth space experiments by Lehoczky and co-workers indicate radial compositional asymmetry in the grown crystals. In the case of HgCdTe the rejected component into the melt upon solidification is HgTe which is denser than the melt. The space grown crystals indicate the presence of three dimensional flow with the heavier HgTe-rich material clearly aligned with the residual gravity (0.55-1.55 micro g) vector. This flow stems from double-diffusive convection, namely, thermal and solutal buoyancy driven flow in the melt. The study of double-diffusive convection is multi-faceted and rather vast. In our investigation, we seek to focus on one specific aspect of this discipline that is of direct relevance to materials processing especially crystal growth, namely, the side ways heating regime. This problem has been widely studied, both experimentally and numerically, in the context of solar ponds wherein the system is characterized by a linear salt (solutal) gradient with an imposed lateral temperature gradient. The induced flow instabilities arise from the wide disparity between the fluid thermal diffusivity and the solute diffusivity. The extension of the analysis to practical crystal growth applications has however not been rigorously made and understood. One subtle but important difference in crystal growth systems is the fact that die system solute gradient is non-linear (typically exponential). Besides, the crystal growth problem has the added complexities of solidification, both lateral and longitudinal thermal gradients and segregation phenomena in systems where binary and ternary compounds are being grown. This paper treats the side ways heating problem alone in a model fluid system. Results from detailed numerical calculations, mainly two dimensional are provided. The interactions between a non-linear solute gradient and an imposed transverse thermal gradient are investigated. The buoyancy effects are treated in the traditional Boussinesq approximation and also in a more complete density formulation to address recent concerns of the first approach especially in simulations of the system response in a reduced gravity environment. Detailed flow, temperature and solute field plots along with heat and mass transfer results are presented in the paper. Implications to practical crystal growth systems as discerned from the modeling results are also explored and reported.

Eddy diffusivity of quasi-neutrally-buoyant inertial particles

NASA Astrophysics Data System (ADS)

Martins Afonso, Marco; Muratore-Ginanneschi, Paolo; Gama, Sílvio M. A.; Mazzino, Andrea

2018-04-01

We investigate the large-scale transport properties of quasi-neutrally-buoyant inertial particles carried by incompressible zero-mean periodic or steady ergodic flows. We show how to compute large-scale indicators such as the inertial-particle terminal velocity and eddy diffusivity from first principles in a perturbative expansion around the limit of added-mass factor close to unity. Physically, this limit corresponds to the case where the mass density of the particles is constant and close in value to the mass density of the fluid, which is also constant. Our approach differs from the usual over-damped expansion inasmuch as we do not assume a separation of time scales between thermalization and small-scale convection effects. For a general flow in the class of incompressible zero-mean periodic velocity fields, we derive closed-form cell equations for the auxiliary quantities determining the terminal velocity and effective diffusivity. In the special case of parallel flows these equations admit explicit analytic solution. We use parallel flows to show that our approach sheds light onto the behavior of terminal velocity and effective diffusivity for Stokes numbers of the order of unity.

The effect of gravity modulation on thermosolutal convection

NASA Technical Reports Server (NTRS)

Saunders, Bonita V.; Murray, Bruce T.; Mcfadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1992-01-01

In a gravitational field, the opposing effects of components of different diffusivities, for example, temperature and solute, in the density profile in a fluid may produce convective instabilities that exhibit a broad range of dynamical behavior. The effect of time periodic vertical gravity modulation on the onset of these instabilities in an infinite horizontal layer with stress free boundaries is examined. This work is viewed as a first step in expanding previous results in solidification to the full problem of characterizing the effects of gravity modulation in thermosolutal convection during the directional solidification of binary alloys. Calculations carried out both with and without steady background acceleration are presented, the latter results being relevant to microgravity conditions.

Low-gravity fluid dynamics and transport phenomena. Progress in Astronautics and Aeronautics. Vol. 130

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koster, J.N.; Sani, R.L.

1990-01-01

Various papers on low-gravity fluid dynamics and transport phenomena are presented. Individual topics addressed include: fluid management in low gravity, nucleate pool boiling in variable gravity, application of energy-stability theory to problems in crystal growth, thermosolutal convection in liquid HgCdTe near the liquidus temperature, capillary surfaces in microgravity, thermohydrodynamic instabilities and capillary flows, interfacial oscillators, effects of gravity jitter on typical fluid science experiments and on natural convection in a vertical cylinder. Also discussed are: double-diffusive convection and its effects under reduced gravity, segregation and convection in dendritic alloys, fluid flow and microstructure development, analysis of convective situations with themore » Soret effect, complex natural convection in low Prandtl number metals, separation physics, phase partitioning in reduced gravity, separation of binary alloys with miscibility gap in the melt, Ostwald ripening in liquids, particle cloud combustion in reduced gravity, opposed-flow flame spread with implications for combustion at microgravity.« less

Effects of radial distribution of entropy diffusivity on critical modes of anelastic thermal convection in rotating spherical shells

NASA Astrophysics Data System (ADS)

Sasaki, Youhei; Takehiro, Shin-ichi; Ishiwatari, Masaki; Yamada, Michio

2018-03-01

Linear stability analysis of anelastic thermal convection in a rotating spherical shell with entropy diffusivities varying in the radial direction is performed. The structures of critical convection are obtained in the cases of four different radial distributions of entropy diffusivity; (1) κ is constant, (2) κT0 is constant, (3) κρ0 is constant, and (4) κρ0T0 is constant, where κ is the entropy diffusivity, T0 is the temperature of basic state, and ρ0 is the density of basic state, respectively. The ratio of inner and outer radii, the Prandtl number, the polytropic index, and the density ratio are 0.35, 1, 2, and 5, respectively. The value of the Ekman number is 10-3 or 10-5 . In the case of (1), where the setup is same as that of the anelastic dynamo benchmark (Jones et al., 2011), the structure of critical convection is concentrated near the outer boundary of the spherical shell around the equator. However, in the cases of (2), (3) and (4), the convection columns attach the inner boundary of the spherical shell. A rapidly rotating annulus model for anelastic systems is developed by assuming that convection structure is uniform in the axial direction taking into account the strong effect of Coriolis force. The annulus model well explains the characteristics of critical convection obtained numerically, such as critical azimuthal wavenumber, frequency, Rayleigh number, and the cylindrically radial location of convection columns. The radial distribution of entropy diffusivity, or more generally, diffusion properties in the entropy equation, is important for convection structure, because it determines the distribution of radial basic entropy gradient which is crucial for location of convection columns.

Semi-analytical study of the tokamak pedestal density profile in a single-null diverted plasma with puffing-recycling gas sources

NASA Astrophysics Data System (ADS)

Shi, Bingren

2010-10-01

The tokamak pedestal density structure is generally studied using a diffusion-dominant model. Recent investigations (Stacey and Groebner 2009 Phys. Plasmas 16 102504) from first principle based physics have shown a plausible existence of large inward convection in the pedestal region. The diffusion-convection equation with rapidly varying convection and diffusion coefficients in the near edge region and model puffing-recycling neutral particles is studied in this paper. A peculiar property of its solution for the existence of the large convection case is that the pedestal width of the density profile, qualitatively different from the diffusion-dominant case, depends mainly on the width of the inward convection and only weakly on the neutral penetration length and its injection position.

The solar Lithium problem: is the explanation due solely to mixing or also to the e-capture decay rate of 7Be?

NASA Astrophysics Data System (ADS)

Vescovi, Diego; Busso, Maurizio; Palmerini, Sara; Trippella, Oscar

2018-01-01

The nucleosynthesis of 7Li is one of the most crucial problems in nuclear as- trophysics, as its observations in several sites are hard to be explained. Concerning the Sun, the most common interpretations of the low Li abundance invoke either burning in early stages or non-convective mixing below the envelope. Here we apply a diffusive mechanism of mixing, together with a recent estimate of the rate for e-captures on 7Be, to establish whether the solar Li destruction should be attributed to purely pre-Main Se- quence (MS) nuclear processes or if the coupling of mixing and nucleosynthesis on the MS can account for it. Our preliminary results indicate that, whether Li survives the pre- MS phase, the changes of the 7Be e--capture rate do not affect its production/destruction. The low Li abundance should then depend only on diffusion processes from the bottom of the convective envelope to the lowerlying tachocline zone. We suggest that, if diffusive processes occurred over the age of the Sun, they required diffusive mass transfers of a few 10-13 M⊙/yr to explain the Li drop. This is a high estimate: future works will tell us if it is realistic or not. In this second case, pre-MS burning would remain the only alternative.

Energy and variance budgets of a diffusive staircase with implications for heat flux scaling

NASA Astrophysics Data System (ADS)

Hieronymus, M.; Carpenter, J. R.

2016-02-01

Diffusive convection, the mode of double-diffusive convection that occur when both temperature and salinity increase with increasing depth, is commonplace throughout the high latitude oceans and diffusive staircases constitute an important heat transport process in the Arctic Ocean. Heat and buoyancy fluxes through these staircases are often estimated using flux laws deduced either from laboratory experiments, or from simplified energy or variance budgets. We have done direct numerical simulations of double-diffusive convection at a range of Rayleigh numbers and quantified the energy and variance budgets in detail. This allows us to compare the fluxes in our simulations to those derived using known flux laws and to quantify how well the simplified energy and variance budgets approximate the full budgets. The fluxes are found to agree well with earlier estimates at high Rayleigh numbers, but we find large deviations at low Rayleigh numbers. The close ties between the heat and buoyancy fluxes and the budgets of thermal variance and energy have been utilized to derive heat flux scaling laws in the field of thermal convection. The result is the so called GL-theory, which has been found to give accurate heat flux scaling laws in a very wide parameter range. Diffusive convection has many similarities to thermal convection and an extension of the GL-theory to diffusive convection is also presented and its predictions are compared to the results from our numerical simulations.

Model unification and scale-adaptivity in the Eddy-Diffusivity Mass-Flux (EDMF) approach

NASA Astrophysics Data System (ADS)

Neggers, R.; Siebesma, P.

2011-12-01

It has long been understood that the turbulent-convective transport of heat, moisture and momentum plays an important role in the dynamics and climate of the earth's atmosphere. Accordingly, the representation of these processes in General Circulation Models (GCMs) has always been an active research field. Turbulence and convection act on temporal and spatial scales that are unresolved by most present-day GCMs, and have to be represented through parametric relations. Over the years a variety of schemes has been successfully developed. Although differing widely in their details, only two basic transport models stand at the basis of most of these schemes. The first is the diffusive transport model, which can only act down-gradient. An example is the turbulent mixing at small scales. The second is the advective transport model, which can act both down-gradient and counter-gradient. A good example is the transport of heat and moisture by convective updrafts that overshoot into stable layers of air. In practice, diffusive models often make use of a K-profile method or a prognostic TKE budget, while advective models make use of a rising (and entraining) plume budget. While most transport schemes classicaly apply either the diffusive model or advective model, the relatively recently introduced Eddy-Diffusivity Mass-Flux (EDMF) approach aims to combine both techniques. By applying advection and diffusion simultaneously, one can make use of the benefits of both approaches. Since its emergence about a decade ago, the EDMF approach has been successfully applied in both research and operational circulation models. This presentation is dedicated to the EDMF framework. Apart from a short introduction to the EDMF concept and a short overview of its current implementations, our main goal is to elaborate on the opportunities EDMF brings in addressing some long-standing problems in the parameterization of turbulent-convective transport. The first problem is the need for a unified approach in the parameterization of distinct transport regimes. The main objections to a separate representation of regimes are i) artificially discrete regime-transitions, and ii) superfluous and intransparent coding. For a unified approach we need to establish what complexity is sufficient to achieve general applicability. We argue that adding only little complexity already enables the standard EDMF framework to represent multiple boundary-layer transport regimes and smooth transitions between those. The second long-standing problem is that the ever increasing computational capacity and speed has lead to increasingly fine discretizations in GCMs, which requires scale-adaptivity in a sub-grid transport model. It is argued that a flexible partitioning between advection and diffusion within EDMF, as well as the potential to introduce stochastic elements in the advective part of EDMF, creates opportunities to introduce such adaptivity. In the final part of the presentation we will attempt to give an overview of currently ongoing developments of the EDMF framework, both concerning model formulation as well as evaluation efforts of key assumptions against observational datasets and large-eddy simulation results.

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1975-10-01

The computer code block VENTURE, designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P$sub 1$) in up to three- dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First- order perturbation analysis capability is available at the macroscopic cross section level. (auth)

Investigation of micromixing by acoustically oscillated sharp-edges

PubMed Central

Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco

2016-01-01

Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel. PMID:27158292

Investigation of micromixing by acoustically oscillated sharp-edges.

PubMed

Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco

2016-03-01

Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel.

Analysis of the discontinuous Galerkin method applied to the European option pricing problem

NASA Astrophysics Data System (ADS)

Hozman, J.

2013-12-01

In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options. We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.

Modeling of FMISO [F18] nanoparticle PET tracer in normal-cancerous tissue based on real clinical image.

PubMed

Asgari, Hanie; Soltani, M; Sefidgar, Mostafa

2018-07-01

Hypoxia as one of the principal properties of tumor cells is a reaction to the deprivation of oxygen. The location of tumor cells could be identified by assessment of oxygen and nutrient level in human body. Positron emission tomography (PET) is a well-known non-invasive method that is able to measure hypoxia based on the FMISO (Fluoromisonidazole) tracer dynamic. This paper aims to study the PET tracer concentration through convection-diffusion-reaction equations in a real human capillary-like network. A non-uniform oxygen pressure along the capillary path and convection mechanism for FMISO transport are taken into account to accurately model the characteristics of the tracer. To this end, a multi-scale model consists of laminar blood flow through the capillary network, interstitial pressure, oxygen pressure, FMISO diffusion and FMISO convection transport in the extravascular region is developed. The present model considers both normal and tumor tissue regions in computational domain. The accuracy of numerical model is verified with the experimental results available in the literature. The convection and diffusion types of transport mechanism are employed in order to calculate the concentration of FMISO in the normal and tumor sub-domain. The influences of intravascular oxygen pressure, FMISO transport mechanisms, capillary density and different types of tissue on the FMISO concentration have been investigated. According to result (Table 4) the convection mechanism of FMISO molecules transportation is negligible, but it causes more accuracy of the proposed model. The approach of present study can be employed in order to investigate the effects of various parameters, such as tumor shape, on the dynamic behavior of different PET tracers, such as FDG, can be extended to different case study problems, such as drug delivery. Copyright © 2018 Elsevier Inc. All rights reserved.

Confronting Practical Problems for Initiation of On-line Hemodiafiltration Therapy.

PubMed

Kim, Yang Wook; Park, Sihyung

2016-06-01

Conventional hemodialysis, which is based on the diffusive transport of solutes, is the most widely used renal replacement therapy. It effectively removes small solutes such as urea and corrects fluid, electrolyte and acid-base imbalance. However, solute diffusion coefficients decreased rapidly as molecular size increased. Because of this, middle and large molecules are not removed effectively and clinical problem such as dialysis amyloidosis might occur. Online hemodiafiltration which is combined by diffusive and convective therapies can overcome such problems by removing effectively middle and large solutes. Online hemodiafiltration is safe, very effective, economically affordable, improving session tolerance and may improve the mortality superior to high flux hemodialysis. However, there might be some potential limitations for setting up online hemodiafiltaration. In this article, we review the uremic toxins associated with dialysis, definition of hemodiafiltration, indication and prescription of hemodiafiltration and the limitations of setting up hemodiafiltration.

Bridging the Transition from Mesoscale to Microscale Turbulence in Numerical Weather Prediction Models

NASA Astrophysics Data System (ADS)

Muñoz-Esparza, Domingo; Kosović, Branko; Mirocha, Jeff; van Beeck, Jeroen

2014-12-01

With a focus towards developing multiscale capabilities in numerical weather prediction models, the specific problem of the transition from the mesoscale to the microscale is investigated. For that purpose, idealized one-way nested mesoscale to large-eddy simulation (LES) experiments were carried out using the Weather Research and Forecasting model framework. It is demonstrated that switching from one-dimensional turbulent diffusion in the mesoscale model to three-dimensional LES mixing does not necessarily result in an instantaneous development of turbulence in the LES domain. On the contrary, very large fetches are needed for the natural transition to turbulence to occur. The computational burden imposed by these long fetches necessitates the development of methods to accelerate the generation of turbulence on a nested LES domain forced by a smooth mesoscale inflow. To that end, four new methods based upon finite amplitude perturbations of the potential temperature field along the LES inflow boundaries are developed, and investigated under convective conditions. Each method accelerated the development of turbulence within the LES domain, with two of the methods resulting in a rapid generation of production and inertial range energy content associated to microscales that is consistent with non-nested simulations using periodic boundary conditions. The cell perturbation approach, the simplest and most efficient of the best performing methods, was investigated further under neutral and stable conditions. Successful results were obtained in all the regimes, where satisfactory agreement of mean velocity, variances and turbulent fluxes, as well as velocity and temperature spectra, was achieved with reference non-nested simulations. In contrast, the non-perturbed LES solution exhibited important energy deficits associated to a delayed establishment of fully-developed turbulence. The cell perturbation method has negligible computational cost, significantly accelerates the generation of realistic turbulence, and requires minimal parameter tuning, with the necessary information relatable to mean inflow conditions provided by the mesoscale solution.

Finite Volume Scheme for Double Convection-Diffusion Exchange of Solutes in Bicarbonate High-Flux Hollow-Fiber Dialyzer Therapy

PubMed Central

Annan, Kodwo

2012-01-01

The efficiency of a high-flux dialyzer in terms of buffering and toxic solute removal largely depends on the ability to use convection-diffusion mechanism inside the membrane. A two-dimensional transient convection-diffusion model coupled with acid-base correction term was developed. A finite volume technique was used to discretize the model and to numerically simulate it using MATLAB software tool. We observed that small solute concentration gradients peaked and were large enough to activate solute diffusion process in the membrane. While CO2 concentration gradients diminished from their maxima and shifted toward the end of the membrane, HCO3 − concentration gradients peaked at the same position. Also, CO2 concentration decreased rapidly within the first 47 minutes while optimal HCO3 − concentration was achieved within 30 minutes of the therapy. Abnormally high diffusion fluxes were observed near the blood-membrane interface that increased diffusion driving force and enhanced the overall diffusive process. While convective flux dominated total flux during the dialysis session, there was a continuous interference between convection and diffusion fluxes that call for the need to seek minimal interference between these two mechanisms. This is critical for the effective design and operation of high-flux dialyzers. PMID:23197994

Effect of natural convection in a horizontally oriented cylinder on NMR imaging of the distribution of diffusivity

PubMed

Mohoric; Stepisnik

2000-11-01

This paper describes the influence of natural convection on NMR measurement of a self-diffusion constant of fluid in the earth's magnetic field. To get an estimation of the effect, the Lorenz model of natural convection in a horizontally oriented cylinder, heated from below, is derived. Since the Lorenz model of natural convection is derived for the free boundary condition, its validity is of a limited value for the natural no-slip boundary condition. We point out that even a slight temperature gradient can cause significant misinterpretation of measurements. The chaotic nature of convection enhances the apparent self-diffusion constant of the liquid.

WE-AB-204-07: Spatiotemporal Distribution of the FDG PET Tracer in Solid Tumors: Contributions of Diffusion and Convection Mechanisms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soltani, M; Sefidgar, M; Bazmara, H

2015-06-15

Purpose: In this study, a mathematical model is utilized to simulate FDG distribution in tumor tissue. In contrast to conventional compartmental modeling, tracer distributions across space and time are directly linked together (i.e. moving beyond ordinary differential equations (ODEs) to utilizing partial differential equations (PDEs) coupling space and time). The diffusion and convection transport mechanisms are both incorporated to model tracer distribution. We aimed to investigate the contributions of these two mechanisms on FDG distribution for various tumor geometries obtained from PET/CT images. Methods: FDG transport was simulated via a spatiotemporal distribution model (SDM). The model is based on amore » 5K compartmental model. We model the fact that tracer concentration in the second compartment (extracellular space) is modulated via convection and diffusion. Data from n=45 patients with pancreatic tumors as imaged using clinical FDG PET/CT imaging were analyzed, and geometrical information from the tumors including size, shape, and aspect ratios were classified. Tumors with varying shapes and sizes were assessed in order to investigate the effects of convection and diffusion mechanisms on FDG transport. Numerical methods simulating interstitial flow and solute transport in tissue were utilized. Results: We have shown the convection mechanism to depend on the shape and size of tumors whereas diffusion mechanism is seen to exhibit low dependency on shape and size. Results show that concentration distribution of FDG is relatively similar for the considered tumors; and that the diffusion mechanism of FDG transport significantly dominates the convection mechanism. The Peclet number which shows the ratio of convection to diffusion rates was shown to be of the order of 10−{sup 3} for all considered tumors. Conclusion: We have demonstrated that even though convection leads to varying tracer distribution profiles depending on tumor shape and size, the domination of the diffusion phenomenon prevents these factors from modulating FDG distribution.« less

Single-drop reactive extraction/extractive reaction with forced convective diffusion and interphase mass transfer

NASA Technical Reports Server (NTRS)

Kleinman, Leonid S.; Reed, X. B., Jr.

1995-01-01

An algorithm has been developed for the forced convective diffusion-reaction problem for convection inside and outside a droplet by a recirculating flow field hydrodynamically coupled at the droplet interface with an external flow field that at infinity becomes a uniform streaming flow. The concentration field inside the droplet is likewise coupled with that outside by boundary conditions at the interface. A chemical reaction can take place either inside or outside the droplet or reactions can take place in both phases. The algorithm has been implemented and results are shown here for the case of no reaction and for the case of an external first order reaction, both for unsteady behavior. For pure interphase mass transfer, concentration isocontours, local and average Sherwood numbers, and average droplet concentrations have been obtained as a function of the physical properties and external flow field. For mass transfer enhanced by an external reaction, in addition to the above forms of results, we present the enhancement factor, with the results now also depending upon the (dimensionless) rate of reaction.

Hydrodynamic Stability of Multicomponent Droplet Gasification in Reduced Gravity

NASA Technical Reports Server (NTRS)

Aharon, I.; Shaw, B. D.

1995-01-01

This investigation addresses the problem of hydrodynamic stability of a two-component droplet undergoing spherically-symmetrical gasification. The droplet components are assumed to have characteristic liquid species diffusion times that are large relative to characteristic droplet surface regression times. The problem is formulated as a linear stability analysis, with a goal of predicting when spherically-symmetric droplet gasification can be expected to be hydrodynamically unstable from surface-tension gradients acting along the surface of a droplet which result from perturbations. It is found that for the conditions assumed in this paper (quasisteady gas phase, no initial droplet temperature gradients, diffusion-dominated gasification), surface tension gradients do not play a role in the stability characteristics. In addition, all perturbations are predicted to decay such that droplets were hydrodynamically stable. Conditions are identified, however, that deserve more analysis as they may lead to hydrodynamic instabilities driven by capillary effects.

Diffusive-convective physical vapor transport of PbTe from a Te-rich solid source

NASA Technical Reports Server (NTRS)

Zoutendyk, J.; Akutagawa, W.

1982-01-01

Crystal growth of PbTe by physical vapor transport (sublimation) in a closed ampoule is governed by the vapor species in thermal equilibrium with the solid compound. Deviations from stoichiometry in the source material cause diffusion limitation of the transport rate, which can be modified by natural (gravity-driven) convection. Mass-transport experiments have been performed using Te-rich material wherein sublimation rates have been measured in order to study the effects of natural convection in diffusion-limited vapor transport. Linear velocities for both crystal growth and evaporation (back sublimation) have been measured for transport in the direction of gravity, horizontally, and opposite to gravity. The experimental results are discussed in terms of both the one-dimensional diffusive-advective model and current, more sophisticated theory which includes natural convection. There is some evidence that convection effects from radial temperature gradients and solutal density gradients have been observed.

Demonstrating Diffusion: Why the Confusion?

ERIC Educational Resources Information Center

Panizzon, Debra Lee

1998-01-01

Examines the principles of diffusion and how it may be confused with convection. Suggests that educators may be misleading students and clouding their understanding of the process. Provides two contemporary examples to explain the process of diffusion and how it differs from convection. (Author/CCM)

Testing density-dependent groundwater models: Two-dimensional steady state unstable convection in infinite, finite and inclined porous layers

USGS Publications Warehouse

Weatherill, D.; Simmons, C.T.; Voss, C.I.; Robinson, N.I.

2004-01-01

This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA-A model for saturated-unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4??2 and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature. ?? 2004 Elsevier Ltd. All rights reserved.

Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA)

DTIC Science & Technology

2013-01-01

Gravity Wave. A slice of the potential temperature perturbation (at y=50 km) after 700 s for 30× 30× 5 elements with 4th-order polynomials . The contour...CONSTANTINESCU ‡ Key words. cloud-resolving model; compressible flow; element-based Galerkin methods; Euler; global model; IMEX; Lagrange; Legendre ...methods in terms of accuracy and efficiency for two types of geophysical fluid dynamics problems: buoyant convection and inertia- gravity waves. These

Numerical simulations of the convective flame in white dwarfs

NASA Technical Reports Server (NTRS)

Livne, Eli

1993-01-01

A first step toward better understanding of the mechanism driving convective flames in exploding white dwarfs is presented. The propagation of the convective flame is examined using a two-dimensional implicit hydrodynamical code. The large scales of the instability are captured by the grid while the scales that are smaller than the grid resolution are approximated by a mixing-length approximation. It is found that largescale perturbations (of order of the pressure scale height) do grow significantly during the expansion, leading to a very nonspherical burning front. The combustion rate is strongly enhanced (compared to the unperturbed case) during the first second, but later the expansion of the star suppresses the flame speed, leading to only partial incineration of the nuclear fuel. Our results imply that large-scale perturbations by themselves are not enough to explain the mechanism by which convective flames are driven, and a study of the whole spectrum of relevant perturbations is needed. The implications of these preliminary results on future simulations, in the context of current models for Type Ia supernovae, are discussed.

Discontinuous Galerkin (DG) Method for solving time dependent convection-diffusion type temperature equation : Demonstration and Comparison with Other Methods in the Mantle Convection Code ASPECT

NASA Astrophysics Data System (ADS)

He, Y.; Puckett, E. G.; Billen, M. I.; Kellogg, L. H.

2016-12-01

For a convection-dominated system, like convection in the Earth's mantle, accurate modeling of the temperature field in terms of the interaction between convective and diffusive processes is one of the most common numerical challenges. In the geodynamics community using Finite Element Method (FEM) with artificial entropy viscosity is a popular approach to resolve this difficulty, but introduce numerical diffusion. The extra artificial viscosity added into the temperature system will not only oversmooth the temperature field where the convective process dominates, but also change the physical properties by increasing the local material conductivity, which will eventually change the local conservation of energy. Accurate modeling of temperature is especially important in the mantle, where material properties are strongly dependent on temperature. In subduction zones, for example, the rheology of the cold sinking slab depends nonlinearly on the temperature, and physical processes such as slab detachment, rollback, and melting all are sensitively dependent on temperature and rheology. Therefore methods that overly smooth the temperature may inaccurately represent the physical processes governing subduction, lithospheric instabilities, plume generation and other aspects of mantle convection. Here we present a method for modeling the temperature field in mantle dynamics simulations using a new solver implemented in the ASPECT software. The new solver for the temperature equation uses a Discontinuous Galerkin (DG) approach, which combines features of both finite element and finite volume methods, and is particularly suitable for problems satisfying the conservation law, and the solution has a large variation locally. Furthermore, we have applied a post-processing technique to insure that the solution satisfies a local discrete maximum principle in order to eliminate the overshoots and undershoots in the temperature locally. To demonstrate the capabilities of this new method we present benchmark results (e.g., falling sphere), and a simple subduction models with kinematic surface boundary condition. To evaluate the trade-offs in computational speed and solution accuracy we present results for the same benchmarks using the Finite Element entropy viscosity method available in ASPECT.

Longitudinal structure of MHD perturbations at the boundary of convective stability in the Kruskal-Oberman model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arsenin, V. V.

2010-10-15

It is shown that, in contrast to the MHD model, a perturbation at the boundary of convective stability of a finite-pressure plasma in confinement systems without an averaged minB in the Kruskal-Oberman model is not generally a purely flute one. The reasons for this discrepancy are clarified. The analysis is carried out for axisymmetric configurations formed by a poloidal magnetic field.

A Green's function method for simulation of time-dependent solute transport and reaction in realistic microvascular geometries

PubMed Central

Secomb, Timothy W.

2016-01-01

A novel theoretical method is presented for simulating the spatially resolved convective and diffusive transport of reacting solutes between microvascular networks and the surrounding tissues. The method allows for efficient computational solution of problems involving convection and non-linear binding of solutes in blood flowing through microvascular networks with realistic 3D geometries, coupled with transvascular exchange and diffusion and reaction in the surrounding tissue space. The method is based on a Green's function approach, in which the solute concentration distribution in the tissue is expressed as a sum of fields generated by time-varying distributions of discrete sources and sinks. As an example of the application of the method, the washout of an inert diffusible tracer substance from a tissue region perfused by a network of microvessels is simulated, showing its dependence on the solute's transvascular permeability and tissue diffusivity. Exponential decay of the washout concentration is predicted, with rate constants that are about 10–30% lower than the rate constants for a tissue cylinder model with the same vessel length, vessel surface area and blood flow rate per tissue volume. PMID:26443811

Convection-diffusion effects in marathon race dynamics

NASA Astrophysics Data System (ADS)

Rodriguez, E.; Espinosa-Paredes, G.; Alvarez-Ramirez, J.

2014-01-01

In the face of the recent terrorist attack event on the 2013 Boston Marathon, the increasing participation of recreational runners in large marathon races has imposed important logistical and safety issues for organizers and city authorities. An accurate understanding of the dynamics of the marathon pack along the race course can provide important insights for improving safety and performance of these events. On the other hand, marathon races can be seen as a model of pedestrian movement under confined conditions. This work used data of the 2011 Chicago Marathon event for modeling the dynamics of the marathon pack from the corral zone to the finish line. By considering the marathon pack as a set of particles moving along the race course, the dynamics are modeled as a convection-diffusion partial differential equation with position-dependent mean velocity and diffusion coefficient. A least-squares problem is posed and solved with optimization techniques for fitting field data from the 2011 Chicago Marathon. It was obtained that the mean pack velocity decreases while the diffusion coefficient increases with distance. This means that the dispersion rate of the initially compact marathon pack increases as the marathon race evolves along the race course.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stagg, Alan K; Yoon, Su-Jong

This report describes the Consortium for Advanced Simulation of Light Water Reactors (CASL) work conducted for completion of the Thermal Hydraulics Methods (THM) Level 3 Milestone THM.CFD.P11.02: Hydra-TH Extensions for Multispecies and Thermosolutal Convection. A critical requirement for modeling reactor thermal hydraulics is to account for species transport within the fluid. In particular, this capability is needed for modeling transport and diffusion of boric acid within water for emergency, reactivity-control scenarios. To support this need, a species transport capability has been implemented in Hydra-TH for binary systems (for example, solute within a solvent). A species transport equation is solved formore » the species (solute) mass fraction, and both thermal and solutal buoyancy effects are handled with specification of a Boussinesq body force. Species boundary conditions can be specified with a Dirichlet condition on mass fraction or a Neumann condition on diffusion flux. To enable enhanced species/fluid mixing in turbulent flow, the molecular diffusivity for the binary system is augmented with a turbulent diffusivity in the species transport calculation. The new capabilities are demonstrated by comparison of Hydra-TH calculations to the analytic solution for a thermosolutal convection problem, and excellent agreement is obtained.« less

Does shaking increase the pressure inside a bottle of champagne?

PubMed

Vreme, A; Pouligny, B; Nadal, F; Liger-Belair, G

2015-02-01

Colas, beers and sparkling wines are all concentrated solutions of carbon dioxide in aqueous solvents. Any such carbonated liquid is ordinarily conditioned inside a closed bottle or a metal can as a liquid-gas 2-phase system. At thermodynamic equilibrium, the partial pressure of carbon-dioxide in the gas phase and its concentration in the liquid are proportional (Henry's law). In practical conditions and use (transport, opening of the container, exterior temperature change, etc.), Henry's equilibrium can be perturbed. The goal of this paper is to describe and understand how the system responds to such perturbations and evolves towards a new equilibrium state. Formally, we investigate the dynamics around Henry's equilibrium of a closed system, through dedicated experiments and modeling. We focus on the response to a sudden pressure change and to mechanical shaking (the latter point inspired the article's title). Observations are rationalized through basic considerations including molecular diffusion, bubble dynamics (based on Epstein-Plesset theory) and chemi-convective hydrodynamic instabilities. Copyright © 2014 Elsevier Inc. All rights reserved.

Marangoni convection in Casson liquid flow due to an infinite disk with exponential space dependent heat source and cross-diffusion effects

NASA Astrophysics Data System (ADS)

Mahanthesh, B.; Gireesha, B. J.; Shashikumar, N. S.; Hayat, T.; Alsaedi, A.

2018-06-01

Present work aims to investigate the features of the exponential space dependent heat source (ESHS) and cross-diffusion effects in Marangoni convective heat mass transfer flow due to an infinite disk. Flow analysis is comprised with magnetohydrodynamics (MHD). The effects of Joule heating, viscous dissipation and solar radiation are also utilized. The thermal and solute field on the disk surface varies in a quadratic manner. The ordinary differential equations have been obtained by utilizing Von Kármán transformations. The resulting problem under consideration is solved numerically via Runge-Kutta-Fehlberg based shooting scheme. The effects of involved pertinent flow parameters are explored by graphical illustrations. Results point out that the ESHS effect dominates thermal dependent heat source effect on thermal boundary layer growth. The concentration and temperature distributions and their associated layer thicknesses are enhanced by Marangoni effect.

Vibration effect on the Soret-induced convection of ternary mixture in a rectangular cavity heated from below

NASA Astrophysics Data System (ADS)

Lyubimova, T. P.; Zubova, N. A.

2017-06-01

This paper presents the results of numerical simulation of the Soret-induced convection of ternary mixture in the rectangular cavity elongated in horizontal direction in gravity field. The cavity has rigid impermeable boundaries. It is heated from the bellow and undergoes translational linearly polarized vibrations of finite amplitude and frequency in the horizontal direction. The problem is solved by finite difference method in the framework of full unsteady non-linear approach. The procedure of diagonalization of the molecular diffusion coefficient matrix is applied, allowing to eliminate cross-diffusion components in the equations and to reduce the number of the governing parameters. The calculations are performed for model ternary mixture with positive separation ratios of the components. The data on the vibration effect on temporal evolution of instantaneous and average fields and integral characteristics of the flow and heat and mass transfer at different levels of gravity are obtained.

A space-time discretization procedure for wave propagation problems

NASA Technical Reports Server (NTRS)

Davis, Sanford

1989-01-01

Higher order compact algorithms are developed for the numerical simulation of wave propagation by using the concept of a discrete dispersion relation. The dispersion relation is the imprint of any linear operator in space-time. The discrete dispersion relation is derived from the continuous dispersion relation by examining the process by which locally plane waves propagate through a chosen grid. The exponential structure of the discrete dispersion relation suggests an efficient splitting of convective and diffusive terms for dissipative waves. Fourth- and eighth-order convection schemes are examined that involve only three or five spatial grid points. These algorithms are subject to the same restrictions that govern the use of dispersion relations in the constructions of asymptotic expansions to nonlinear evolution equations. A new eighth-order scheme is developed that is exact for Courant numbers of 1, 2, 3, and 4. Examples are given of a pulse and step wave with a small amount of physical diffusion.

Evolution Nonlinear Diffusion-Convection PDE Models for Spectrogram Enhancement

NASA Astrophysics Data System (ADS)

Dugnol, B.; Fernández, C.; Galiano, G.; Velasco, J.

2008-09-01

In previous works we studied the application of PDE-based image processing techniques applied to the spectrogram of audio signals in order to improve the readability of the signal. In particular we considered the implementation of the nonlinear diffusive model proposed by Álvarez, Lions and Morel [1](ALM) combined with a convective term inspired by the differential reassignment proposed by Chassandre-Mottin, Daubechies, Auger and Flandrin [2]-[3]. In this work we consider the possibility of replacing the diffusive model of ALM by diffusive terms in divergence form. In particular we implement finite element approximations of nonlinear diffusive terms studied by Chen, Levine, Rao [4] and Antontsev, Shmarev [5]-[8] with a convective term.

Supernova simulations from a 3D progenitor model - Impact of perturbations and evolution of explosion properties

NASA Astrophysics Data System (ADS)

Müller, Bernhard; Melson, Tobias; Heger, Alexander; Janka, Hans-Thomas

2017-11-01

We study the impact of large-scale perturbations from convective shell burning on the core-collapse supernova explosion mechanism using 3D multigroup neutrino hydrodynamics simulations of an 18M⊙ progenitor. Seed asphericities in the O shell, obtained from a recent 3D model of O shell burning, help trigger a neutrino-driven explosion 330 ms after bounce whereas the shock is not revived in a model based on a spherically symmetric progenitor for at least another 300 ms. We tentatively infer a reduction of the critical luminosity for shock revival by ˜ 20 {per cent} due to pre-collapse perturbations. This indicates that convective seed perturbations play an important role in the explosion mechanism in some progenitors. We follow the evolution of the 18M⊙ model into the explosion phase for more than 2 s and find that the cycle of accretion and mass ejection is still ongoing at this stage. With a preliminary value of 7.7 × 1050 erg for the diagnostic explosion energy, a baryonic neutron star mass of 1.85M⊙, a neutron star kick of ˜ 600 km s^{-1} and a neutron star spin period of ˜ 20 ms at the end of the simulation, the explosion and remnant properties are slightly atypical, but still lie comfortably within the observed distribution. Although more refined simulations and a larger survey of progenitors are still called for, this suggests that a solution to the problem of shock revival and explosion energies in the ballpark of observations is within reach for neutrino-driven explosions in 3D.

Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects

NASA Astrophysics Data System (ADS)

Bian, Dongfen; Liu, Jitao

2017-12-01

This paper is concerned with the initial-boundary value problem to 2D magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. First, we establish the global weak solutions under the minimal initial assumption. Then by imposing higher regularity assumption on the initial data, we obtain the global strong solution with uniqueness. Moreover, the exponential decay rates of weak solutions and strong solution are obtained respectively.

Determining the inertial states of low Prandtl number fluids using electrochemical cells

NASA Astrophysics Data System (ADS)

Crunkleton, Daniel Wray

The quality of crystals grown from the melt is often deteriorated by the presence of buoyancy-induced convection, produced by temperature or concentration inhomogenities. It is, therefore, important to develop techniques to visualize such flows. In this study, a novel technique is developed that uses solid-state electrochemical cells to establish and measure dissolved oxygen boundary conditions. To visualize convection, a packet of oxygen is electrochemically introduced at a specific location in the melt. As the fluid convects, this oxygen packet follows the flow, acting as a tracer. Electrochemical sensors located along the enclosure then detect the oxygen as it passes. Over sufficiently long times, oxygen diffusion is important; consequently, the oxygen diffusivity in the fluid is measured. This diffusivity is determined using both transient and steady state experiments with tin and tin-lead alloys as model fluids. It is concluded that the presence of convection due to solutal gradients and/or tilt increases the measured diffusivity by one-half to one order of magnitude. The oxygen diffusivity in tin-lead alloys is measured and the results show that the alloy diffusivities are lower than those of the corresponding pure metals. This concentration functionality is explained with a multicomponent diffusion model and shows good agreement. Rayleigh-Benard convection was used to validate the electrochemical approach to flow visualization. Thus, a numerical characterization of the second critical Rayleigh numbers in liquid tin was conducted for a variety of Cartesian aspect ratios. The extremely low Prandtl number of tin represents the lowest value studied numerically. Additionally, flow field oscillations are visualized and the effect of tilt on convecting systems is quantified. Finally, experimental studies of the effect of convection in liquid tin are presented. Three geometries are studied: (1) double cell with vertical concentration gradients; (2) double cell with horizontal concentration gradients; and (3) multiple cell with vertical temperature gradients. The first critical Rayleigh number transition is detected with geometry (1) and it is concluded that current measurements are not as affected by convection as EMF measurements. The system is compared with numerical simulations in geometry (2), and oscillating convection is detected with geometry (3).

Chaotic dynamics of large-scale double-diffusive convection in a porous medium

NASA Astrophysics Data System (ADS)

Kondo, Shutaro; Gotoda, Hiroshi; Miyano, Takaya; Tokuda, Isao T.

2018-02-01

We have studied chaotic dynamics of large-scale double-diffusive convection of a viscoelastic fluid in a porous medium from the viewpoint of dynamical systems theory. A fifth-order nonlinear dynamical system modeling the double-diffusive convection is theoretically obtained by incorporating the Darcy-Brinkman equation into transport equations through a physical dimensionless parameter representing porosity. We clearly show that the chaotic convective motion becomes much more complicated with increasing porosity. The degree of dynamic instability during chaotic convective motion is quantified by two important measures: the network entropy of the degree distribution in the horizontal visibility graph and the Kaplan-Yorke dimension in terms of Lyapunov exponents. We also present an interesting on-off intermittent phenomenon in the probability distribution of time intervals exhibiting nearly complete synchronization.

Optimal Control of Evolution Mixed Variational Inclusions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alduncin, Gonzalo, E-mail: alduncin@geofisica.unam.mx

2013-12-15

Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.

Helium, Iron and Electron Particle Transport and Energy Transport Studies on the TFTR Tokamak

DOE R&D Accomplishments Database

Synakowski, E. J.; Efthimion, P. C.; Rewoldt, G.; Stratton, B. C.; Tang, W. M.; Grek, B.; Hill, K. W.; Hulse, R. A.; Johnson, D .W.; Mansfield, D. K.; McCune, D.; Mikkelsen, D. R.; Park, H. K.; Ramsey, A. T.; Redi, M. H.; Scott, S. D.; Taylor, G.; Timberlake, J.; Zarnstorff, M. C. (Princeton Univ., NJ (United States). Plasma Physics Lab.); Kissick, M. W. (Wisconsin Univ., Madison, WI (United States))

1993-03-01

Results from helium, iron, and electron transport on TFTR in L-mode and Supershot deuterium plasmas with the same toroidal field, plasma current, and neutral beam heating power are presented. They are compared to results from thermal transport analysis based on power balance. Particle diffusivities and thermal conductivities are radially hollow and larger than neoclassical values, except possibly near the magnetic axis. The ion channel dominates over the electron channel in both particle and thermal diffusion. A peaked helium profile, supported by inward convection that is stronger than predicted by neoclassical theory, is measured in the Supershot The helium profile shape is consistent with predictions from quasilinear electrostatic drift-wave theory. While the perturbative particle diffusion coefficients of all three species are similar in the Supershot, differences are found in the L-Mode. Quasilinear theory calculations of the ratios of impurity diffusivities are in good accord with measurements. Theory estimates indicate that the ion heat flux should be larger than the electron heat flux, consistent with power balance analysis. However, theoretical values of the ratio of the ion to electron heat flux can be more than a factor of three larger than experimental values. A correlation between helium diffusion and ion thermal transport is observed and has favorable implications for sustained ignition of a tokamak fusion reactor.

Laminar natural convection from a vertical plate with a step change in wall temperature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, S.; Yovanovich, M.M.

1991-05-01

The study of natural convection heat transfer from a vertical flat plate in a quiescent medium has attracted a great deal of interest from many investigators in the past few decades. The plate with various thermal conditions that allow similarity transformations as well as those that are continuous and well defined have been examined. However, practical problems often involve wall conditions that are arbitrary and unknown a priori. To understand and solve problems involving general nonsimilar conditions at the wall, it is useful to investigate problems subjected to a step change in wall temperature. The problems impose a mathematical singularitymore » and severe nonsimilar conditions at the wall. In this paper, a new analytical model that can deal with a discontinuous wall temperature variation is presented. The method results in a set of approximate solutions for temperature and velocity distributions. The validity and accuracy of the model is demonstrated by comparisons with the results of the aforementioned investigators. The agreement is excellent and the results obtained with the solution of this work are remarkably close to existing numerical data of Hayday et al. and the perturbation series solution of Kao.« less

The Analysis and Construction of Perfectly Matched Layers for the Linearized Euler Equations

NASA Technical Reports Server (NTRS)

Hesthaven, J. S.

1997-01-01

We present a detailed analysis of a recently proposed perfectly matched layer (PML) method for the absorption of acoustic waves. The split set of equations is shown to be only weakly well-posed, and ill-posed under small low order perturbations. This analysis provides the explanation for the stability problems associated with the split field formulation and illustrates why applying a filter has a stabilizing effect. Utilizing recent results obtained within the context of electromagnetics, we develop strongly well-posed absorbing layers for the linearized Euler equations. The schemes are shown to be perfectly absorbing independent of frequency and angle of incidence of the wave in the case of a non-convecting mean flow. In the general case of a convecting mean flow, a number of techniques is combined to obtain a absorbing layers exhibiting PML-like behavior. The efficacy of the proposed absorbing layers is illustrated though computation of benchmark problems in aero-acoustics.

[Penetration of external thermal perturbations into homeothermic organisms, part I (author's transl)].

PubMed

Theves, B

1978-03-20

The general importance of the mean surface curvature for heat conduction problems is explained and a special symmetry with constant mean curvature on the isothermal surfaces is defined. The applicability for the body shapes of homeothermic organisms is demonstrated and the partial differential equation of heat conduction for this case is derived. The definition: heat release = real heat production + convective pseudoproduction eliminates the term of convective heat transfer through the blood stream and allows the reduction to a mere heat conduction problem. Formulas for the heat loss to the environment and for steady state temperature profiles are given. In case of sudden change of heat loss the partial differential equation is solved and a formula is derived, using dimensionless coordinates of time and distance. The mean surface curvature has strongest influence to the interior temperature field. The solution shows clearly the importance of thermal inertia of the homeothermic organism, for the external temperature wave penetrates into the body with a long phase displacement in time.

Double-diffusive convection in geothermal systems: the salton sea, California, geothermal system as a likely candidate

USGS Publications Warehouse

Fournier, R.O.

1990-01-01

Much has been published about double-diffusive convection as a mechanism for explaining variations in composition and temperature within all-liquid natural systems. However, relatively little is known about the applicability of this phenomenon within the heterogeneous rocks of currently active geothermal systems where primary porosity may control fluid flow in some places and fractures may control it in others. The main appeal of double-diffusive convection within hydrothermal systems is-that it is a mechanism that may allow efficient transfer of heat mainly by convection, while at the same time maintaining vertical and lateral salinity gradients. The Salton Sea geothermal system exhibits the following reservoir characteristics: (1) decreasing salinity and temperature from bottom to top and center toward the sides, (2) a very high heat flow from the top of the system that seems to require a major component of convective transfer of heat within the chemically stratified main reservoir, and (3) a relatively uniform density of the reservoir fluid throughout the system at all combinations of subsurface temperature, pressure, and salinity. Double-diffusive convection can account for these characteristics very nicely whereas other previously suggested models appear to account either for the thermal structure or for the salinity variations, but not both. Hydrologists, reservoir engineers, and particularly geochemists should consider the possibility and consequences of double-diffusive convection when formulating models of hydrothermal processes, and of the response of reservoirs to testing and production. ?? 1990.

The Onset of Double Diffusive Convection in a Viscoelastic Fluid-Saturated Porous Layer with Non-Equilibrium Model

PubMed Central

Yang, Zhixin; Wang, Shaowei; Zhao, Moli; Li, Shucai; Zhang, Qiangyong

2013-01-01

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically. PMID:24312193

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer with non-equilibrium model.

PubMed

Yang, Zhixin; Wang, Shaowei; Zhao, Moli; Li, Shucai; Zhang, Qiangyong

2013-01-01

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.

Effects of variable thermal diffusivity on the structure of convection

NASA Astrophysics Data System (ADS)

Shcheritsa, O. V.; Getling, A. V.; Mazhorova, O. S.

2018-03-01

The structure of multiscale convection in a thermally stratified plane horizontal fluid layer is investigated by means of numerical simulations. The thermal diffusivity is assumed to produce a thin boundary sublayer convectively much more unstable than the bulk of the layer. The simulated flow is a superposition of cellular structures with three different characteristic scales. In contrast to the largest convection cells, the smaller ones are localised in the upper portion of the layer. The smallest cells are advected by the larger-scale convective flows. The simulated flow pattern qualitatively resembles that observed on the Sun.

Perturbations of the Richardson number field by gravity waves

NASA Technical Reports Server (NTRS)

Wurtele, M. G.; Sharman, R. D.

1985-01-01

An analytic solution is presented for a stratified fluid of arbitrary constant Richardson number. By computer aided analysis the perturbation fields, including that of the Richardson number can be calculated. The results of the linear analytic model were compared with nonlinear simulations, leading to the following conclusions: (1) the perturbations in the Richardson number field, when small, are produced primarily by the perturbations of the shear; (2) perturbations of in the Richardson number field, even when small, are not symmetric, the increase being significantly larger than the decrease (the linear analytic solution and the nonlinear simulations both confirm this result); (3) as the perturbations grow, this asymmetry increases, but more so in the nonlinear simulations than in the linear analysis; (4) for large perturbations of the shear flow, the static stability, as represented by N2, is the dominating mechanism, becoming zero or negative, and producing convective overturning; and (5) the convectional measure of linearity in lee wave theory, NH/U, is no longer the critical parameter (it is suggested that (H/u sub 0) (du sub 0/dz) takes on this role in a shearing flow).

The feasibility of thermal and compositional convection in Earth's inner core

NASA Astrophysics Data System (ADS)

Lythgoe, Karen H.; Rudge, John F.; Neufeld, Jerome A.; Deuss, Arwen

2015-05-01

Inner core convection, and the corresponding variations in grain size and alignment, has been proposed to explain the complex seismic structure of the inner core, including its anisotropy, lateral variations and the F-layer at the base of the outer core. We develop a parametrized convection model to investigate the possibility of convection in the inner core, focusing on the dominance of the plume mode of convection versus the translation mode. We investigate thermal and compositional convection separately so as to study the end-members of the system. In the thermal case the dominant mode of convection is strongly dependent on the viscosity of the inner core, the magnitude of which is poorly constrained. Furthermore recent estimates of a large core thermal conductivity result in stable thermal stratification, hindering convection. However, an unstable density stratification may arise due to the pressure dependant partition coefficient of certain light elements. We show that this unstable stratification leads to compositionally driven convection, and that inner core translation is likely to be the dominant convective mode due to the low compositional diffusivity. The style of convection resulting from a combination of both thermal and compositional effects is not easy to understand. For reasonable parameter estimates, the stabilizing thermal buoyancy is greater than the destabilizing compositional buoyancy. However we anticipate complex double diffusive processes to occur given the very different thermal and compositional diffusivities.

The Feasibility of Thermal and Compositional Convection in Earth's Inner Core

NASA Astrophysics Data System (ADS)

Lythgoe, K.; Rudge, J. F.; Neufeld, J. A.; Deuss, A. F.

2014-12-01

Inner core convection, and the corresponding variations in grain size and alignment, has been proposed to explain the complex seismic structure of the inner core, including its anisotropy, lateral variations and the F-layer at the base of the outer core. We develop a parameterised convection model to investigate the possibility of convection in the inner core, focusing on the dominance of the plume mode of convection versus the translation mode. We investigate thermal and compositional convection separately so as to study the end-members of the system. In the thermal case the dominant mode of convection is strongly dependent on the viscosity of the inner core, the magnitude of which is poorly constrained. Furthermore recent estimates of a large core thermal conductivity result in stable thermal stratification, hindering convection. However, an unstable density stratification may arise due to the pressure dependant partition coefficient of certain light elements. We show that this unstable stratification leads to compositionally driven convection, and that inner core translation is likely to be the dominant convective mode due to the low compositional diffusivity. The style of convection resulting from a combination of both thermal and compositional effects is not easy to understand. The stabilising thermal buoyancy is greater than the destabilising compositional buoyancy, however we anticipate complex double diffusive processes to occur given the very different thermal and compositional diffusivities and more work is needed to understand these processes.

Modeling condensation with a noncondensable gas for mixed convection flow

NASA Astrophysics Data System (ADS)

Liao, Yehong

2007-05-01

This research theoretically developed a novel mixed convection model for condensation with a noncondensable gas. The model developed herein is comprised of three components: a convection regime map; a mixed convection correlation; and a generalized diffusion layer model. These components were developed in a way to be consistent with the three-level methodology in MELCOR. The overall mixed convection model was implemented into MELCOR and satisfactorily validated with data covering a wide variety of test conditions. In the development of the convection regime map, two analyses with approximations of the local similarity method were performed to solve the multi-component two-phase boundary layer equations. The first analysis studied effects of the bulk velocity on a basic natural convection condensation process and setup conditions to distinguish natural convection from mixed convection. It was found that the superimposed velocity increases condensation heat transfer by sweeping away the noncondensable gas accumulated at the condensation boundary. The second analysis studied effects of the buoyancy force on a basic forced convection condensation process and setup conditions to distinguish forced convection from mixed convection. It was found that the superimposed buoyancy force increases condensation heat transfer by thinning the liquid film thickness and creating a steeper noncondensable gas concentration profile near the condensation interface. In the development of the mixed convection correlation accounting for suction effects, numerical data were obtained from boundary layer analysis for the three convection regimes and used to fit a curve for the Nusselt number of the mixed convection regime as a function of the Nusselt numbers of the natural and forced convection regimes. In the development of the generalized diffusion layer model, the driving potential for mass transfer was expressed as the temperature difference between the bulk and the liquid-gas interface using the Clausius-Clapeyron equation. The model was developed on a mass basis instead of a molar basis to be consistent with general conservation equations. It was found that vapor diffusion is not only driven by a gradient of the molar fraction but also a gradient of the mixture molecular weight at the diffusion layer.

Non-Boussinesq Dissolution-Driven Convection in Porous Media

NASA Astrophysics Data System (ADS)

Amooie, M. A.; Soltanian, M. R.; Moortgat, J.

2017-12-01

Geological carbon dioxide (CO2) sequestration in deep saline aquifers has been increasingly recognized as a feasible technology to stabilize the atmospheric carbon concentrations and subsequently mitigate the global warming. Solubility trapping is one of the most effective storage mechanisms, which is associated initially with diffusion-driven slow dissolution of gaseous CO2 into the aqueous phase, followed by density-driven convective mixing of CO2 throughout the aquifer. The convection includes both diffusion and fast advective transport of the dissolved CO2. We study the fluid dynamics of CO2 convection in the underlying single aqueous-phase region. Two modeling approaches are employed to define the system: (i) a constant-concentration condition for CO2 in aqueous phase at the top boundary, and (ii) a sufficiently low, constant injection-rate for CO2 from top boundary. The latter allows for thermodynamically consistent evolution of the CO2 composition and the aqueous phase density against the rate at which the dissolved CO2 convects. Here we accurately model the full nonlinear phase behavior of brine-CO2 mixture in a confined domain altered by dissolution and compressibility, while relaxing the common Boussinesq approximation. We discover new flow regimes and present quantitative scaling relations for global characters of spreading, mixing, and dissolution flux in two- and three-dimensional media for the both model types. We then revisit the universal Sherwood-Rayleigh scaling that is under debate for porous media convective flows. Our findings confirm the sublinear scaling for the constant-concentration case, while reconciling the classical linear scaling for the constant-injection model problem. The results provide a detailed perspective into how the available modeling strategies affect the prediction ability for the total amount of CO2 dissolved in the long term within saline aquifers of different permeabilities.

Review of problems in application of supersonic combustion

NASA Technical Reports Server (NTRS)

Ferri, A.

1977-01-01

The problem of air-breathing engines capable of flying at very high Mach numbers is described briefly. Possible performance of supersonic combustion ramjets is outlined briefly and the supersonic combustion process is described. Two mechanisms of combustion are outlined: one is supersonic combustion controlled by convection process, and the second is controlled by diffusion. The parameters related to the combustion process are discussed in detail. Data and analyses of reaction rates and mixing phenomena are represented; the flame mechanism is discussed, and experimental results are presented.

An experimental study of the role of particle diffusive convection on the residence time of volcanic ash clouds

NASA Astrophysics Data System (ADS)

Deal, E.; Carazzo, G.; Jellinek, M.

2013-12-01

The longevity of volcanic ash clouds generated by explosive volcanic plumes is difficult to predict. Diffusive convective instabilities leading to the production of internal layering are known to affect the stability and longevity of these clouds, but the detailed mechanisms controlling particle dynamics and sedimentation are poorly understood. We present results from a series of analog experiments reproducing diffusive convection in a 2D (Hele-Shaw) geometry, which allow us to constrain conditions for layer formation, sedimentation regime and cloud residence time as a function of only the source conditions. We inject a turbulent particle-laden jet sideways into a tank containing a basal layer of salt water and an upper layer of fresh water, which ultimately spreads as a gravity current. After the injection is stopped, particles in suspension settle through the cloud to form particle boundary layers (PBL) at the cloud base. We vary the initial particle concentration of the plume and the injection velocity over a wide range of conditions to identify and characterize distinct regimes of sedimentation. Our experiments show that convective instabilities driven as a result of differing diffusivities of salt and particles lead to periodic layering over a wide range of conditions expected in nature. The flux of particles from layered clouds and the thicknesses of the layers are understood using classical theory for double diffusive convection adjusted for the hydrodynamic diffusion of particles. Although diffusive convection increases sedimentation rates for the smallest particles (<30 μm) its overall effect is to extend the cloud residence time to several hours by maintaining larger particles in suspension within the layers, which is several orders of magnitude longer than expected when considering individual settling rates.

From convection rolls to finger convection in double-diffusive turbulence

PubMed Central

Verzicco, Roberto; Lohse, Detlef

2016-01-01

Double-diffusive convection (DDC), which is the buoyancy-driven flow with fluid density depending on two scalar components, is ubiquitous in many natural and engineering environments. Of great interests are scalars' transfer rate and flow structures. Here we systematically investigate DDC flow between two horizontal plates, driven by an unstable salinity gradient and stabilized by a temperature gradient. Counterintuitively, when increasing the stabilizing temperature gradient, the salinity flux first increases, even though the velocity monotonically decreases, before it finally breaks down to the purely diffusive value. The enhanced salinity transport is traced back to a transition in the overall flow pattern, namely from large-scale convection rolls to well-organized vertically oriented salt fingers. We also show and explain that the unifying theory of thermal convection originally developed by Grossmann and Lohse for Rayleigh–Bénard convection can be directly applied to DDC flow for a wide range of control parameters (Lewis number and density ratio), including those which cover the common values relevant for ocean flows. PMID:26699474

Numerical modeling of physical vapor transport under microgravity conditions: Effect of thermal creep and stress

NASA Technical Reports Server (NTRS)

Mackowski, Daniel W.; Knight, Roy W.

1993-01-01

One of the most promising applications of microgravity (micro-g) environments is the manufacture of exotic and high-quality crystals in closed cylindrical ampoules using physical vapor transport (PVT) processes. The quality enhancements are believed to be due to the absence of buoyant convection in the weightless environment - resulting in diffusion-limited transport of the vapor. In a typical experiment, solid-phase sample material is initially contained at one end of the ampoule. The sample is made to sublime into the vapor phase and deposit onto the opposite end by maintaining the source at an elevated temperature with respect to the deposit. Identification of the physical factors governing both the rates and uniformity of crystal growth, and the optimization of the micro-g technology, will require an accurate modeling of the vapor transport within the ampoule. Previous micro-g modeling efforts have approached the problem from a 'classical' convective/diffusion formulation, in which convection is driven by the action of buoyancy on thermal and solutal density differences. The general conclusion of these works have been that in low gravity environments the effect of buoyancy on vapor transport is negligible, and vapor transport occurs in a diffusion-limited mode. However, it has been recently recognized than in the non-isothermal (and often low total pressure) conditions encountered in ampoules, the commonly-assumed no-slip boundary condition to the differential equations governing fluid motion can be grossly unrepresentative of the actual situation. Specifically, the temperature gradients can give rise to thermal creep flows at the ampoule side walls. In addition, temperature gradients in the vapor itself can, through the action of thermal stress, lead to bulk fluid convection.

Introduction to the Focus Issue: Chemo-Hydrodynamic Patterns and Instabilities

NASA Astrophysics Data System (ADS)

De Wit, A.; Eckert, K.; Kalliadasis, S.

2012-09-01

Pattern forming instabilities are often encountered in a wide variety of natural phenomena and technological applications, from self-organization in biological and chemical systems to oceanic or atmospheric circulation and heat and mass transport processes in engineering systems. Spatio-temporal structures are ubiquitous in hydrodynamics where numerous different convective instabilities generate pattern formation and complex spatiotemporal dynamics, which have been much studied both theoretically and experimentally. In parallel, reaction-diffusion processes provide another large family of pattern forming instabilities and spatio-temporal structures which have been analyzed for several decades. At the intersection of these two fields, "chemo-hydrodynamic patterns and instabilities" resulting from the coupling of hydrodynamic and reaction-diffusion processes have been less studied. The exploration of the new instability and symmetry-breaking scenarios emerging from the interplay between chemical reactions, diffusion and convective motions is a burgeoning field in which numerous exciting problems have emerged during the last few years. These problems range from fingering instabilities of chemical fronts and reactive fluid-fluid interfaces to the dynamics of reaction-diffusion systems in the presence of chaotic mixing. The questions to be addressed are at the interface of hydrodynamics, chemistry, engineering or environmental sciences to name a few and, as a consequence, they have started to draw the attention of several communities including both the nonlinear chemical dynamics and hydrodynamics communities. The collection of papers gathered in this Focus Issue sheds new light on a wide range of phenomena in the general area of chemo-hydrodynamic patterns and instabilities. It also serves as an overview of the current research and state-of-the-art in the field.

A Novel Methodology for Applying Multivoxel MR Spectroscopy to Evaluate Convection-Enhanced Drug Delivery in Diffuse Intrinsic Pontine Gliomas.

PubMed

Guisado, D I; Singh, R; Minkowitz, S; Zhou, Z; Haque, S; Peck, K K; Young, R J; Tsiouris, A J; Souweidane, M M; Thakur, S B

2016-07-01

Diffuse intrinsic pontine gliomas are inoperable high-grade gliomas with a median survival of less than 1 year. Convection-enhanced delivery is a promising local drug-delivery technique that can bypass the BBB in diffuse intrinsic pontine glioma treatment. Evaluating tumor response is critical in the assessment of convection-enhanced delivery of treatment. We proposed to determine the potential of 3D multivoxel (1)H-MR spectroscopy to evaluate convection-enhanced delivery treatment effect in these tumors. We prospectively analyzed 3D multivoxel (1)H-MR spectroscopy data for 6 patients with nonprogressive diffuse intrinsic pontine gliomas who received convection-enhanced delivery treatment of a therapeutic antibody (Phase I clinical trial NCT01502917). To compare changes in the metabolite ratios with time, we tracked the metabolite ratios Cho/Cr and Cho/NAA at several ROIs: normal white matter, tumor within the convection-enhanced delivery infusion site, tumor outside of the infused area, and the tumor average. There was a comparative decrease in both Cho/Cr and Cho/NAA metabolite ratios at the tumor convection-enhanced delivery site versus tumor outside the infused area. We used MR spectroscopy voxels with dominant white matter as a reference. The difference between changes in metabolite ratios became more prominent with increasing time after convection-enhanced delivery treatment. The comparative change in metabolite ratios between the convection-enhanced delivery site and the tumor site outside the infused area suggests that multivoxel (1)H-MR spectroscopy, in combination with other imaging modalities, may provide a clinical tool to accurately evaluate local tumor response after convection-enhanced delivery treatment. © 2016 by American Journal of Neuroradiology.

Spatial model of convective solute transport in brain extracellular space does not support a "glymphatic" mechanism.

PubMed

Jin, Byung-Ju; Smith, Alex J; Verkman, Alan S

2016-12-01

A "glymphatic system," which involves convective fluid transport from para-arterial to paravenous cerebrospinal fluid through brain extracellular space (ECS), has been proposed to account for solute clearance in brain, and aquaporin-4 water channels in astrocyte endfeet may have a role in this process. Here, we investigate the major predictions of the glymphatic mechanism by modeling diffusive and convective transport in brain ECS and by solving the Navier-Stokes and convection-diffusion equations, using realistic ECS geometry for short-range transport between para-arterial and paravenous spaces. Major model parameters include para-arterial and paravenous pressures, ECS volume fraction, solute diffusion coefficient, and astrocyte foot-process water permeability. The model predicts solute accumulation and clearance from the ECS after a step change in solute concentration in para-arterial fluid. The principal and robust conclusions of the model are as follows: (a) significant convective transport requires a sustained pressure difference of several mmHg between the para-arterial and paravenous fluid and is not affected by pulsatile pressure fluctuations; (b) astrocyte endfoot water permeability does not substantially alter the rate of convective transport in ECS as the resistance to flow across endfeet is far greater than in the gaps surrounding them; and (c) diffusion (without convection) in the ECS is adequate to account for experimental transport studies in brain parenchyma. Therefore, our modeling results do not support a physiologically important role for local parenchymal convective flow in solute transport through brain ECS. © 2016 Jin et al.

Buoyancy-driven convection around chemical fronts traveling in covered horizontal solution layers.

PubMed

Rongy, L; Goyal, N; Meiburg, E; De Wit, A

2007-09-21

Density differences across an autocatalytic chemical front traveling horizontally in covered thin layers of solution trigger hydrodynamic flows which can alter the concentration profile. We theoretically investigate the spatiotemporal evolution and asymptotic dynamics resulting from such an interplay between isothermal chemical reactions, diffusion, and buoyancy-driven convection. The studied model couples the reaction-diffusion-convection evolution equation for the concentration of an autocatalytic species to the incompressible Stokes equations ruling the evolution of the flow velocity in a two-dimensional geometry. The dimensionless parameter of the problem is a solutal Rayleigh number constructed upon the characteristic reaction-diffusion length scale. We show numerically that the asymptotic dynamics is one steady vortex surrounding, deforming, and accelerating the chemical front. This chemohydrodynamic structure propagating at a constant speed is quite different from the one obtained in the case of a pure hydrodynamic flow resulting from the contact between two solutions of different density or from the pure reaction-diffusion planar traveling front. The dynamics is symmetric with regard to the middle of the layer thickness for positive and negative Rayleigh numbers corresponding to products, respectively, lighter or heavier than the reactants. A parametric study shows that the intensity of the flow, the propagation speed, and the deformation of the front are increasing functions of the Rayleigh number and of the layer thickness. In particular, the asymptotic mixing length and reaction-diffusion-convection speed both scale as square root Ra for Ra>5. The velocity and concentration fields in the asymptotic dynamics are also found to exhibit self-similar properties with Ra. A comparison of the dynamics in the case of a monostable versus bistable kinetics is provided. Good agreement is obtained with experimental data on the speed of iodate-arsenous acid fronts propagating in horizontal capillaries. We furthermore compare the buoyancy-driven dynamics studied here to Marangoni-driven deformation of traveling chemical fronts in solution open to the air in the absence of gravity previously studied in the same geometry [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)].

Permeability and diffusion in vitreous humor: implications for drug delivery.

PubMed

Xu, J; Heys, J J; Barocas, V H; Randolph, T W

2000-06-01

Previous experimental work suggests that convection may be important in determining the biodistribution of drugs implanted or injected in the vitreous humor. To develop accurate biodistribution models, the relative importance of diffusion and convection in intravitreal transport must be assessed. This requires knowledge of both the diffusivity of candidate drugs and the hydraulic conductivity of the vitreous humor. Hydraulic conductivity of cadaveric bovine vitreous humor was measured by confined compression tests at constant loads of 0.15 and 0.2 N and analyzed numerically using a two-phase model. Diffusion coefficient of acid orange 8, a model compound, in the same medium was measured in a custom-built diffusion cell. Acid orange 8 diffusivity within vitreous humor is about half that in free solution. When viscous effects are properly accounted for, the hydraulic conductivity of bovine vitreous humor is 8.4+/-4.5 x 10(-7) cm2/Pa x s. We predict that convection does not contribute significantly to transport in the mouse eye, particularly for low-molecular-weight compounds. For delivery to larger animals, such as humans we conclude that convection accounts for roughly 30% of the total intravitreal drug transport. This effect should be magnified for higher-molecular-weight compounds, which diffuse more slowly, and in glaucoma, which involves higher intraocular pressure and thus potentially faster convective flow. Thus, caution should be exercised in the extrapolation of small-animal-model biodistribution data to human scale.

Effects of Wind and Freshwater on the Atlantic Meridional Overturning Circulation: Role of Sea Ice and Vertical Diffusion

NASA Astrophysics Data System (ADS)

Wang, Kun; Yang, Haijun; Dai, Haijin; Wang, Yuxing; Li, Qing

2015-04-01

Effects of wind and fresh water on the Atlantic meridional overturning circulation (AMOC) are investigated in a fully coupled climate model (CESM1.0). The AMOC can change significantly when perturbing either the wind stress or fresh water flux in the northern North Atlantic. This work pays special attention on the wind stress effect. Our model results show that the wind forcing is a crucial element in maintaining the AMOC. When the wind-stress is reduced, the vertical convection and diffusion are weakened immediately, triggering a salt deficit in the northern North Atlantic that prevents the deep water formation there. The salinity advection from the south, however, plays a contrary role to salt the upper ocean. As the AMOC weakens, the sea ice expends southward and melts, freshening the upper ocean that weakens the AMOC further. There is a positive feedback between the sea ice melting and AMOC strength, which eventually determines the AMOC strength in the reduced wind world.

Double-Diffusive Convection at Low Prandtl Number

NASA Astrophysics Data System (ADS)

Garaud, Pascale

2018-01-01

This work reviews present knowledge of double-diffusive convection at low Prandtl number obtained using direct numerical simulations, in both the fingering regime and the oscillatory regime. Particular emphasis is given to modeling the induced turbulent mixing and its impact in various astrophysical applications. The nonlinear saturation of fingering convection at low Prandtl number usually drives small-scale turbulent motions whose transport properties can be predicted reasonably accurately using a simple semi-analytical model. In some instances, large-scale internal gravity waves can be excited by a collective instability and eventually cause layering. The nonlinear saturation of oscillatory double-diffusive convection exhibits much more complex behavior. Weakly stratified systems always spontaneously transition into layered convection associated with very efficient mixing. More strongly stratified systems remain dominated by weak wave turbulence unless they are initialized into a layered state. The effects of rotation, shear, lateral gradients, and magnetic fields are briefly discussed.

Magnetic damping of thermocapillary convection in the floating-zone growth of semiconductor crystals

NASA Astrophysics Data System (ADS)

Morthland, Timothy Edward

The floating zone is one process used to grow high purity semiconductor single crystals. In the floating-zone process, a liquid bridge of molten semiconductor, or melt, is held by surface tension between the upper, melting polycrystalline feed rod and the lower, solidifying single crystal. A perfect crystal would require a quiescent melt with pure diffusion of dopants during the entire period needed to grow the crystal. However, temperature variations along the free surface of the melt lead to gradients of the temperature-dependent surface tension, driving a strong and unsteady flow in the melt, commonly labeled thermocapillary or Marangoni convection. For small temperature differences along the free surface, unsteady thermocapillary convection occurs, disrupting the diffusion controlled solidification and creating undesirable dopant concentration variations in the semiconductor single crystal. Since molten semiconductors are good electrical conductors, an externally applied, steady magnetic field can eliminate the unsteadiness in the melt and can reduce the magnitude of the residual steady motion. Crystal growers hope that a strong enough magnetic field will lead to diffusion controlled solidification, but the magnetic field strengths needed to damp the unsteady thermocapillary convection as a function of floating-zone process parameters is unknown. This research has been conducted in the area of the magnetic damping of thermocapillary convection in floating zones. Both steady and unsteady flows have been investigated. Due to the added complexities in solving Maxwells equations in these magnetohydrodynamic problems and due to the thin boundary layers in these flows, a direct numerical simulation of the fluid and heat transfer in the floating zone is virtually impossible, and it is certainly impossible to run enough simulations to search for neutral stability as a function of magnetic field strength over the entire parameter space. To circumvent these difficulties, we have used matched asymptotic expansions, linear stability theory and numerics to characterize these flows. Some fundamental aspects of the heat transfer and fluid mechanics in these magnetohydrodynamic flows are elucidated in addition to the calculation of the magnetic field strengths required to damp unsteady thermocapillary convection as a function of process parameters.

Lithium Depletion in Solar-like Stars: Effect of Overshooting Based on Realistic Multi-dimensional Simulations

NASA Astrophysics Data System (ADS)

Baraffe, I.; Pratt, J.; Goffrey, T.; Constantino, T.; Folini, D.; Popov, M. V.; Walder, R.; Viallet, M.

2017-08-01

We study lithium depletion in low-mass and solar-like stars as a function of time, using a new diffusion coefficient describing extra-mixing taking place at the bottom of a convective envelope. This new form is motivated by multi-dimensional fully compressible, time-implicit hydrodynamic simulations performed with the MUSIC code. Intermittent convective mixing at the convective boundary in a star can be modeled using extreme value theory, a statistical analysis frequently used for finance, meteorology, and environmental science. In this Letter, we implement this statistical diffusion coefficient in a one-dimensional stellar evolution code, using parameters calibrated from multi-dimensional hydrodynamic simulations of a young low-mass star. We propose a new scenario that can explain observations of the surface abundance of lithium in the Sun and in clusters covering a wide range of ages, from ˜50 Myr to ˜4 Gyr. Because it relies on our physical model of convective penetration, this scenario has a limited number of assumptions. It can explain the observed trend between rotation and depletion, based on a single additional assumption, namely, that rotation affects the mixing efficiency at the convective boundary. We suggest the existence of a threshold in stellar rotation rate above which rotation strongly prevents the vertical penetration of plumes and below which rotation has small effects. In addition to providing a possible explanation for the long-standing problem of lithium depletion in pre-main-sequence and main-sequence stars, the strength of our scenario is that its basic assumptions can be tested by future hydrodynamic simulations.

Lithium Depletion in Solar-like Stars: Effect of Overshooting Based on Realistic Multi-dimensional Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baraffe, I.; Pratt, J.; Goffrey, T.

We study lithium depletion in low-mass and solar-like stars as a function of time, using a new diffusion coefficient describing extra-mixing taking place at the bottom of a convective envelope. This new form is motivated by multi-dimensional fully compressible, time-implicit hydrodynamic simulations performed with the MUSIC code. Intermittent convective mixing at the convective boundary in a star can be modeled using extreme value theory, a statistical analysis frequently used for finance, meteorology, and environmental science. In this Letter, we implement this statistical diffusion coefficient in a one-dimensional stellar evolution code, using parameters calibrated from multi-dimensional hydrodynamic simulations of a youngmore » low-mass star. We propose a new scenario that can explain observations of the surface abundance of lithium in the Sun and in clusters covering a wide range of ages, from ∼50 Myr to ∼4 Gyr. Because it relies on our physical model of convective penetration, this scenario has a limited number of assumptions. It can explain the observed trend between rotation and depletion, based on a single additional assumption, namely, that rotation affects the mixing efficiency at the convective boundary. We suggest the existence of a threshold in stellar rotation rate above which rotation strongly prevents the vertical penetration of plumes and below which rotation has small effects. In addition to providing a possible explanation for the long-standing problem of lithium depletion in pre-main-sequence and main-sequence stars, the strength of our scenario is that its basic assumptions can be tested by future hydrodynamic simulations.« less

The Effect of Global-Scale, Steady-State Convection and Elastic-Gravitational Asphericities on Helioseismic Oscillations

NASA Astrophysics Data System (ADS)

Lavely, Eugene M.; Ritzwoller, Michael H.

1992-06-01

In this paper we derive a theory, based on quasi-degenerate perturbation theory, that governs the effect of global-scale, steady-state convection and associated static asphericities in the elastic-gravitational variables (adiabatic bulk modulus kappa , density ρ , and gravitational potential φ ) on helioseismic eigenfrequencies and eigenfunctions and present a formalism with which this theory can be applied computationally. The theory rests on three formal assumptions: (1) that convection is temporally steady in a frame corotating with the Sun, (2) that accurate eigenfrequencies and eigenfunctions can be determined by retaining terms in the seismically perturbed equations of motion only to first order in p-mode displacement, and (3) that we are justified in retaining terms only to first order in convective velocity (this is tantamount to assuming that the convective flow is anelastic). The most physically unrealistic assumption is (1), and we view the results of this paper as the first step toward a more general theory governing the seismic effects of time-varying fields. Although the theory does not govern the seismic effects of non-stationary flows, it can be used to approximate the effects of unsteady flows on the acoustic wavefield if the flow is varying smoothly in time. The theory does not attempt to model seismic modal amplitudes since these are governed, in part, by the exchange of energy between convection and acoustic motions which is not a part of this theory. However, we show how theoretical wavefields can be computed given a description of the stress field produced by a source process such as turbulent convection. The basic reference model that will be perturbed by rotation, convection, structural asphericities, and acoustic oscillations is a spherically symmetric, non-rotating, non-magnetic, isotropic, static solar model that, when subject to acoustic oscillations, oscillates adiabatically. We call this the SNRNMAIS model. An acoustic mode of the SNRNMAIS model is denoted by k = (n,l,m), where n is the radial order, l is the harmonic degree, and m is the azimuthal order of the mode. The main result of the paper is the general matrix element Hn'n,l'lm'm for steady-state convection satisfying the anelastic condition with static structural asphericities. It is written in terms of the radial, scalar eigenfunctions of the SNRNMAIS model, resulting in equations (90)-(110). We prove Rayleigh's principle in our derivation of quasi-degenerate perturbation theory which, as a by-product, yields the general matrix element. Within this perturbative method, modes need not be exactly degenerate in the SNRNMAIS solar model to couple, only nearly so. General matrix elements compose the hermitian supermatrix Z. The eigenvalues of the supermatrix are the eigenfrequency perturbations of the convecting, aspherical model and the eigenvector components of Z are the expansion coefficients in the linear combination forming the eigenfunctions in which the eigenfunctions of the SNRNMAIS solar model act as basis functions. The properties of the Wigner 3j symbols and the reduced matrix elements composing Hn'n,l'lm' produce selection rules governing the coupling of SNRNMAIS modes that hold even for time-varying flows. We state selection rules for both quasi-degenerate and degenerate perturbation theories. For example, within degenerate perturbation theory, only odd-degree s toroidal flows and even degree structural asphericities, both with s <= 2l, will couple and/or split acoustic modes with harmonic degree l. In addition, the frequency perturbations caused by a toroidal flow display odd symmetry with respect to the degenerate frequency when ordered from the minimum to the maximum frequency perturbation. We consider the special case of differential rotation, the odd-degree, axisymmetric, toroidal component of general convection, and present the general matrix element and selection rules under quasi-degenerate perturbation theory. We argue that due to the spacing of modes that satisfy the selection rules, quasi-degenerate coupling can, for all practical purposes, be neglected in modelling the effect of low-degree differential rotation on helioseismic data. In effect, modes that can couple through low-degree differential rotation are too far separated in frequency to couple strongly. This is not the case for non-axisymmetric flows and asphericities where near degeneracies will regularly occur, and couplings can be relatively strong especially among SNRNMAIS modes within the same multiplet. All derivations are performed and all solutions are presented in a frame corotating with the mean solar angular rotation rate. Equation (18) shows how to transform the eigenfrequencies and eigenfunctions in the corotating frame into an inertial frame. The transformation has the effect that each eigenfunction in the inertial frame is itself time varying. That is, a mode of oscillation, which is defined to have a single frequency in the corotating frame, becomes multiply periodic in the inertial frame.

Diffusion with Varying Drag; the Runaway Problem.

NASA Astrophysics Data System (ADS)

Rollins, David Kenneth

We study the motion of electrons in an ionized plasma of electrons and ions in an external electric field. A probability distribution function describes the electron motion and is a solution of a Fokker-Planck equation. In zero field, the solution approaches an equilibrium Maxwellian. For arbitrarily small field, electrons overcome the diffusive effects and are freely accelerated by the field. This is the electron runaway phenomenon. We treat the electric field as a small perturbation. We consider various diffusion coefficients for the one dimensional problem and determine the runaway current as a function of the field strength. Diffusion coefficients, non-zero on a finite interval are examined. Some non-trivial cases of these can be solved exactly in terms of known special functions. The more realistic case where the diffusion coefficient decays with velocity are then considered. To determine the runaway current, the equivalent Schrodinger eigenvalue problem is analysed. The smallest eigenvalue is shown to be equal to the runaway current. Using asymptotic matching a solution can be constructed which is then used to evaluate the runaway current. The runaway current is exponentially small as a function of field strength. This method is used to extract results from the three dimensional problem.

A Green's function method for simulation of time-dependent solute transport and reaction in realistic microvascular geometries.

PubMed

Secomb, Timothy W

2016-12-01

A novel theoretical method is presented for simulating the spatially resolved convective and diffusive transport of reacting solutes between microvascular networks and the surrounding tissues. The method allows for efficient computational solution of problems involving convection and non-linear binding of solutes in blood flowing through microvascular networks with realistic 3D geometries, coupled with transvascular exchange and diffusion and reaction in the surrounding tissue space. The method is based on a Green's function approach, in which the solute concentration distribution in the tissue is expressed as a sum of fields generated by time-varying distributions of discrete sources and sinks. As an example of the application of the method, the washout of an inert diffusible tracer substance from a tissue region perfused by a network of microvessels is simulated, showing its dependence on the solute's transvascular permeability and tissue diffusivity. Exponential decay of the washout concentration is predicted, with rate constants that are about 10-30% lower than the rate constants for a tissue cylinder model with the same vessel length, vessel surface area and blood flow rate per tissue volume. © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Fem Simulation of Triple Diffusive Natural Convection Along Inclined Plate in Porous Medium: Prescribed Surface Heat, Solute and Nanoparticles Flux

NASA Astrophysics Data System (ADS)

Goyal, M.; Goyal, R.; Bhargava, R.

2017-12-01

In this paper, triple diffusive natural convection under Darcy flow over an inclined plate embedded in a porous medium saturated with a binary base fluid containing nanoparticles and two salts is studied. The model used for the nanofluid is the one which incorporates the effects of Brownian motion and thermophoresis. In addition, the thermal energy equations include regular diffusion and cross-diffusion terms. The vertical surface has the heat, mass and nanoparticle fluxes each prescribed as a power law function of the distance along the wall. The boundary layer equations are transformed into a set of ordinary differential equations with the help of group theory transformations. A wide range of parameter values are chosen to bring out the effect of buoyancy ratio, regular Lewis number and modified Dufour parameters of both salts and nanofluid parameters with varying angle of inclinations. The effects of parameters on the velocity, temperature, solutal and nanoparticles volume fraction profiles, as well as on the important parameters of heat and mass transfer, i.e., the reduced Nusselt, regular and nanofluid Sherwood numbers, are discussed. Such problems find application in extrusion of metals, polymers and ceramics, production of plastic films, insulation of wires and liquid packaging.

Inter-Diffusion in the Presence of Free Convection

NASA Technical Reports Server (NTRS)

Gupta, Prabhat K.

1999-01-01

Because of their technological importance, establishment of the precise values of interdiffusion coefficients is important in multicomponent fluid systems. Such values are not available because diffusion is influenced by free convection due to compositionally induced density variations. In this project, earth based diffusion experiments are being performed in a viscous fluid system PbO-SiO2 at temperatures between 500-1000 C. This system is chosen because it shows a large variation in density with small changes in composition and is expected to show a large free convection effect. Infinite diffusion couples at different temperatures and times are being studied with different orientations with respect to gravity. Composition fields will be measured using an Electron Microprobe Analyzer and will be compared with the results of a complementary modeling study to extract the values of the true diffusion coefficient from the measured diffusion profiles.

A New Homotopy Perturbation Scheme for Solving Singular Boundary Value Problems Arising in Various Physical Models

NASA Astrophysics Data System (ADS)

Roul, Pradip; Warbhe, Ujwal

2017-08-01

The classical homotopy perturbation method proposed by J. H. He, Comput. Methods Appl. Mech. Eng. 178, 257 (1999) is useful for obtaining the approximate solutions for a wide class of nonlinear problems in terms of series with easily calculable components. However, in some cases, it has been found that this method results in slowly convergent series. To overcome the shortcoming, we present a new reliable algorithm called the domain decomposition homotopy perturbation method (DDHPM) to solve a class of singular two-point boundary value problems with Neumann and Robin-type boundary conditions arising in various physical models. Five numerical examples are presented to demonstrate the accuracy and applicability of our method, including thermal explosion, oxygen-diffusion in a spherical cell and heat conduction through a solid with heat generation. A comparison is made between the proposed technique and other existing seminumerical or numerical techniques. Numerical results reveal that only two or three iterations lead to high accuracy of the solution and this newly improved technique introduces a powerful improvement for solving nonlinear singular boundary value problems (SBVPs).

Physics, stability, and dynamics of supply networks

NASA Astrophysics Data System (ADS)

Helbing, Dirk; Lämmer, Stefan; Seidel, Thomas; Šeba, Pétr; Płatkowski, Tadeusz

2004-12-01

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the nonlinear behavior is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed “bullwhip effect” in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by damped or growing oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.

A Simple Demonstration of Convective Effects on Reaction-Diffusion Systems: A Burning Cigarette.

ERIC Educational Resources Information Center

Pojman, John A.

1990-01-01

Described is a demonstration that provides an introduction to nonequilibrium reaction-diffusion systems and the coupling of hydrodynamics to chemical reactions. Experiments that demonstrate autocatalytic behavior that are effected by gravity and convection are included. (KR)

Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions

NASA Astrophysics Data System (ADS)

Elwakil, S. A.; El-Labany, S. K.; Zahran, M. A.; Sabry, R.

2004-04-01

The modified extended tanh-function method were applied to the general class of nonlinear diffusion-convection equations where the concentration-dependent diffusivity, D( u), was taken to be a constant while the concentration-dependent hydraulic conductivity, K( u) were taken to be in a power law. The obtained solutions include rational-type, triangular-type, singular-type, and solitary wave solutions. In fact, the profile of the obtained solitary wave solutions resemble the characteristics of a shock-wave like structure for an arbitrary m (where m>1 is the power of the nonlinear convection term).

Angiogenic Signaling in Living Breast Tumor Models

DTIC Science & Technology

2006-06-01

SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON USAMRMC a. REPORT U b. ABSTRACT U c ...convection versus diffusion in transport out of a tumor vessel during steady state conditions. C . Determine relative contribution of convection...on the results of the diffusion/convection measurements. Consequently, implicit in Tasks 1b and c (the use of MPFRAP in vivo) is the establishment

The Overshoot Phenomenon in Geodynamics Codes

NASA Astrophysics Data System (ADS)

Kommu, R. K.; Heien, E. M.; Kellogg, L. H.; Bangerth, W.; Heister, T.; Studley, E. H.

2013-12-01

The overshoot phenomenon is a common occurrence in numerical software when a continuous function on a finite dimensional discretized space is used to approximate a discontinuous jump, in temperature and material concentration, for example. The resulting solution overshoots, and undershoots, the discontinuous jump. Numerical simulations play an extremely important role in mantle convection research. This is both due to the strong temperature and stress dependence of viscosity and also due to the inaccessibility of deep earth. Under these circumstances, it is essential that mantle convection simulations be extremely accurate and reliable. CitcomS and ASPECT are two finite element based mantle convection simulations developed and maintained by the Computational Infrastructure for Geodynamics. CitcomS is a finite element based mantle convection code that is designed to run on multiple high-performance computing platforms. ASPECT, an adaptive mesh refinement (AMR) code built on the Deal.II library, is also a finite element based mantle convection code that scales well on various HPC platforms. CitcomS and ASPECT both exhibit the overshoot phenomenon. One attempt at controlling the overshoot uses the Entropy Viscosity method, which introduces an artificial diffusion term in the energy equation of mantle convection. This artificial diffusion term is small where the temperature field is smooth. We present results from CitcomS and ASPECT that quantify the effect of the Entropy Viscosity method in reducing the overshoot phenomenon. In the discontinuous Galerkin (DG) finite element method, the test functions used in the method are continuous within each element but are discontinuous across inter-element boundaries. The solution space in the DG method is discontinuous. FEniCS is a collection of free software tools that automate the solution of differential equations using finite element methods. In this work we also present results from a finite element mantle convection simulation implemented in FEniCS that investigates the effect of using DG elements in reducing the overshoot problem.

Impurity confinement and transport in high confinement regimes without edge localized modes on DIII-D [Impurity confinement and transport in high confinement regimes without ELMs on DIII-D

DOE PAGES

Grierson, Brian A.; Burrell, Keith H.; Nazikian, Raffi M.; ...

2015-04-17

Here, impurity transport in the DIII-D tokamak is investigated in stationary high confinement (H-mode) regimes without edge localized modes (ELMs). In plasmas maintained by resonant magnetic perturbation (RMP) ELM-suppression and QH-mode the confinement time of fluorine (Z=9) is equivalent to that in ELMing discharges with 40 Hz ELMs. For selected discharges with impurity injection the impurity particle confinement time compared to the energy confinement time is in the range of τ p/τ e ≈ 2 $-$ 3. In QH-mode operation the impurity confinement time is shown to be smaller for intense, coherent magnetic and density fluctuations of the edge harmonicmore » oscillation than weaker fluctuations. Transport coefficients are derived from the time evolution of the impurity density profile and compared to neoclassical and turbulent transport models NEO and TGLF. Neoclassical transport of fluorine is found to be small compared to the experimental values. In the ELMing and RMP ELM-suppressed plasma the impurity transport is affected by the presence of tearing modes. For radii larger than the mode radius the TGLF diffusion coefficient is smaller than the experimental value by a factor of 2-3, while the convective velocity is within error estimates. Low levels of diffusion are observed for radii smaller than the tearing mode radius. In the QH-mode plasma investigated, the TGLF diffusion coefficient higher inside of ρ = 0.4 and lower outside of 0.4 than the experiment, and the TGLF convective velocity is more negative by a factor of approximately 1.7.« less

Controlling mechanisms of moisture diffusion in convective drying of leather

NASA Astrophysics Data System (ADS)

Benmakhlouf, Naima; Azzouz, Soufien; Monzó-Cabrera, Juan; Khdhira, Hechmi; ELCafsi, Afif

2017-04-01

Leather manufacturing involves a crucial energy-intensive drying stage in the finishing process to remove its residual moisture. It occurs several times in the tanning course. As it is the target of this paper to depict an experimental way to determine moisture diffusion in the convective drying of leather. The effective diffusion coefficient is estimated by a method derived from Fick's law and by analytic method. The effective diffusion coefficients are obtained from drying tests and the diffusivity behaviour is studied versus the controlling parameter such as the convective airflow temperature. The experiments were conducted at hot air temperatures of 40, 45, 50, 55 and 60 °C and hot air speed of 1 m/s. The hot air temperature had significant effect on the effective moisture diffusivity of the leather sample. The average effective moisture diffusivity in rosehip ranged between 5.87 × 10-11 and 14.48 × 10-11 m2/s for leather at the temperatures studied. Activation energy for convective drying was found to be 38.46 kJ/mol for leather. The obtained results fully confirm the theoretical study in which an exponentially increasing relationship between effective diffusivity and temperature is predicted. The results of this study provide a better understanding of the drying mechanisms and may lead to a series of recommendations for leather drying optimization. It opens the possibility for further investigations on the description of drying conditions.

Stability of the Tonks–Langmuir discharge pre-sheath

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tskhakaya, D. D.; Kos, L.; Tskhakaya, D.

The article formulates the stability problem of the plasma sheath in the Tonks–Langmuir discharge. Using the kinetic description of the ion gas, i.e., the stability of the potential shape in the quasi-neutral pre-sheath regarding the high and low frequency, the perturbations are investigated. The electrons are assumed to be Maxwell–Boltzmann distributed. Regarding high-frequency perturbations, the pre-sheath is shown to be stable. The stability problem regarding low-frequency perturbations can be reduced to an analysis of the “diffusion like” equation, which results in the instability of the potential distribution in the pre-sheath. By means of the Particle in Cell simulations, also themore » nonlinear stage of low frequency oscillations is investigated. Comparing the figure obtained with the figure for linear stage, one can find obvious similarity in the spatial-temporal behavior of the potential.« less

The Sensitivity of Atmospheric Water Isotopes to Entrainment and Precipitation Efficiency in a Bulk Plume Model of Convection

NASA Astrophysics Data System (ADS)

Duan, S.; Wright, J. S.; Romps, D. M.

2016-12-01

Atmospheric water isotopes have been proposed as potentially powerful constraints on the physics of convective clouds and parameterizations of convective processes in models. We have previously derived an analytical model of water vapor (H2O) and one of its heavy isotopes (HDO) in convective environments based on a bulk-plume convective water budget in radiative convective equilibrium. This analytical model provides a useful starting point for examining the joint responses of water vapor and its isotopic composition to changes in convective parameters; however, certain idealistic assumptions are required to make the model analytically solvable. Here, we develop a more flexible numerical framework that enables a wider range of model configurations and includes additional isotopic tracers. This model provides a bridge between Rayleigh distillation, which is simple but inflexible, and more complicated convection schemes and cloud resolving models, which are more realistic but also more difficult to perturb and interpret. Application of realistic in-cloud water profiles in our model produces vertical distributions of δD that qualitatively match satellite observations from the Tropospheric Emission Spectrometer (TES). We test the sensitivity of water vapor and its isotopic composition to a wide range of perturbations in the model parameters and their vertical profiles. In this presentation, we focus especially on establishing constraints for convective entrainment and precipitation efficiency. We conclude by discussing the potential application of this model as part of a larger water isotope toolkit for use with offline diagnostics provided by reanalyses and GCMs.

Bio-Fluid Dynamics in a Centimeter-Scale Diagnostics Incubator with Integrated Perfusion

NASA Astrophysics Data System (ADS)

Vukasinovic, J.; Cullen, D. K.; Glezer, A.; Laplaca, M. C.

2006-11-01

Growing demands for long-term incubation of biologically faithful, three-dimensional neuronal and other cultures during extended physiological studies require efficient perfusion platforms with functional vasculatures that mimic the in vivo condition in a thermally regulated environment. While thermostatically controlled incubation baths with capillary action perfusion are available, their use is confined to specific experimental conditions. The interstitial nutrient and gas delivery remains diffusion limited over the long term and cultures decay metabolically. To overcome these problems, we describe simple fabrication and experimental characterization of a compact, diagnostics incubator that allows in situ monitoring of culture activity with a superior control of critical biological functions using convectively enhanced heat and mass transport. To overcome intercellular diffusion barriers culture is exposed to a direct flow of media issuing from an array of micro-nozzles that are directed normal to the substrate upholding the culture, and further improved by 3-D convection induced by jet interactions and biased, peripheral perfusate extraction through an array of microchannels as demonstrated by microPIV measurements.

Exact Solution to Stationary Onset of Convection Due to Surface Tension Variation in a Multicomponent Fluid Layer With Interfacial Deformation

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond Lee; McCaughan, Frances E.

1998-01-01

Stationary onset of convection due to surface tension variation in an unbounded multicomponent fluid layer is considered. Surface deformation is included and general flux boundary conditions are imposed on the stratifying agencies (temperature/composition) disturbance equations. Exact solutions are obtained to the general N-component problem for both finite and infinitesimal wavenumbers. Long wavelength instability may coexist with a finite wavelength instability for certain sets of parameter values, often referred to as frontier points. For an impermeable/insulated upper boundary and a permeable/conductive lower boundary, frontier boundaries are computed in the space of Bond number, Bo, versus Crispation number, Cr, over the range 5 x 10(exp -7) less than or equal to Bo less than or equal to 1. The loci of frontier points in (Bo, Cr) space for different values of N, diffusivity ratios, and, Marangoni numbers, collapsed to a single curve in (Bo, D(dimensional variable)Cr) space, where D(dimensional variable) is a Marangoni number weighted diffusivity ratio.

Combined effects of drift waves and neoclassical transport on density profiles in tokamaks

NASA Astrophysics Data System (ADS)

Houlberg, W. A.; Strand, P.

2005-10-01

The relative importance of neoclassical and anomalous particle transport depends on the charge number of the species being studied. The detailed particle balance including the EDWM [1] drift wave model for anomalous transport that includes ITG, TEM and in some cases ETG modes, and the neoclassical model NCLASS [2], are illustrated by simulations with the DEA particle transport code. DEA models the evolution of all ion species, and can be run in a mode to evaluate dynamic responses to perturbations or to conditions far from equilibrium by perturbing the profiles from the experimental measurements. The perturbations allow the fluxes to be decomposed into diffusive and convective (pinch) terms. The different scaling with charge number between drift wave and neoclassical models favors a stronger component of neoclassical transport for higher Z impurities through the effective pinch term. Although trace impurities illustrate a simple Ficks Law form, the main ions as well as higher concentrations of intrinsic impurities exhibit non-linear responses to the density gradients as well as off-diagonal gradient dependencies, leading to a more complicated response for the particle fluxes.[1] H. Nordman, et al., Plasma Phys. Control. Fusion 47 (2005) L11. [2] W.A. Houlberg, et al., Phys. Plasmas 4 (1997) 3230.

Spatial model of convective solute transport in brain extracellular space does not support a “glymphatic” mechanism

PubMed Central

Jin, Byung-Ju; Smith, Alex J.

2016-01-01

A “glymphatic system,” which involves convective fluid transport from para-arterial to paravenous cerebrospinal fluid through brain extracellular space (ECS), has been proposed to account for solute clearance in brain, and aquaporin-4 water channels in astrocyte endfeet may have a role in this process. Here, we investigate the major predictions of the glymphatic mechanism by modeling diffusive and convective transport in brain ECS and by solving the Navier–Stokes and convection–diffusion equations, using realistic ECS geometry for short-range transport between para-arterial and paravenous spaces. Major model parameters include para-arterial and paravenous pressures, ECS volume fraction, solute diffusion coefficient, and astrocyte foot-process water permeability. The model predicts solute accumulation and clearance from the ECS after a step change in solute concentration in para-arterial fluid. The principal and robust conclusions of the model are as follows: (a) significant convective transport requires a sustained pressure difference of several mmHg between the para-arterial and paravenous fluid and is not affected by pulsatile pressure fluctuations; (b) astrocyte endfoot water permeability does not substantially alter the rate of convective transport in ECS as the resistance to flow across endfeet is far greater than in the gaps surrounding them; and (c) diffusion (without convection) in the ECS is adequate to account for experimental transport studies in brain parenchyma. Therefore, our modeling results do not support a physiologically important role for local parenchymal convective flow in solute transport through brain ECS. PMID:27836940

Model of two-temperature convective transfer in porous media

NASA Astrophysics Data System (ADS)

Gruais, Isabelle; Poliševski, Dan

2017-12-01

In this paper, we study the asymptotic behaviour of the solution of a convective heat transfer boundary problem in an ɛ -periodic domain which consists of two interwoven phases, solid and fluid, separated by an interface. The fluid flow and its dependence with respect to the temperature are governed by the Boussinesq approximation of the Stokes equations. The tensors of thermal diffusion of both phases are ɛ -periodic, as well as the heat transfer coefficient which is used to describe the first-order jump condition on the interface. We find by homogenization that the two-scale limits of the solutions verify the most common system used to describe local thermal non-equilibrium phenomena in porous media (see Nield and Bejan in Convection in porous media, Springer, New York, 1999; Rees and Pop in Transport phenomena in porous media III, Elsevier, Oxford, 2005). Since now, this system was justified only by volume averaging arguments.

Symbolic Computational Approach to the Marangoni Convection Problem With Soret Diffusion

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond

1998-01-01

A recently reported solution for stationary stability of a thermosolutal system with Soret diffusion is re-derived and examined using a symbolic computational package. Symbolic computational languages are well suited for such an analysis and facilitate a pragmatic approach that is adaptable to similar problems. Linearization of the equations, normal mode analysis, and extraction of the final solution are performed in a Mathematica notebook format. An exact solution is obtained for stationary stability in the limit of zero gravity. A closed form expression is also obtained for the location of asymptotes in relevant parameter, (Sm(sub c), Mac(sub c)), space. The stationary stability behavior is conveniently examined within the symbolic language environment. An abbreviated version of the Mathematica notebook is given in the Appendix.

Convection, diffusion and reaction in a surface-based biosensor: modeling of cooperativity and binding site competition on the surface and in the hydrogel.

PubMed

Lebedev, Konstantin; Mafé, Salvador; Stroeve, Pieter

2006-04-15

We study theoretically the transport and kinetic processes underlying the operation of a biosensor (particularly the surface plasmon sensor "Biacore") used to study the surface binding kinetics of biomolecules in solution to immobilized receptors. Unlike previous studies, we concentrate mainly on the modeling of system-specific phenomena rather than on the influence of mass transport limitations on the intrinsic kinetic rate constants determined from binding data. In the first problem, the case of two-site binding where each receptor unit on the surface can accommodate two analyte molecules on two different sites is considered. One analyte molecule always binds first to a specific site. Subsequently, the second analyte molecule can bind to the adjacent unoccupied site. In the second problem, two different analytes compete for one binding site on the same surface receptor. Finally, the third problem considers the case of positive cooperativity among bound molecules in the hydrogel using a simple mean-field approach. The transport in both the flow channel and the hydrogel phases of the biosensor is taken into account in this case (with few exceptions, most previous studies assume a simpler model in which the hydrogel is treated as a planar surface with the receptors). We consider simultaneously diffusion and convection through the flow channel together with diffusion and cooperativity binding on the surface and in the hydrogel. In each case, typical results for the concentration contours of the free and bound molecules in the flow channel and hydrogel regions are presented together with the time-dependent association/dissociation curves and reaction rates. For binding site competition, the analysis predicts overshoot phenomena.

Dynamics of A + B --> C reaction fronts in the presence of buoyancy-driven convection.

PubMed

Rongy, L; Trevelyan, P M J; De Wit, A

2008-08-22

The dynamics of A+B-->C fronts in horizontal solution layers can be influenced by buoyancy-driven convection as soon as the densities of A, B, and C are not all identical. Such convective motions can lead to front propagation even in the case of equal diffusion coefficients and initial concentration of reactants for which reaction-diffusion (RD) scalings predict a nonmoving front. We show theoretically that the dynamics in the presence of convection can in that case be predicted solely on the basis of the knowledge of the one-dimensional RD density profile across the front.

Theoretical limit of spatial resolution in diffuse optical tomography using a perturbation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Konovalov, A B; Vlasov, V V

2014-03-28

We have assessed the limit of spatial resolution of timedomain diffuse optical tomography (DOT) based on a perturbation reconstruction model. From the viewpoint of the structure reconstruction accuracy, three different approaches to solving the inverse DOT problem are compared. The first approach involves reconstruction of diffuse tomograms from straight lines, the second – from average curvilinear trajectories of photons and the third – from total banana-shaped distributions of photon trajectories. In order to obtain estimates of resolution, we have derived analytical expressions for the point spread function and modulation transfer function, as well as have performed a numerical experiment onmore » reconstruction of rectangular scattering objects with circular absorbing inhomogeneities. It is shown that in passing from reconstruction from straight lines to reconstruction using distributions of photon trajectories we can improve resolution by almost an order of magnitude and exceed the accuracy of reconstruction of multi-step algorithms used in DOT. (optical tomography)« less

Perturbative studies of toroidal momentum transport in KSTAR H-mode and the effect of ion temperature perturbation

NASA Astrophysics Data System (ADS)

Yang, S. M.; Na, Yong-Su; Na, D. H.; Park, J.-K.; Shi, Y. J.; Ko, W. H.; Lee, S. G.; Hahm, T. S.

2018-06-01

Perturbative experiments have been carried out using tangential neutral beam injection (NBI) and non-resonant magnetic perturbation (NRMP) to analyze the momentum transport properties in KSTAR H-modes. Diffusive and non-diffusive terms of momentum transport are evaluated from the transient analysis. Although the operating conditions and methodologies applied in the two cases are similar, the momentum transport properties obtained show clear differences. The estimated momentum diffusivity and pinch obtained in the NBI modulation experiments is larger than that in the NRMP modulation experiments. We found that this discrepancy could be a result of uncertainties in the assumption for the analysis. By introducing time varying momentum transport coefficients depending on the temperature gradient, the linearized equation shows that if the temperature perturbation exists, the evolution of toroidal rotation perturbation could be faster than the transport rate of mean quantity, since the evolution of toroidal rotation perturbation is related to , a momentum diffusivity from perturbative analysis. This could explain the estimated higher momentum diffusivity using time independent transport coefficients in NBI experiments with higher ion temperature perturbation compared to that in NRMP modulation experiments. The differences in the momentum transport coefficient with NRMP and NBI are much reduced by considering time varying momentum transport coefficients in the time dependent transport simulation.

Salt-Finger Convection in a Stratified Fluid Layer Induced by Thermal and Solutal Capillary Motion

NASA Technical Reports Server (NTRS)

Chen, Chuan F.; Chan, Cho Lik

1996-01-01

Salt-finger convection in a double-diffusive system is a motion driven by the release of gravitational potential due to different diffusion rates. Normally, when the gravitational field is reduced, salt-finger convection together with other convective motions driven by buoyancy forces will be rapidly suppressed. However, because the destabilizing effect of the concentration gradient is amplified by the Lewis number, with values varying from 10(exp 2) for aqueous salt solutions to 10 (exp 4) for liquid metals, salt-finger convection may be generated at much reduced gravity levels. In the microgravity environment, the surface tension gradient assumes a dominant role in causing fluid motion. In this paper, we report on some experimental results showing the generation of salt-finger convection due to capillary motio on the surface of a stratified fluid layer. A numerical simulation is presented to show the cause of salt-finger convection.

Test of the 'glymphatic' hypothesis demonstrates diffusive and aquaporin-4-independent solute transport in rodent brain parenchyma.

PubMed

Smith, Alex J; Yao, Xiaoming; Dix, James A; Jin, Byung-Ju; Verkman, Alan S

2017-08-21

Transport of solutes through brain involves diffusion and convection. The importance of convective flow in the subarachnoid and paravascular spaces has long been recognized; a recently proposed 'glymphatic' clearance mechanism additionally suggests that aquaporin-4 (AQP4) water channels facilitate convective transport through brain parenchyma. Here, the major experimental underpinnings of the glymphatic mechanism were re-examined by measurements of solute movement in mouse brain following intracisternal or intraparenchymal solute injection. We found that: (i) transport of fluorescent dextrans in brain parenchyma depended on dextran size in a manner consistent with diffusive rather than convective transport; (ii) transport of dextrans in the parenchymal extracellular space, measured by 2-photon fluorescence recovery after photobleaching, was not affected just after cardiorespiratory arrest; and (iii) Aqp4 gene deletion did not impair transport of fluorescent solutes from sub-arachnoid space to brain in mice or rats. Our results do not support the proposed glymphatic mechanism of convective solute transport in brain parenchyma.

Test of the 'glymphatic' hypothesis demonstrates diffusive and aquaporin-4-independent solute transport in rodent brain parenchyma

PubMed Central

Yao, Xiaoming; Dix, James A; Jin, Byung-Ju

2017-01-01

Transport of solutes through brain involves diffusion and convection. The importance of convective flow in the subarachnoid and paravascular spaces has long been recognized; a recently proposed ‘glymphatic’ clearance mechanism additionally suggests that aquaporin-4 (AQP4) water channels facilitate convective transport through brain parenchyma. Here, the major experimental underpinnings of the glymphatic mechanism were re-examined by measurements of solute movement in mouse brain following intracisternal or intraparenchymal solute injection. We found that: (i) transport of fluorescent dextrans in brain parenchyma depended on dextran size in a manner consistent with diffusive rather than convective transport; (ii) transport of dextrans in the parenchymal extracellular space, measured by 2-photon fluorescence recovery after photobleaching, was not affected just after cardiorespiratory arrest; and (iii) Aqp4 gene deletion did not impair transport of fluorescent solutes from sub-arachnoid space to brain in mice or rats. Our results do not support the proposed glymphatic mechanism of convective solute transport in brain parenchyma. PMID:28826498

Experimental validation of convection-diffusion discretisation scheme employed for computational modelling of biological mass transport

PubMed Central

2010-01-01

Background The finite volume solver Fluent (Lebanon, NH, USA) is a computational fluid dynamics software employed to analyse biological mass-transport in the vasculature. A principal consideration for computational modelling of blood-side mass-transport is convection-diffusion discretisation scheme selection. Due to numerous discretisation schemes available when developing a mass-transport numerical model, the results obtained should either be validated against benchmark theoretical solutions or experimentally obtained results. Methods An idealised aneurysm model was selected for the experimental and computational mass-transport analysis of species concentration due to its well-defined recirculation region within the aneurysmal sac, allowing species concentration to vary slowly with time. The experimental results were obtained from fluid samples extracted from a glass aneurysm model, using the direct spectrophometric concentration measurement technique. The computational analysis was conducted using the four convection-diffusion discretisation schemes available to the Fluent user, including the First-Order Upwind, the Power Law, the Second-Order Upwind and the Quadratic Upstream Interpolation for Convective Kinetics (QUICK) schemes. The fluid has a diffusivity of 3.125 × 10-10 m2/s in water, resulting in a Peclet number of 2,560,000, indicating strongly convection-dominated flow. Results The discretisation scheme applied to the solution of the convection-diffusion equation, for blood-side mass-transport within the vasculature, has a significant influence on the resultant species concentration field. The First-Order Upwind and the Power Law schemes produce similar results. The Second-Order Upwind and QUICK schemes also correlate well but differ considerably from the concentration contour plots of the First-Order Upwind and Power Law schemes. The computational results were then compared to the experimental findings. An average error of 140% and 116% was demonstrated between the experimental results and those obtained from the First-Order Upwind and Power Law schemes, respectively. However, both the Second-Order upwind and QUICK schemes accurately predict species concentration under high Peclet number, convection-dominated flow conditions. Conclusion Convection-diffusion discretisation scheme selection has a strong influence on resultant species concentration fields, as determined by CFD. Furthermore, either the Second-Order or QUICK discretisation schemes should be implemented when numerically modelling convection-dominated mass-transport conditions. Finally, care should be taken not to utilize computationally inexpensive discretisation schemes at the cost of accuracy in resultant species concentration. PMID:20642816

Effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Astrophysics Data System (ADS)

Saunders, B. V.; Murray, B. T.; McFadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1991-10-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress free boundaries is studied using Floquet theory for the linear stability analysis. Situations are considered for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double diffusive convection. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency.

Effects of convergent diffusion and charge transfer kinetics on the diffusion layer thickness of spherical micro- and nanoelectrodes.

PubMed

Molina, A; Laborda, E; González, J; Compton, R G

2013-05-21

Nuances of the linear diffusion layer approximation are examined for slow charge transfer reactions at (hemi)spherical micro- and nanoelectrodes. This approximation is widely employed in Electrochemistry to evaluate the extent of electrolyte solution perturbed by the electrode process, which is essential to the understanding of the effects arising from thin-layer diffusion, convergent diffusion, convection, coupled chemical reactions and the double layer. The concept was well established for fast charge transfer processes at macroelectrodes, but remains unclear under other conditions such that a thorough assessment of its meaning was necessary. In a previous publication [A. Molina, J. González, E. Laborda and R. G. Compton, Phys. Chem. Chem. Phys., 2013, 15, 2381-2388] we shed some light on the influence of the reversibility degree. In the present work, the meaning of the diffusion layer thickness is investigated when very small electrodes are employed and so the contribution of convergent diffusion to the mass transport is very important. An analytical expression is given to calculate the linear diffusion layer thickness at (hemi)spherical electrodes and its behaviour is studied for a wide range of conditions of reversibility (from reversible to fully-irreversible processes) and electrode size (from macro- to nano-electrodes). Rigorous analytical solutions are deduced for true concentration profiles, surface concentrations, linear diffusion layer thickness and current densities when a potential pulse is applied at (hemi)spherical electrodes. The expressions for the magnitudes mentioned above are valid for electrodes of any size (including (hemi)spherical nanoelectrodes) and for any degree of reversibility, provided that mass transport occurs exclusively via diffusion. The variation of the above with the electrode size, applied potential and charge transfer kinetics is studied.

THE AXISYMMETRIC FREE-CONVECTION HEAT TRANSFER ALONG A VERTICAL THIN CYLINDER WITH CONSTANT SURFACE TEMPERATURE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Viskanta, R.

1963-01-01

Laminar free-convection flow produced by a heated, vertical, circular cylinder for which the temperature at the outer surface of the cylinder is assumed to be uniform is analyzed. The solution of the boundary-layer equations was obtained by the perturbation method of Sparrow and Gregg, which is valid only for small values of the axial distance parameter xi ; and the integral method of Hama et al., for large values of the parameter xi . Heat-transfer results were calculated for Prandtl numbers (Pr) of 100, the Nusselt numbers (Nu) for the cylinder were higher than those for the flat plate, andmore » this difference increased as Pr decreased. It was also found that the perturbation method of solution of the free-convection boundary-layer equations becomes useless for small values of Pr because of the slow convergence of the series. The results obtained by the integral method were in good agreement with those calculated by the perturbation method for Pr approximately 1 and 0.1 < xi < 1 only; they deviated considerably for smaller values of xi . (auth)« less

The Effect of Weak Resistivity and Weak Thermal Diffusion on Short-wavelength Magnetic Buoyancy Instability

NASA Astrophysics Data System (ADS)

Gradzki, Marek J.; Mizerski, Krzysztof A.

2018-03-01

Magnetic buoyancy instability in weakly resistive and thermally conductive plasma is an important mechanism of magnetic field expulsion in astrophysical systems. It is often invoked, e.g., in the context of the solar interior. Here, we revisit a problem introduc`ed by Gilman: the short-wavelength linear stability of a plane layer of compressible isothermal and weakly diffusive fluid permeated by a horizontal magnetic field of strength decreasing with height. In this physical setting, we investigate the effect of weak resistivity and weak thermal conductivity on the short-wavelength perturbations, localized in the vertical direction, and show that the presence of diffusion allows to establish the wavelength of the most unstable mode, undetermined in an ideal fluid. When diffusive effects are neglected, the perturbations are amplified at a rate that monotonically increases as the wavelength tends to zero. We demonstrate that, when the resistivity and thermal conduction are introduced, the wavelength of the most unstable perturbation is established and its scaling law with the diffusion parameters depends on gradients of the mean magnetic field, temperature, and density. Three main dynamical regimes are identified, with the wavelength of the most unstable mode scaling as either λ /d∼ {{ \\mathcal U }}κ 3/5 or λ /d∼ {{ \\mathcal U }}κ 3/4 or λ /d∼ {{ \\mathcal U }}κ 1/3, where d is the layer thickness and {{ \\mathcal U }}κ is the ratio of the characteristic thermal diffusion velocity scale to the free-fall velocity. Our analytic results are backed up by a series of numerical solutions. The two-dimensional interchange modes are shown to dominate over three-dimensional ones when the magnetic field and/or temperature gradients are strong enough.

Possible effects of free convection on fire behavior - laminar and turbulent line and point sources of heat

Treesearch

S. Scesa; F. M. Sauer

1954-01-01

The transfer theory is applied to the problem of atmospheric diffusion of momentum and heat induced by line and point sources of heat on the surface of the earth. In order that the validity of the approximations of the boundary layer theory be realized, the thickness of the layer in which the temperatures and velocities differ appreciably from the values at...

Charging of a conducting sphere in a weakly ionized collisional plasma: Temporal dynamics and stationary state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grach, V. S., E-mail: vsgrach@app.sci-nnov.ru; Garasev, M. A.

2015-07-15

We consider the interaction of a isolated conducting sphere with a collisional weakly ionized plasma in an external field. We assume that the plasma consists of two species of ions neglecting of electrons. We take into account charging of the sphere due to sedimentation of plasma ions on it, the field of the sphere charge and the space charge, as well as recombination and molecular diffusion. The nonstationary problem of interaction of the sphere with the surrounding plasma is solved numerically. The temporal dynamics of the sphere charge and plasma perturbations is analyzed, as well as the properties of themore » stationary state. It is shown that the duration of transient period is determined by the recombination time and by the reverse conductivity of ions. The temporal dynamics of the sphere charge and plasma perturbations is determined by the intensity of recombination processes relative to the influence of the space charge field and diffusion. The stationary absolute value of the sphere charge increases linearly with the external electric field, decreases with the relative intensity of recombination processes and increases in the presence of substantial diffusion. The scales of the perturbed region in the plasma are determined by the radius of the sphere, the external field, the effect of diffusion, and the relative intensity of recombination processes. In the limiting case of the absence of molecular diffusion and a strong external field, the properties of the stationary state coincide with those obtained earlier as a result of approximate solution.« less

A Transition in the Cumulative Reaction Rate of Two Species Diffusion with Bimolecular Reaction

NASA Astrophysics Data System (ADS)

Rajaram, Harihar; Arshadi, Masoud

2015-04-01

Diffusion and bimolecular reaction between two initially separated reacting species is a prototypical small-scale description of reaction induced by transverse mixing. It is also relevant to diffusion controlled transport regimes as encountered in low-permeability matrix blocks in fractured media. In previous work, the reaction-diffusion problem has been analyzed as a Stefan problem involving a distinct moving boundary (reaction front), which predicts that front motion scales as √t, and the cumulative reaction rate scales as 1/√t-. We present a general non-dimensionalization of the problem and a perturbation analysis to show that there is an early time regime where the cumulative reaction rate scales as √t- rather than 1/√t. The duration of this early time regime (where the cumulative rate is kinetically rather than diffusion controlled) depends on the rate parameter, in a manner that is consistently predicted by our non-dimensionalization. We also present results on the scaling of the reaction front width. We present numerical simulations in homogeneous and heterogeneous porous media to demonstrate the limited influence of heterogeneity on the behavior of the reaction-diffusion system. We illustrate applications to the practical problem of in-situ chemical oxidation of TCE and PCE by permanganate, which is employed to remediate contaminated sites where the DNAPLs are largely dissolved in the rock matrix.

Pattern formations and optimal packing.

PubMed

Mityushev, Vladimir

2016-04-01

Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary value problems. We demonstrate an intimate connection between pattern formations and optimal random packing on the plane. The main study is based on the following two points. First, the diffusive flux in reaction-diffusion systems is approximated by piecewise linear functions in the framework of structural approximations. This leads to a discrete network approximation of the considered continuous problem. Second, the discrete energy minimization yields optimal random packing of the domains (disks) in the representative cell. Therefore, the general problem of pattern formations based on the reaction-diffusion equations is reduced to the geometric problem of random packing. It is demonstrated that all random packings can be divided onto classes associated with classes of isomorphic graphs obtained from the Delaunay triangulation. The unique optimal solution is constructed in each class of the random packings. If the number of disks per representative cell is finite, the number of classes of isomorphic graphs, hence, the number of optimal packings is also finite. Copyright © 2016 Elsevier Inc. All rights reserved.

Thermocapillary flow stability in floating zone under low gravity

NASA Astrophysics Data System (ADS)

Bouizi, O.; Dang Vu-Delcarte, C.; Kasperski, G.

The floating zone is a crucible-free process used to produce high-quality crystals. A molten zone is created by a lateral heating between a feed and a single crystal rod, and helds by capillary forces. The translation of the material through the heat flux induces the solidification of the crystal. Temperature gradients induce surface tension variations which are the source of thermocapillary convection. In order to reduce buoyancy effects, experiments have been performed in a low gravity environment te{Croll} and have demonstrated that thermocapillary convection alone can induce defects in the product due to flow instabilities. A major goal is to identify the mechanisms leading to the growth of those instabilities. The experimental difficulty comes from the fact that measurements in the core of the flow are usually limited to transparent fluids, that is having a Prandtl number value (Pr), ratio of the characteristic thermal to dynamical diffusion times, larger than 6 or so. However, it has been shown that, just as well in real experiments as in numerical experiences, performed on the simplified half-zone model, the transitions thresholds strongly depend on the Prandtl number value te{Carotenuto}, te{Levenstam}. It is thus interesting to study the nature and thresholds of the instabilities of the thermocapillary flow in a full liquid bridge as a function of the Prandtl number. In that case, a 2D study te{kasper1} has shown an important variation of the thresholds with Pr. The considered model consists of a vertical cylindrical liquid bridge, between two isothermal parallel concentric rigid disks, %of radius Rwhich are separated by a distance H and presenting a non-deformable free surface. This surface is submitted to a steady heating flux symmetrical about the horizontal mid-plane. The parameters of the model are the Prandtl number, the Marangoni number (Ma) which characterises the thermal convective regime and the aspect ratio A=H/2R fixed here to 1. Gravity is absent. The capillary convective flow is governed by the Navier-Stokes and energy equations associated to boundary conditions which include the source of the flow. The mathematical system is solved with a spectral collocation code using a projection-diffusion method te{Batoul_94a} in order to uncouple the pressure and velocity fields. The steady flows are calculated with a Newton method, the first unstable eigenmodes using an Arnoldi method te{chenier-Stability}. These tools, in addition to direct numerical simulation, are necessary to observe transitions related to the mid-plane symmetry breaking of the 2D flow te{chenier-mult}, due to the low values of the growth rates of the instabilities. The sensitivity of the solutions to the treatment of a vorticity singularity at the junction free surface/solid boundaries was studied in te{kasper4}. An first analysis of the most sensitive regions of the flow to local thermal perturbations with the adjoint technique has been initiated te{Bouizi}. In the present contribution, we study the perturbation of the 2-D axisymmetric steady state through azimuthal modes as a function of the Prandtl and Marangoni number values. We will show that the critical Marangoni values are lower for 3D than for 2D perturbations for all Prandtl numbers but the azimutal Fourier modes, the bifurcation types and the threshold Ma_c values highly depend on the Prandtl number.

Convective mixing of air in firn at four polar sites

NASA Astrophysics Data System (ADS)

Kawamura, Kenji; Severinghaus, Jeffrey P.; Ishidoya, Shigeyuki; Sugawara, Satoshi; Hashida, Gen; Motoyama, Hideaki; Fujii, Yoshiyuki; Aoki, Shuji; Nakazawa, Takakiyo

2006-04-01

Air withdrawn from the firn at four polar sites (Dome Fuji, H72 and YM85, Antarctica and North GRIP, Greenland) was measured for δ15N of N 2 and δ18O of O 2 to test for the presence of convective air mixing in the top part of the firn, known as the "convective zone". Understanding the convective zone and its possible relationship to surface conditions is important for constructing accurate ice-core greenhouse gas chronologies and their phasing with respect to climate change. The thickness of the convective zone was inferred from a regression line with barometric slope of the data in the deep firn. It is less than a few meters at H72 and NGRIP, whereas a substantial convective zone is found at Dome Fuji (8.6 ± 2.6 m) and YM85 (14.0 ± 1.8 m). By matching the outputs of a diffusion model to the data, effective eddy diffusivities required to mix the firn air are found. At the surface of Dome Fuji and YM85, these are found to be several times greater than the molecular diffusivity in free air. The crossover from dominance of convection to molecular diffusion takes place at 7 ± 2, 11 ± 2 and 0.5 ± 0.5 m at Dome Fuji, YM85 and NGRIP, respectively. These depths can be used as an alternative definition of the convective zone thickness. The firn permeability at Dome Fuji is expected to be high because of intense firn metamorphism due to the low accumulation rate and large seasonal air temperature variation at the site. The firn layers in the top several meters are exposed to strong temperature gradients for several decades, leading to large firn grains and depth hoar that enhance permeability. The thick convective zone at YM85 is unexpected because the temperature, accumulation rate and near-surface density are comparable to NGRIP. The strong katabatic wind at YM85 is probably responsible for creating the deep convection. The largest convective zone found in this study is still only half of the current inconsistency implied from the deep ice core gas isotopes and firn densification models.

Effects of Buoyancy on Laminar, Transitional, and Turbulent Gas Jet Diffusion Flames

NASA Technical Reports Server (NTRS)

Bahadori, M. Yousef; Stocker, Dennis P.; Vaughan, David F.; Zhou, Liming; Edelman, Raymond B.

1993-01-01

Gas jet diffusion flames have been a subject of research for many years. However, a better understanding of the physical and chemical phenomena occurring in these flames is still needed, and, while the effects of gravity on the burning process have been observed, the basic mechanisms responsible for these changes have yet to be determined. The fundamental mechanisms that control the combustion process are in general coupled and quite complicated. These include mixing, radiation, kinetics, soot formation and disposition, inertia, diffusion, and viscous effects. In order to understand the mechanisms controlling a fire, laboratory-scale laminar and turbulent gas-jet diffusion flames have been extensively studied, which have provided important information in relation to the physico-chemical processes occurring in flames. However, turbulent flames are not fully understood and their understanding requires more fundamental studies of laminar diffusion flames in which the interplay of transport phenomena and chemical kinetics is more tractable. But even this basic, relatively simple flame is not completely characterized in relation to soot formation, radiation, diffusion, and kinetics. Therefore, gaining an understanding of laminar flames is essential to the understanding of turbulent flames, and particularly fires, in which the same basic phenomena occur. In order to improve and verify the theoretical models essential to the interpretation of data, the complexity and degree of coupling of the controlling mechanisms must be reduced. If gravity is isolated, the complication of buoyancy-induced convection would be removed from the problem. In addition, buoyant convection in normal gravity masks the effects of other controlling parameters on the flame. Therefore, the combination of normal-gravity and microgravity data would provide the information, both theoretical and experimental, to improve our understanding of diffusion flames in general, and the effects of gravity on the burning process in particular.

Permeability Sensitivity Functions and Rapid Simulation of Hydraulic-Testing Measurements Using Perturbation Theory

NASA Astrophysics Data System (ADS)

Escobar Gómez, J. D.; Torres-Verdín, C.

2018-03-01

Single-well pressure-diffusion simulators enable improved quantitative understanding of hydraulic-testing measurements in the presence of arbitrary spatial variations of rock properties. Simulators of this type implement robust numerical algorithms which are often computationally expensive, thereby making the solution of the forward modeling problem onerous and inefficient. We introduce a time-domain perturbation theory for anisotropic permeable media to efficiently and accurately approximate the transient pressure response of spatially complex aquifers. Although theoretically valid for any spatially dependent rock/fluid property, our single-phase flow study emphasizes arbitrary spatial variations of permeability and anisotropy, which constitute key objectives of hydraulic-testing operations. Contrary to time-honored techniques, the perturbation method invokes pressure-flow deconvolution to compute the background medium's permeability sensitivity function (PSF) with a single numerical simulation run. Subsequently, the first-order term of the perturbed solution is obtained by solving an integral equation that weighs the spatial variations of permeability with the spatial-dependent and time-dependent PSF. Finally, discrete convolution transforms the constant-flow approximation to arbitrary multirate conditions. Multidimensional numerical simulation studies for a wide range of single-well field conditions indicate that perturbed solutions can be computed in less than a few CPU seconds with relative errors in pressure of <5%, corresponding to perturbations in background permeability of up to two orders of magnitude. Our work confirms that the proposed joint perturbation-convolution (JPC) method is an efficient alternative to analytical and numerical solutions for accurate modeling of pressure-diffusion phenomena induced by Neumann or Dirichlet boundary conditions.

Non-radial instabilities and progenitor asphericities in core-collapse supernovae

NASA Astrophysics Data System (ADS)

Müller, B.; Janka, H.-Th.

2015-04-01

Since core-collapse supernova simulations still struggle to produce robust neutrino-driven explosions in 3D, it has been proposed that asphericities caused by convection in the progenitor might facilitate shock revival by boosting the activity of non-radial hydrodynamic instabilities in the post-shock region. We investigate this scenario in depth using 42 relativistic 2D simulations with multigroup neutrino transport to examine the effects of velocity and density perturbations in the progenitor for different perturbation geometries that obey fundamental physical constraints (like the anelastic condition). As a framework for analysing our results, we introduce semi-empirical scaling laws relating neutrino heating, average turbulent velocities in the gain region, and the shock deformation in the saturation limit of non-radial instabilities. The squared turbulent Mach number, , reflects the violence of aspherical motions in the gain layer, and explosive runaway occurs for ≳ 0.3, corresponding to a reduction of the critical neutrino luminosity by ˜ 25 per cent compared to 1D. In the light of this theory, progenitor asphericities aid shock revival mainly by creating anisotropic mass flux on to the shock: differential infall efficiently converts velocity perturbations in the progenitor into density perturbations δρ/ρ at the shock of the order of the initial convective Mach number Maprog. The anisotropic mass flux and ram pressure deform the shock and thereby amplify post-shock turbulence. Large-scale (ℓ = 2, ℓ = 1) modes prove most conducive to shock revival, whereas small-scale perturbations require unrealistically high convective Mach numbers. Initial density perturbations in the progenitor are only of the order of Ma_prog^2 and therefore play a subdominant role.

Collective phase description of oscillatory convection

NASA Astrophysics Data System (ADS)

Kawamura, Yoji; Nakao, Hiroya

2013-12-01

We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase. The theory can be considered as a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, stable time-periodic solutions to partial differential equations, representing the oscillatory convection. We derive the phase sensitivity function, which quantifies the phase response of the oscillatory convection to weak perturbations applied at each spatial point, and analyze the phase synchronization between two weakly coupled Hele-Shaw cells exhibiting oscillatory convection on the basis of the derived phase equations.

Zonal flow evolution and overstability in accretion discs

NASA Astrophysics Data System (ADS)

Vanon, R.; Ogilvie, G. I.

2017-04-01

This work presents a linear analytical calculation on the stability and evolution of a compressible, viscous self-gravitating (SG) Keplerian disc with both horizontal thermal diffusion and a constant cooling time-scale when an axisymmetric structure is present and freely evolving. The calculation makes use of the shearing sheet model and is carried out for a range of cooling times. Although the solutions to the inviscid problem with no cooling or diffusion are well known, it is non-trivial to predict the effect caused by the introduction of cooling and of small diffusivities; this work focuses on perturbations of intermediate wavelengths, therefore representing an extension to the classical stability analysis on thermal and viscous instabilities. For density wave modes, the analysis can be simplified by means of a regular perturbation analysis; considering both shear and thermal diffusivities, the system is found to be overstable for intermediate and long wavelengths for values of the Toomre parameter Q ≲ 2; a non-SG instability is also detected for wavelengths ≳18H, where H is the disc scale-height, as long as γ ≲ 1.305. The regular perturbation analysis does not, however, hold for the entropy and potential vorticity slow modes as their ideal growth rates are degenerate. To understand their evolution, equations for the axisymmetric structure's amplitudes in these two quantities are analytically derived and their instability regions obtained. The instability appears boosted by increasing the value of the adiabatic index and of the Prandtl number, while it is quenched by efficient cooling.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Debojyoti; Constantinescu, Emil M.

The numerical simulation of meso-, convective-, and microscale atmospheric flows requires the solution of the Euler or the Navier-Stokes equations. Nonhydrostatic weather prediction algorithms often solve the equations in terms of derived quantities such as Exner pressure and potential temperature (and are thus not conservative) and/or as perturbations to the hydrostatically balanced equilibrium state. This paper presents a well-balanced, conservative finite difference formulation for the Euler equations with a gravitational source term, where the governing equations are solved as conservation laws for mass, momentum, and energy. Preservation of the hydrostatic balance to machine precision by the discretized equations is essentialmore » because atmospheric phenomena are often small perturbations to this balance. The proposed algorithm uses the weighted essentially nonoscillatory and compact-reconstruction weighted essentially nonoscillatory schemes for spatial discretization that yields high-order accurate solutions for smooth flows and is essentially nonoscillatory across strong gradients; however, the well-balanced formulation may be used with other conservative finite difference methods. The performance of the algorithm is demonstrated on test problems as well as benchmark atmospheric flow problems, and the results are verified with those in the literature.« less

G-Jitter Induced Magnetohydrodynamics Flow of Nanofluid with Constant Convective Thermal and Solutal Boundary Conditions

PubMed Central

Uddin, Mohammed J.; Khan, Waqar A.; Ismail, Ahmad Izani Md.

2015-01-01

Taking into account the effect of constant convective thermal and mass boundary conditions, we present numerical solution of the 2-D laminar g-jitter mixed convective boundary layer flow of water-based nanofluids. The governing transport equations are converted into non-similar equations using suitable transformations, before being solved numerically by an implicit finite difference method with quasi-linearization technique. The skin friction decreases with time, buoyancy ratio, and thermophoresis parameters while it increases with frequency, mixed convection and Brownian motion parameters. Heat transfer rate decreases with time, Brownian motion, thermophoresis and diffusion-convection parameters while it increases with the Reynolds number, frequency, mixed convection, buoyancy ratio and conduction-convection parameters. Mass transfer rate decreases with time, frequency, thermophoresis, conduction-convection parameters while it increases with mixed convection, buoyancy ratio, diffusion-convection and Brownian motion parameters. To the best of our knowledge, this is the first paper on this topic and hence the results are new. We believe that the results will be useful in designing and operating thermal fluids systems for space materials processing. Special cases of the results have been compared with published results and an excellent agreement is found. PMID:25933066

A solar dynamo surface wave at the interface between convection and nonuniform rotation

NASA Technical Reports Server (NTRS)

Parker, E. N.

1993-01-01

A simple dynamo surface wave is presented to illustrate the basic principles of a dynamo operating in the thin layer of shear and suppressed eddy diffusion beneath the cyclonic convection in the convection zone of the sun. It is shown that the restriction of the shear delta(Omega)/delta(r) to a region below the convective zone provides the basic mode with a greatly reduced turbulent diffusion coefficient in the region of strong azimuthal field. The dynamo takes on the character of a surface wave tied to the lower surface z = 0 of the convective zone. There is a substantial body of evidence suggesting a fibril state for the principal flux bundles beneath the surface of the sun, with fundamental implications for the solar dynamo.

Approximate methods for the fast computation of EPR and ST-EPR spectra. V. Application of the perturbation approach to the problem of anisotropic motion

NASA Astrophysics Data System (ADS)

Robinson, B. H.; Dalton, L. R.

1981-01-01

The modulation perturbation treatment of Galloway and Dalton is applied to the solution of the stochastic Liouville equation for the spin density matrix which incorporates an anisotropic rotational diffusion operator. Pseudosecular and saturation terms of the spin hamiltonian are explicitly considered as is the interaction of the electron spins with the applied Zeeman modulation field. The modulation perturbation treatment results in a factor of four improvement in computational speed relative to inversion of the full supermatrix with little or no loss of computational accuracy. The theoretical simulations of EPR and ST-EPR spectra are in nearly quantitative agreement with experimental spectra taken under high resolution conditions.

Evaluation of experimental parameters for growth of homogeneous solid solutions

NASA Astrophysics Data System (ADS)

Scheel, Hans J.; Swendsen, Robert H.

2001-12-01

In this paper, we discuss the experimental conditions required to grow large two-component crystals from homogeneous solid solutions. Building on the work of Burton, Prim, and Slichter and that of Van Erk, we are able to establish that the concentration fluctuations for diffusion-limited growth are rather insensitive to hydrodynamic fluctuations. This enables a crystal grower to take advantage of forced convection to optimize growth rates without aggravating the striation problem.

Order of accuracy of QUICK and related convection-diffusion schemes

NASA Technical Reports Server (NTRS)

Leonard, B. P.

1993-01-01

This report attempts to correct some misunderstandings that have appeared in the literature concerning the order of accuracy of the QUICK scheme for steady-state convective modeling. Other related convection-diffusion schemes are also considered. The original one-dimensional QUICK scheme written in terms of nodal-point values of the convected variable (with a 1/8-factor multiplying the 'curvature' term) is indeed a third-order representation of the finite volume formulation of the convection operator average across the control volume, written naturally in flux-difference form. An alternative single-point upwind difference scheme (SPUDS) using node values (with a 1/6-factor) is a third-order representation of the finite difference single-point formulation; this can be written in a pseudo-flux difference form. These are both third-order convection schemes; however, the QUICK finite volume convection operator is 33 percent more accurate than the single-point implementation of SPUDS. Another finite volume scheme, writing convective fluxes in terms of cell-average values, requires a 1/6-factor for third-order accuracy. For completeness, one can also write a single-point formulation of the convective derivative in terms of cell averages, and then express this in pseudo-flux difference form; for third-order accuracy, this requires a curvature factor of 5/24. Diffusion operators are also considered in both single-point and finite volume formulations. Finite volume formulations are found to be significantly more accurate. For example, classical second-order central differencing for the second derivative is exactly twice as accurate in a finite volume formulation as it is in single-point.

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Astrophysics Data System (ADS)

Saunders, B. V.; Murray, B. T.; McFadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1992-06-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Technical Reports Server (NTRS)

Saunders, B. V.; Murray, B. T.; Mcfadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1992-01-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

Linear analysis on the growth of non-spherical perturbations in supersonic accretion flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Takahashi, Kazuya; Yamada, Shoichi, E-mail: ktakahashi@heap.phys.waseda.ac.jp

We analyzed the growth of non-spherical perturbations in supersonic accretion flows. We have in mind an application to the post-bounce phase of core-collapse supernovae (CCSNe). Such non-spherical perturbations have been suggested by a series of papers by Arnett, who has numerically investigated violent convections in the outer layers of pre-collapse stars. Moreover, Couch and Ott demonstrated in their numerical simulations that such perturbations may lead to a successful supernova even for a progenitor that fails to explode without fluctuations. This study investigated the linear growth of perturbations during the infall onto a stalled shock wave. The linearized equations are solvedmore » as an initial and boundary value problem with the use of a Laplace transform. The background is a Bondi accretion flow whose parameters are chosen to mimic the 15 M {sub ☉} progenitor model by Woosley and Heger, which is supposed to be a typical progenitor of CCSNe. We found that the perturbations that are given at a large radius grow as they flow down to the shock radius; the density perturbations can be amplified by a factor of 30, for example. We analytically show that the growth rate is proportional to l, the index of the spherical harmonics. We also found that the perturbations oscillate in time with frequencies that are similar to those of the standing accretion shock instability. This may have an implication for shock revival in CCSNe, which will be investigated in our forthcoming paper in more detail.« less

Can nudging be used to quantify model sensitivities in precipitation and cloud forcing?

NASA Astrophysics Data System (ADS)

Lin, Guangxing; Wan, Hui; Zhang, Kai; Qian, Yun; Ghan, Steven J.

2016-09-01

Efficient simulation strategies are crucial for the development and evaluation of high-resolution climate models. This paper evaluates simulations with constrained meteorology for the quantification of parametric sensitivities in the Community Atmosphere Model version 5 (CAM5). Two parameters are perturbed as illustrating examples: the convection relaxation time scale (TAU), and the threshold relative humidity for the formation of low-level stratiform clouds (rhminl). Results suggest that the fidelity of the constrained simulations depends on the detailed implementation of nudging and the mechanism through which the perturbed parameter affects precipitation and cloud. The relative computational costs of nudged and free-running simulations are determined by the magnitude of internal variability in the physical quantities of interest, as well as the magnitude of the parameter perturbation. In the case of a strong perturbation in convection, temperature, and/or wind nudging with a 6 h relaxation time scale leads to nonnegligible side effects due to the distorted interactions between resolved dynamics and parameterized convection, while 1 year free-running simulations can satisfactorily capture the annual mean precipitation and cloud forcing sensitivities. In the case of a relatively weak perturbation in the large-scale condensation scheme, results from 1 year free-running simulations are strongly affected by natural noise, while nudging winds effectively reduces the noise, and reasonably reproduces the sensitivities. These results indicate that caution is needed when using nudged simulations to assess precipitation and cloud forcing sensitivities to parameter changes in general circulation models. We also demonstrate that ensembles of short simulations are useful for understanding the evolution of model sensitivities.

An Eddy-Diffusivity Mass-flux (EDMF) closure for the unified representation of cloud and convective processes

NASA Astrophysics Data System (ADS)

Tan, Z.; Schneider, T.; Teixeira, J.; Lam, R.; Pressel, K. G.

2014-12-01

Sub-grid scale (SGS) closures in current climate models are usually decomposed into several largely independent parameterization schemes for different cloud and convective processes, such as boundary layer turbulence, shallow convection, and deep convection. These separate parameterizations usually do not converge as the resolution is increased or as physical limits are taken. This makes it difficult to represent the interactions and smooth transition among different cloud and convective regimes. Here we present an eddy-diffusivity mass-flux (EDMF) closure that represents all sub-grid scale turbulent, convective, and cloud processes in a unified parameterization scheme. The buoyant updrafts and precipitative downdrafts are parameterized with a prognostic multiple-plume mass-flux (MF) scheme. The prognostic term for the mass flux is kept so that the life cycles of convective plumes are better represented. The interaction between updrafts and downdrafts are parameterized with the buoyancy-sorting model. The turbulent mixing outside plumes is represented by eddy diffusion, in which eddy diffusivity (ED) is determined from a turbulent kinetic energy (TKE) calculated from a TKE balance that couples the environment with updrafts and downdrafts. Similarly, tracer variances are decomposed consistently between updrafts, downdrafts and the environment. The closure is internally coupled with a probabilistic cloud scheme and a simple precipitation scheme. We have also developed a relatively simple two-stream radiative scheme that includes the longwave (LW) and shortwave (SW) effects of clouds, and the LW effect of water vapor. We have tested this closure in a single-column model for various regimes spanning stratocumulus, shallow cumulus, and deep convection. The model is also run towards statistical equilibrium with climatologically relevant large-scale forcings. These model tests are validated against large-eddy simulation (LES) with the same forcings. The comparison of results verifies the capacity of this closure to realistically represent different cloud and convective processes. Implementation of the closure in an idealized GCM allows us to study cloud feedbacks to climate change and to study the interactions between clouds, convections, and the large-scale circulation.

Non-dispersive carrier transport in molecularly doped polymers and the convection-diffusion equation

NASA Astrophysics Data System (ADS)

Tyutnev, A. P.; Parris, P. E.; Saenko, V. S.

2015-08-01

We reinvestigate the applicability of the concept of trap-free carrier transport in molecularly doped polymers and the possibility of realistically describing time-of-flight (TOF) current transients in these materials using the classical convection-diffusion equation (CDE). The problem is treated as rigorously as possible using boundary conditions appropriate to conventional time of flight experiments. Two types of pulsed carrier generation are considered. In addition to the traditional case of surface excitation, we also consider the case where carrier generation is spatially uniform. In our analysis, the front electrode is treated as a reflecting boundary, while the counter electrode is assumed to act either as a neutral contact (not disturbing the current flow) or as an absorbing boundary at which the carrier concentration vanishes. As expected, at low fields transient currents exhibit unusual behavior, as diffusion currents overwhelm drift currents to such an extent that it becomes impossible to determine transit times (and hence, carrier mobilities). At high fields, computed transients are more like those typically observed, with well-defined plateaus and sharp transit times. Careful analysis, however, reveals that the non-dispersive picture, and predictions of the CDE contradict both experiment and existing disorder-based theories in important ways, and that the CDE should be applied rather cautiously, and even then only for engineering purposes.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Aiding flow Thermo-Solutal Convection in Porous Cavity: ANN approach

NASA Astrophysics Data System (ADS)

Jafer Kazi1, Mohammed; Ameer Ahamad, N.; Yunus Khan, T. M.

2017-08-01

The transfer of thermal energy along with the diffusion of mass is common phenomenon that occurs in nature. The thermos-solutal convection in porous medium arises due to combined effect of diffusion of heat as well as mass inside the domain. The density variation of fluid due to absorbed heat at one end of porous cavity leads to fluid movement which in turn initiates the heat transfer. The mass diffusion inside the porous regime occurs due to concentration difference between two ends of cavity. Generally this phenomenon is studied with the help of numerical methods but current work emphasis the successful usage of artificial neural network in predicting the thermos-solutal convection of aiding flow in porous medium.

Stochastic Convection Parameterizations: The Eddy-Diffusivity/Mass-Flux (EDMF) Approach (Invited)

NASA Astrophysics Data System (ADS)

Teixeira, J.

2013-12-01

In this presentation it is argued that moist convection parameterizations need to be stochastic in order to be realistic - even in deterministic atmospheric prediction systems. A new unified convection and boundary layer parameterization (EDMF) that optimally combines the Eddy-Diffusivity (ED) approach for smaller-scale boundary layer mixing with the Mass-Flux (MF) approach for larger-scale plumes is discussed. It is argued that for realistic simulations stochastic methods have to be employed in this new unified EDMF. Positive results from the implementation of the EDMF approach in atmospheric models are presented.

Collective phase description of oscillatory convection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kawamura, Yoji, E-mail: ykawamura@jamstec.go.jp; Nakao, Hiroya

We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase. The theory can be considered as a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, stable time-periodic solutions to partial differential equations, representing the oscillatory convection. We derive the phase sensitivity function, which quantifies the phase response of the oscillatory convection to weak perturbations applied at each spatial point, and analyze the phase synchronization between two weakly coupled Hele-Shawmore » cells exhibiting oscillatory convection on the basis of the derived phase equations.« less

New imaging algorithm in diffusion tomography

NASA Astrophysics Data System (ADS)

Klibanov, Michael V.; Lucas, Thomas R.; Frank, Robert M.

1997-08-01

A novel imaging algorithm for diffusion/optical tomography is presented for the case of the time dependent diffusion equation. Numerical tests are conducted for ranges of parameters realistic for applications to an early breast cancer diagnosis using ultrafast laser pulses. This is a perturbation-like method which works for both homogeneous a heterogeneous background media. Its main innovation lies in a new approach for a novel linearized problem (LP). Such an LP is derived and reduced to a boundary value problem for a coupled system of elliptic partial differential equations. As is well known, the solution of such a system amounts to the factorization of well conditioned, sparse matrices with few non-zero entries clustered along the diagonal, which can be done very rapidly. Thus, the main advantages of this technique are that it is fast and accurate. The authors call this approach the elliptic systems method (ESM). The ESM can be extended for other data collection schemes.

General solution of a fractional Parker diffusion-convection equation describing the superdiffusive transport of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Elhanbaly, A.; Schlickeiser, Reinhard

2018-06-01

Anomalous diffusion models of energetic particles in space plasmas are developed by introducing the fractional Parker diffusion-convection equation. Analytical solution of the space-time fractional equation is obtained by use of the Caputo and Riesz-Feller fractional derivatives with the Laplace-Fourier transforms. The solution is given in terms of the Fox H-function. Profiles of particle densities are illustrated for different values of the space fractional order and the so-called skewness parameter.

Multi-Dimensional, Non-Pyrolyzing Ablation Test Problems

NASA Technical Reports Server (NTRS)

Risch, Tim; Kostyk, Chris

2016-01-01

Non-pyrolyzingcarbonaceous materials represent a class of candidate material for hypersonic vehicle components providing both structural and thermal protection system capabilities. Two problems relevant to this technology are presented. The first considers the one-dimensional ablation of a carbon material subject to convective heating. The second considers two-dimensional conduction in a rectangular block subject to radiative heating. Surface thermochemistry for both problems includes finite-rate surface kinetics at low temperatures, diffusion limited ablation at intermediate temperatures, and vaporization at high temperatures. The first problem requires the solution of both the steady-state thermal profile with respect to the ablating surface and the transient thermal history for a one-dimensional ablating planar slab with temperature-dependent material properties. The slab front face is convectively heated and also reradiates to a room temperature environment. The back face is adiabatic. The steady-state temperature profile and steady-state mass loss rate should be predicted. Time-dependent front and back face temperature, surface recession and recession rate along with the final temperature profile should be predicted for the time-dependent solution. The second problem requires the solution for the transient temperature history for an ablating, two-dimensional rectangular solid with anisotropic, temperature-dependent thermal properties. The front face is radiatively heated, convectively cooled, and also reradiates to a room temperature environment. The back face and sidewalls are adiabatic. The solution should include the following 9 items: final surface recession profile, time-dependent temperature history of both the front face and back face at both the centerline and sidewall, as well as the time-dependent surface recession and recession rate on the front face at both the centerline and sidewall. The results of the problems from all submitters will be collected, summarized, and presented at a later conference.

Magneto-Hydrodynamic Damping of Convection During Vertical Bridgman-Stockbarger Growth of HgCdTe

NASA Technical Reports Server (NTRS)

Watring, D. A.; Lehoczky, S. L.

1996-01-01

In order to quantify the effects of convection on segregation, Hg(0.8)Cd(0.2)Te crystals were grown by the vertical Bridgman-Stockbarger method in the presence of an applied axial magnetic field of 50 kG. The influence of convection, by magneto-hydrodynamic damping, on mass transfer in the melt and segregation at the solid-liquid interface was investigated by measuring the axial and radial compositional variations in the grown samples. The reduction of convective mixing in the melt through the application of the magnetic field is found to decrease radial segregation to the diffusion-limited regime. It was also found that the suppression of the convective cell near the solid-liquid interface results in an increase in the slope of the diffusion-controlled solute boundary layer, which can lead to constitutional supercooling.

Optimal error analysis of the intraseasonal convection due to uncertainties of the sea surface temperature in a coupled model

NASA Astrophysics Data System (ADS)

Li, Xiaojing; Tang, Youmin; Yao, Zhixiong

2017-04-01

The predictability of the convection related to the Madden-Julian Oscillation (MJO) is studied using a coupled model CESM (Community Earth System Model) and the climatically relevant singular vector (CSV) approach. The CSV approach is an ensemble-based strategy to calculate the optimal initial error on climate scale. In this study, we focus on the optimal initial error of the sea surface temperature in Indian Ocean, where is the location of the MJO onset. Six MJO events are chosen from the 10 years model simulation output. The results show that the large values of the SVs are mainly located in the bay of Bengal and the south central IO (around (25°S, 90°E)), which is a meridional dipole-like pattern. The fast error growth of the CSVs have important impacts on the prediction of the convection related to the MJO. The initial perturbations with the SV pattern result in the deep convection damping more quickly in the east Pacific Ocean. Moreover, the sensitivity studies of the CSVs show that different initial fields do not affect the CSVs obviously, while the perturbation domain is a more responsive factor to the CSVs. The rapid growth of the CSVs is found to be related to the west bay of Bengal, where the wind stress starts to be perturbed due to the CSV initial error. These results contribute to the establishment of an ensemble prediction system, as well as the optimal observation network. In addition, the analysis of the error growth can provide us some enlightment about the relationship between SST and the intraseasonal convection related to the MJO.

Fingering convection induced by atomic diffusion in stars: 3D numerical computations and applications to stellar models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zemskova, Varvara; Garaud, Pascale; Deal, Morgan

2014-11-10

Iron-rich layers are known to form in the stellar subsurface through a combination of gravitational settling and radiative levitation. Their presence, nature, and detailed structure can affect the excitation process of various stellar pulsation modes and must therefore be modeled carefully in order to better interpret Kepler asteroseismic data. In this paper, we study the interplay between atomic diffusion and fingering convection in A-type stars, as well as its role in the establishment and evolution of iron accumulation layers. To do so, we use a combination of three-dimensional idealized numerical simulations of fingering convection (which neglect radiative transfer and complexmore » opacity effects) and one-dimensional realistic stellar models. Using the three-dimensional simulations, we first validate the mixing prescription for fingering convection recently proposed by Brown et al. (within the scope of the aforementioned approximation) and identify what system parameters (total mass of iron, iron diffusivity, thermal diffusivity, etc.) play a role in the overall evolution of the layer. We then implement the Brown et al. prescription in the Toulouse-Geneva Evolution Code to study the evolution of the iron abundance profile beneath the stellar surface. We find, as first discussed by Théado et al., that when the concurrent settling of helium is ignored, this accumulation rapidly causes an inversion in the mean molecular weight profile, which then drives fingering convection. The latter mixes iron with the surrounding material very efficiently, and the resulting iron layer is very weak. However, taking helium settling into account partially stabilizes the iron profile against fingering convection, and a large iron overabundance can accumulate. The opacity also increases significantly as a result, and in some cases it ultimately triggers dynamical convection. The direct effects of radiative acceleration on the dynamics of fingering convection (especially in the nonlinear regime) remain to be added in the future to improve the quantitative predictions of the model.« less

Addressing model uncertainty through stochastic parameter perturbations within the High Resolution Rapid Refresh (HRRR) ensemble

NASA Astrophysics Data System (ADS)

Wolff, J.; Jankov, I.; Beck, J.; Carson, L.; Frimel, J.; Harrold, M.; Jiang, H.

2016-12-01

It is well known that global and regional numerical weather prediction ensemble systems are under-dispersive, producing unreliable and overconfident ensemble forecasts. Typical approaches to alleviate this problem include the use of multiple dynamic cores, multiple physics suite configurations, or a combination of the two. While these approaches may produce desirable results, they have practical and theoretical deficiencies and are more difficult and costly to maintain. An active area of research that promotes a more unified and sustainable system for addressing the deficiencies in ensemble modeling is the use of stochastic physics to represent model-related uncertainty. Stochastic approaches include Stochastic Parameter Perturbations (SPP), Stochastic Kinetic Energy Backscatter (SKEB), Stochastic Perturbation of Physics Tendencies (SPPT), or some combination of all three. The focus of this study is to assess the model performance within a convection-permitting ensemble at 3-km grid spacing across the Contiguous United States (CONUS) when using stochastic approaches. For this purpose, the test utilized a single physics suite configuration based on the operational High-Resolution Rapid Refresh (HRRR) model, with ensemble members produced by employing stochastic methods. Parameter perturbations were employed in the Rapid Update Cycle (RUC) land surface model and Mellor-Yamada-Nakanishi-Niino (MYNN) planetary boundary layer scheme. Results will be presented in terms of bias, error, spread, skill, accuracy, reliability, and sharpness using the Model Evaluation Tools (MET) verification package. Due to the high level of complexity of running a frequently updating (hourly), high spatial resolution (3 km), large domain (CONUS) ensemble system, extensive high performance computing (HPC) resources were needed to meet this objective. Supercomputing resources were provided through the National Center for Atmospheric Research (NCAR) Strategic Capability (NSC) project support, allowing for a more extensive set of tests over multiple seasons, consequently leading to more robust results. Through the use of these stochastic innovations and powerful supercomputing at NCAR, further insights and advancements in ensemble forecasting at convection-permitting scales will be possible.

Effect of Differential Diffusion in Two-Component Media

NASA Astrophysics Data System (ADS)

Ingel', L. Kh.

2017-03-01

Examples are presented of an exact solution of a nonstationary problem on the development of convection in a binary mixture (seawater) near an infinite vertical surface in which the buoyancy disturbances are determined both by the temperature and by the disturbances of the impurity (salt) concentration. Consideration is given to the development of convection in a homogeneous medium near an infinite vertical surface at whose boundary specification is made of constant (after ″switching on″ at the initial moment) heat fluxes and impurities or variations of these substances, i.e., problems with boundary conditions of 1st and 2nd kind are considered. The obtained analytical solutions demonstrate the possibility of a nontrivial effect associated with the difference in the values of the coefficients of transfer of two substances: the inflows of positive buoyancy may lead, contrary to intuitive notions, to the origination of descending motion of the medium rather than the ascending one. Clarification is provided for the physical meaning of such effects, which can be substantial, for example, in melting of sea ice.

Simultaneous Multi-Scale Diffusion Estimation and Tractography Guided by Entropy Spectrum Pathways

PubMed Central

Galinsky, Vitaly L.; Frank, Lawrence R.

2015-01-01

We have developed a method for the simultaneous estimation of local diffusion and the global fiber tracts based upon the information entropy flow that computes the maximum entropy trajectories between locations and depends upon the global structure of the multi-dimensional and multi-modal diffusion field. Computation of the entropy spectrum pathways requires only solving a simple eigenvector problem for the probability distribution for which efficient numerical routines exist, and a straight forward integration of the probability conservation through ray tracing of the convective modes guided by a global structure of the entropy spectrum coupled with a small scale local diffusion. The intervoxel diffusion is sampled by multi b-shell multi q-angle DWI data expanded in spherical waves. This novel approach to fiber tracking incorporates global information about multiple fiber crossings in every individual voxel and ranks it in the most scientifically rigorous way. This method has potential significance for a wide range of applications, including studies of brain connectivity. PMID:25532167

A discontinuous Galerkin method with a bound preserving limiter for the advection of non-diffusive fields in solid Earth geodynamics

NASA Astrophysics Data System (ADS)

He, Ying; Puckett, Elbridge Gerry; Billen, Magali I.

2017-02-01

Mineral composition has a strong effect on the properties of rocks and is an essentially non-diffusive property in the context of large-scale mantle convection. Due to the non-diffusive nature and the origin of compositionally distinct regions in the Earth the boundaries between distinct regions can be nearly discontinuous. While there are different methods for tracking rock composition in numerical simulations of mantle convection, one must consider trade-offs between computational cost, accuracy or ease of implementation when choosing an appropriate method. Existing methods can be computationally expensive, cause over-/undershoots, smear sharp boundaries, or are not easily adapted to tracking multiple compositional fields. Here we present a Discontinuous Galerkin method with a bound preserving limiter (abbreviated as DG-BP) using a second order Runge-Kutta, strong stability-preserving time discretization method for the advection of non-diffusive fields. First, we show that the method is bound-preserving for a point-wise divergence free flow (e.g., a prescribed circular flow in a box). However, using standard adaptive mesh refinement (AMR) there is an over-shoot error (2%) because the cell average is not preserved during mesh coarsening. The effectiveness of the algorithm for convection-dominated flows is demonstrated using the falling box problem. We find that the DG-BP method maintains sharper compositional boundaries (3-5 elements) as compared to an artificial entropy-viscosity method (6-15 elements), although the over-/undershoot errors are similar. When used with AMR the DG-BP method results in fewer degrees of freedom due to smaller regions of mesh refinement in the neighborhood of the discontinuity. However, using Taylor-Hood elements and a uniform mesh there is an over-/undershoot error on the order of 0.0001%, but this error increases to 0.01-0.10% when using AMR. Therefore, for research problems in which a continuous field method is desired the DG-BP method can provide improved tracking of sharp compositional boundaries. For applications in which strict bound-preserving behavior is desired, use of an element that provides a divergence-free condition on the weak formulation (e.g., Raviart-Thomas) and an improved mesh coarsening scheme for the AMR are required.

Diffusion and convection in collagen gels: implications for transport in the tumor interstitium.

PubMed Central

Ramanujan, Saroja; Pluen, Alain; McKee, Trevor D; Brown, Edward B; Boucher, Yves; Jain, Rakesh K

2002-01-01

Diffusion coefficients of tracer molecules in collagen type I gels prepared from 0-4.5% w/v solutions were measured by fluorescence recovery after photobleaching. When adjusted to account for in vivo tortuosity, diffusion coefficients in gels matched previous measurements in four human tumor xenografts with equivalent collagen concentrations. In contrast, hyaluronan solutions hindered diffusion to a lesser extent when prepared at concentrations equivalent to those reported in these tumors. Collagen permeability, determined from flow through gels under hydrostatic pressure, was compared with predictions obtained from application of the Brinkman effective medium model to diffusion data. Permeability predictions matched experimental results at low concentrations, but underestimated measured values at high concentrations. Permeability measurements in gels did not match previous measurements in tumors. Visualization of gels by transmission electron microscopy and light microscopy revealed networks of long collagen fibers at lower concentrations along with shorter fibers at high concentrations. Negligible assembly was detected in collagen solutions pregelation. However, diffusion was similarly hindered in pre and postgelation samples. Comparison of diffusion and convection data in these gels and tumors suggests that collagen may obstruct diffusion more than convection in tumors. These findings have significant implications for drug delivery in tumors and for tissue engineering applications. PMID:12202388

3-D Spherical Convection Modeling Applied to Mercury: Dislocation Versus Diffusion Rheology

NASA Astrophysics Data System (ADS)

Robertson, S. D.; King, S. D.

2016-12-01

Mercury is the smallest among the terrestrial planets and, prior to NASA's MESSENGER mission was thought to be the least tectonically and volcanically active body. Gravity and moment of inertia from MESSENGER constrain Mercury to have a thin silicate mantle shell of approximately 400 km over a massive iron core. This mantle is thinner than previously thought and the smallest end-member in comparison with the other terrestrial planets. Although Mercury currently has a stagnant lid and the present day mantle is likely not convecting, a significant proportion of Mercury's surface features could have been derived from convection in the viscous mantle. Given Mercury's small size, the amount of volcanism and tectonic activity was a surprise. We investigate the effect of dislocation creep rheology in olivine on the dynamics of Mercury. At the pressures and temperatures of Mercury's mantle, laboratory creep studies indicate that olivine deforms by dislocation creep. Previous studies using diffusion creep rheology find that the thin mantle shell of Mercury quickly becomes diffusive and, this is difficult to reconcile with the surface observations. We use the three-dimensional spherical code, CitcomS, to compare numerical models with both dislocation and diffusion creep. We compare gravity, topography, and mantle temperature as a function of time from the models with constraints on the timing of volcanic and tectonic activity on Mercury. The results show that with the dislocation creep mechanism, there is potential for convective flow in the mantle over billions of years. In contrast, models with the diffusion creep mechanism start with a convecting mantle that transitions to global diffusive cooling within 500 Myrs. Diffusion creep rheology does not adequately produce a dynamic interior that is consistent with the historical volcanic and tectonic evolution of the planet. This research is the result of participation in GLADE, a nine-week summer REU program directed by Dave Stegman (SIO/UCSD).

Internal Wave Generation by Convection

NASA Astrophysics Data System (ADS)

Lecoanet, Daniel Michael

In nature, it is not unusual to find stably stratified fluid adjacent to convectively unstable fluid. This can occur in the Earth's atmosphere, where the troposphere is convective and the stratosphere is stably stratified; in lakes, where surface solar heating can drive convection above stably stratified fresh water; in the oceans, where geothermal heating can drive convection near the ocean floor, but the water above is stably stratified due to salinity gradients; possible in the Earth's liquid core, where gradients in thermal conductivity and composition diffusivities maybe lead to different layers of stable or unstable liquid metal; and, in stars, as most stars contain at least one convective and at least one radiative (stably stratified) zone. Internal waves propagate in stably stratified fluids. The characterization of the internal waves generated by convection is an open problem in geophysical and astrophysical fluid dynamics. Internal waves can play a dynamically important role via nonlocal transport. Momentum transport by convectively excited internal waves is thought to generate the quasi-biennial oscillation of zonal wind in the equatorial stratosphere, an important physical phenomenon used to calibrate global climate models. Angular momentum transport by convectively excited internal waves may play a crucial role in setting the initial rotation rates of neutron stars. In the last year of life of a massive star, convectively excited internal waves may transport even energy to the surface layers to unbind them, launching a wind. In each of these cases, internal waves are able to transport some quantity--momentum, angular momentum, energy--across large, stable buoyancy gradients. Thus, internal waves represent an important, if unusual, transport mechanism. This thesis advances our understanding of internal wave generation by convection. Chapter 2 provides an underlying theoretical framework to study this problem. It describes a detailed calculation of the internal gravity wave spectrum, using the Lighthill theory of wave excitation by turbulence. We use a Green's function approach, in which we convolve a convective source term with the Green's function of different internal gravity waves. The remainder of the thesis is a circuitous attempt to verify these analytical predictions. I test the predictions of Chapter 2 via numerical simulation. The first step is to identify a code suitable for this study. I helped develop the Dedalus code framework to study internal wave generation by convection. Dedalus can solve many different partial differential equations using the pseudo-spectral numerical method. In Chapter 3, I demonstrate Dedalus' ability to solve different equations used to model convection in astrophysics. I consider both the propagation and damping of internal waves, and the properties of low Rayleigh number convective steady states, in six different equation sets used in the astrophysics literature. This shows that Dedalus can be used to solve the equations of interest. Next, in Chapter 4, I verify the high accuracy of Dedalus by comparing it to the popular astrophysics code Athena in a standard Kelvin-Helmholtz instability test problem. Dedalus performs admirably in comparison to Athena, and provides a high standard for other codes solving the fully compressible Navier-Stokes equations. Chapter 5 demonstrates that Dedalus can simulate convective adjacent to a stably stratified region, by studying convective mixing near carbon flames. The convective overshoot and mixing is well-resolved, and is able to generate internal waves. Confident in Dedalus' ability to study the problem at hand, Chapter 6 describes simulations inspired by water experiments of internal wave generation by convection. The experiments exploit water's unusual property that its density maximum is at 4°C, rather than at 0°C. We use a similar equation of state in Dedalus, and study internal gravity waves generation by convection in a water-like fluid. We test two models of wave generation: bulk excitation (equivalent to the Lighthill theory described in Chapter 2), and surface excitation. We find the bulk excitation model accurately reproduces the waves generated in the simulations, validating the calculations of Chapter 2.

An Extended Eddy-Diffusivity Mass-Flux Scheme for Unified Representation of Subgrid-Scale Turbulence and Convection

NASA Astrophysics Data System (ADS)

Tan, Zhihong; Kaul, Colleen M.; Pressel, Kyle G.; Cohen, Yair; Schneider, Tapio; Teixeira, João.

2018-03-01

Large-scale weather forecasting and climate models are beginning to reach horizontal resolutions of kilometers, at which common assumptions made in existing parameterization schemes of subgrid-scale turbulence and convection—such as that they adjust instantaneously to changes in resolved-scale dynamics—cease to be justifiable. Additionally, the common practice of representing boundary-layer turbulence, shallow convection, and deep convection by discontinuously different parameterizations schemes, each with its own set of parameters, has contributed to the proliferation of adjustable parameters in large-scale models. Here we lay the theoretical foundations for an extended eddy-diffusivity mass-flux (EDMF) scheme that has explicit time-dependence and memory of subgrid-scale variables and is designed to represent all subgrid-scale turbulence and convection, from boundary layer dynamics to deep convection, in a unified manner. Coherent up and downdrafts in the scheme are represented as prognostic plumes that interact with their environment and potentially with each other through entrainment and detrainment. The more isotropic turbulence in their environment is represented through diffusive fluxes, with diffusivities obtained from a turbulence kinetic energy budget that consistently partitions turbulence kinetic energy between plumes and environment. The cross-sectional area of up and downdrafts satisfies a prognostic continuity equation, which allows the plumes to cover variable and arbitrarily large fractions of a large-scale grid box and to have life cycles governed by their own internal dynamics. Relatively simple preliminary proposals for closure parameters are presented and are shown to lead to a successful simulation of shallow convection, including a time-dependent life cycle.

An Extended Eddy‐Diffusivity Mass‐Flux Scheme for Unified Representation of Subgrid‐Scale Turbulence and Convection

PubMed Central

Tan, Zhihong; Kaul, Colleen M.; Pressel, Kyle G.; Cohen, Yair; Teixeira, João

2018-01-01

Abstract Large‐scale weather forecasting and climate models are beginning to reach horizontal resolutions of kilometers, at which common assumptions made in existing parameterization schemes of subgrid‐scale turbulence and convection—such as that they adjust instantaneously to changes in resolved‐scale dynamics—cease to be justifiable. Additionally, the common practice of representing boundary‐layer turbulence, shallow convection, and deep convection by discontinuously different parameterizations schemes, each with its own set of parameters, has contributed to the proliferation of adjustable parameters in large‐scale models. Here we lay the theoretical foundations for an extended eddy‐diffusivity mass‐flux (EDMF) scheme that has explicit time‐dependence and memory of subgrid‐scale variables and is designed to represent all subgrid‐scale turbulence and convection, from boundary layer dynamics to deep convection, in a unified manner. Coherent up and downdrafts in the scheme are represented as prognostic plumes that interact with their environment and potentially with each other through entrainment and detrainment. The more isotropic turbulence in their environment is represented through diffusive fluxes, with diffusivities obtained from a turbulence kinetic energy budget that consistently partitions turbulence kinetic energy between plumes and environment. The cross‐sectional area of up and downdrafts satisfies a prognostic continuity equation, which allows the plumes to cover variable and arbitrarily large fractions of a large‐scale grid box and to have life cycles governed by their own internal dynamics. Relatively simple preliminary proposals for closure parameters are presented and are shown to lead to a successful simulation of shallow convection, including a time‐dependent life cycle. PMID:29780442

An algorithm for variational data assimilation of contact concentration measurements for atmospheric chemistry models

NASA Astrophysics Data System (ADS)

Penenko, Alexey; Penenko, Vladimir

2014-05-01

Contact concentration measurement data assimilation problem is considered for convection-diffusion-reaction models originating from the atmospheric chemistry study. High dimensionality of models imposes strict requirements on the computational efficiency of the algorithms. Data assimilation is carried out within the variation approach on a single time step of the approximated model. A control function is introduced into the source term of the model to provide flexibility for data assimilation. This function is evaluated as the minimum of the target functional that connects its norm to a misfit between measured and model-simulated data. In the case mathematical model acts as a natural Tikhonov regularizer for the ill-posed measurement data inversion problem. This provides flow-dependent and physically-plausible structure of the resulting analysis and reduces a need to calculate model error covariance matrices that are sought within conventional approach to data assimilation. The advantage comes at the cost of the adjoint problem solution. This issue is solved within the frameworks of splitting-based realization of the basic convection-diffusion-reaction model. The model is split with respect to physical processes and spatial variables. A contact measurement data is assimilated on each one-dimensional convection-diffusion splitting stage. In this case a computationally-efficient direct scheme for both direct and adjoint problem solution can be constructed based on the matrix sweep method. Data assimilation (or regularization) parameter that regulates ratio between model and data in the resulting analysis is obtained with Morozov discrepancy principle. For the proper performance the algorithm takes measurement noise estimation. In the case of Gaussian errors the probability that the used Chi-squared-based estimate is the upper one acts as the assimilation parameter. A solution obtained can be used as the initial guess for data assimilation algorithms that assimilate outside the splitting stages and involve iterations. Splitting method stage that is responsible for chemical transformation processes is realized with the explicit discrete-analytical scheme with respect to time. The scheme is based on analytical extraction of the exponential terms from the solution. This provides unconditional positive sign for the evaluated concentrations. Splitting-based structure of the algorithm provides means for efficient parallel realization. The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004.

Convection of tin in a Bridgman system. I - Flow characterization by effective diffusivity measurements

NASA Technical Reports Server (NTRS)

Sears, B.; Narayanan, R.; Anderson, T. J.; Fripp, A. L.

1992-01-01

An electrochemical titration method was used to investigate the dynamic states in a cylindrical layer of convecting tin. The liquid tin was contained in a cell, with curved boundaries made of quartz and flat boundaries made of a solid state electrolyte - yttria-stabilized zirconia (YSZ). The electrolyte acted as a window through which a trace amount of oxygen could be pumped in or out by the application of a constant voltage. The concentration at the YSZ interface was monitored by operating the electrochemical cell in the galvanic mode. Experimentally determined effective diffusivities of oxygen were compared with the molecular diffusivity. Dynamic states in the convective flow were thus inferred. Temperature measurements were simultaneously made in order to identify the onset of oscillations from a steady convective regime. The experiments were conducted for two different aspect ratios for various imposed temperature gradients and two different orientations with respect to gravity. Transcritical states were identified and comparison to two-dimensional numerical models were made.

Drying kinetics of onion ( Allium cepa L.) slices with convective and microwave drying

NASA Astrophysics Data System (ADS)

Demiray, Engin; Seker, Anıl; Tulek, Yahya

2017-05-01

Onion slices were dried using two different drying techniques, convective and microwave drying. Convective drying treatments were carried out at different temperatures (50, 60 and 70 °C). Three different microwave output powers 328, 447 and 557 W were used in microwave drying. In convective drying, effective moisture diffusivity was estimated to be between 3.49 × 10-8 and 9.44 × 10-8 m2 s-1 within the temperature range studied. The effect of temperature on the diffusivity was described by the Arrhenius equation with an activation energy of 45.60 kJ mol-1. At increasing microwave power values, the effective moisture diffusivity values ranged from 2.59 × 10-7 and 5.08 × 10-8 m2 s-1. The activation energy for microwave drying of samples was calculated using an exponential expression based on Arrhenius equation. Among of the models proposed, Page's model gave a better fit for all drying conditions used.

A new formulation of the dispersion tensor in homogeneous porous media

NASA Astrophysics Data System (ADS)

Valdés-Parada, Francisco J.; Lasseux, Didier; Bellet, Fabien

2016-04-01

Dispersion is the result of two mass transport processes, namely molecular diffusion, which is a pure mixing effect and hydrodynamic dispersion, which combines mixing and spreading. The identification of each contribution is crucial and is often misinterpreted. Traditionally, under a volume averaging framework, a single closure problem is solved and the resulting fields are substituted into diffusive and dispersive filters. However the diffusive filter (that leads to the effective diffusivity) allows passing information from convection, which leads to an incorrect definition of the effective medium coefficients composing the total dispersion tensor. In this work, we revisit the definitions of the effective diffusivity and hydrodynamic dispersion tensors using the method of volume averaging. Our analysis shows that, in the context of laminar flow with or without inertial effects, two closure problems need to be computed in order to correctly define the corresponding effective medium coefficients. The first closure problem is associated to momentum transport and needs to be solved for a prescribed Reynolds number and flow orientation. The second closure problem is related to mass transport and it is solved first with a zero Péclet number and second with the required Péclet number and flow orientation. All the closure problems are written using closure variables only as required by the upscaling method. The total dispersion tensor is shown to depend on the microstructure, macroscopic flow angles, the cell (or pore) Péclet number and the cell (or pore) Reynolds number. It is non-symmetric in the general case. The condition for quasi-symmetry is highlighted. The functionality of the longitudinal and transverse components of this tensor with the flow angle is investigated for a 2D model porous structure obtaining consistent results with previous studies.

Modeling Thermal Transport and Surface Deformation on Europa using Realistic Rheologies

NASA Astrophysics Data System (ADS)

Linneman, D.; Lavier, L.; Becker, T. W.; Soderlund, K. M.

2017-12-01

Most existing studies of Europa's icy shell model the ice as a Maxwell visco-elastic solid or viscous fluid. However, these approaches do not allow for modeling of localized deformation of the brittle part of the ice shell, which is important for understanding the satellite's evolution and unique geology. Here, we model the shell as a visco-elasto-plastic material, with a brittle Mohr-Coulomb elasto-plastic layer on top of a convective Maxwell viscoelastic layer, to investigate how thermal transport processes relate to the observed deformation and topography on Europa's surface. We use Fast Lagrangian Analysis of Continua (FLAC) code, which employs an explicit time-stepping algorithm to simulate deformation processes in Europa's icy shell. Heat transfer drives surface deformation within the icy shell through convection and tidal dissipation due to its elliptical orbit around Jupiter. We first analyze the visco-elastic behavior of a convecting ice layer and the parameters that govern this behavior. The regime of deformation depends on the magnitude of the stress (diffusion creep at low stresses, grain-size-sensitive creep at intermediate stresses, dislocation creep at high stresses), so we calculate effective viscosity each time step using the constitutive stress-strain equation and a combined flow law that accounts for all types of deformation. Tidal dissipation rate is calculated as a function of the temperature-dependent Maxwell relaxation time and the square of the second invariant of the strain rate averaged over each orbital period. After we initiate convection in the viscoelastic layer by instituting an initial temperature perturbation, we then add an elastoplastic layer on top of the convecting layer and analyze how the brittle ice reacts to stresses from below and any resulting topography. We also take into account shear heating along fractures in the brittle layer. We vary factors such as total shell thickness and minimum viscosity, as these parameters are not well constrained, and determine how this affects the thickness and deformation of the brittle layer.

Darcy-Forchheimer Three-Dimensional Flow of Williamson Nanofluid over a Convectively Heated Nonlinear Stretching Surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2017-09-01

The present study elaborates three-dimensional flow of Williamson nanoliquid over a nonlinear stretchable surface. Fluid flow obeys Darcy-Forchheimer porous medium. A bidirectional nonlinear stretching surface generates the flow. Convective surface condition of heat transfer is taken into consideration. Further the zero nanoparticles mass flux condition is imposed at the boundary. Effects of thermophoresis and Brownian diffusion are considered. Assumption of boundary layer has been employed in the problem formulation. Convergent series solutions for the nonlinear governing system are established through the optimal homotopy analysis method (OHAM). Graphs have been sketched in order to analyze that how the velocity, temperature and concentration distributions are affected by distinct emerging flow parameters. Skin friction coefficients and local Nusselt number are also computed and discussed.

Dynamics of colloidal particles in electrohydrodynamic convection of nematic liquid crystal.

PubMed

Takahashi, Kentaro; Kimura, Yasuyuki

2014-07-01

We have studied the dynamics of micrometer-sized colloidal particles in electrohydrodynamic convection of nematic liquid crystal. Above the onset voltage of electroconvection, the parallel array of convection rolls appears to be perpendicular to the nematic field at first. The particles are forced to rotate by convection flow and are trapped within a single roll in this voltage regime. A slow glide motion along the roll axis is also observed. The frequency of rotational motion and the glide velocity increase with the applied voltage. Under a much larger voltage where the roll axis temporally fluctuates, the particles occasionally hop to the neighbor rolls. In this voltage regime, the motion of the particles becomes two-dimensional. The motion perpendicular to the roll axis exhibits diffusion behavior at a long time period. The effective diffusion constant is 10(3)-10(4) times larger than the molecular one. The observed behavior is compared with the result obtained by a simple stochastic model for the transport of the particles in convection. The enhancement of diffusion can be quantitatively described well by the rotation frequency in a roll, the width of the roll, and the hopping probability to the neighbor rolls.

Theory of transformation thermal convection for creeping flow in porous media: Cloaking, concentrating, and camouflage

NASA Astrophysics Data System (ADS)

Dai, Gaole; Shang, Jin; Huang, Jiping

2018-02-01

Heat can transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively. Unfortunately, thermal convection has seldom been touched in transformation theories due to the lack of a suitable theory, thus limiting applications associated with heat transfer through fluids (liquid or gas). Here, we develop a theory of transformation thermal convection by considering the convection-diffusion equation, the equation of continuity, and the Darcy law. By introducing porous media, we get a set of equations keeping their forms under coordinate transformation. As model applications, the theory helps to show the effects of cloaking, concentrating, and camouflage. Our finite-element simulations confirm the theoretical findings. This work offers a transformation theory for thermal convection, thus revealing novel behaviors associated with potential applications; it not only provides different hints on how to control heat transfer by combining thermal conduction, thermal convection, and thermal radiation, but also benefits mass diffusion and other related fields that contain a set of equations and need to transform velocities at the same time.

Estimation of Mesoscale Atmospheric Latent Heating Profiles from TRMM Rain Statistics Utilizing a Simple One-Dimensional Model

NASA Technical Reports Server (NTRS)

Iacovazzi, Robert A., Jr.; Prabhakara, C.

2002-01-01

In this study, a model is developed to estimate mesoscale-resolution atmospheric latent heating (ALH) profiles. It utilizes rain statistics deduced from Tropical Rainfall Measuring Mission (TRMM) data, and cloud vertical velocity profiles and regional surface thermodynamic climatologies derived from other available data sources. From several rain events observed over tropical ocean and land, ALH profiles retrieved by this model in convective rain regions reveal strong warming throughout most of the troposphere, while in stratiform rain regions they usually show slight cooling below the freezing level and significant warming above. The mesoscale-average, or total, ALH profiles reveal a dominant stratiform character, because stratiform rain areas are usually much larger than convective rain areas. Sensitivity tests of the model show that total ALH at a given tropospheric level varies by less than +/- 10 % when convective and stratiform rain rates and mesoscale fractional rain areas are perturbed individually by +/- 15 %. This is also found when the non-uniform convective vertical velocity profiles are replaced by one that is uniform. Larger variability of the total ALH profiles arises when climatological ocean- and land-surface temperatures (water vapor mixing ratios) are independently perturbed by +/- 1.0 K (+/- 5%) and +/- 5.0 K (+/- 15%), respectively. At a given tropospheric level, such perturbations can cause a +/- 25% variation of total ALH over ocean, and a factor-of-two sensitivity over land. This sensitivity is reduced substantially if perturbations of surface thermodynamic variables do not change surface relative humidity, or are not extended throughout the entire model evaporation layer. The ALH profiles retrieved in this study agree qualitatively with tropical total diabatic heating profiles deduced in earlier studies. Also, from January and July 1999 ALH-profile climatologies generated separately with TRMM Microwave Imager and Precipitation Radar rain statistics, it is shown that ALH profiles can be retrieved utilizing diverse satellite-derived rain products that offer convective and stratiform discrimination. Therefore, the ALH retrieval model developed in this study can be used to make regional estimates of total diabatic heating profiles in the future Global Precipitation Measurement mission, and to assimilate these profiles into numerical weather forecast and climate models.

Estimation of Mesoscale Atmospheric Latent Heating Profiles from TRMM Rain Statistics Utilizing a Simple One-Dimensional Model

NASA Technical Reports Server (NTRS)

Iacovazzi, Robert A., Jr.; Prabhakara, C.; Lau, William K. M. (Technical Monitor)

2001-01-01

In this study, a model is developed to estimate mesoscale-resolution atmospheric latent heating (ALH) profiles. It utilizes rain statistics deduced from Tropical Rainfall Measuring Mission (TRMM) data, and cloud vertical velocity profiles and regional surface thermodynamic climatologies derived from other available data sources. From several rain events observed over tropical ocean and land, ALH profiles retrieved by this model in convective rain regions reveal strong warming throughout most of the troposphere, while in stratiform rain regions they usually show slight cooling below the freezing level and significant warming above. The mesoscale-average, or total, ALH profiles reveal a dominant stratiform character, because stratiform rain areas are usually much larger than convective rain areas. Sensitivity tests of the model show that total ALH at a given tropospheric level varies by less than +/- 10 % when convective and stratiform rain rates and mesoscale fractional rain areas are perturbed individually by 1 15 %. This is also found when the non-uniform convective vertical velocity profiles are replaced by one that is uniform. Larger variability of the total ALH profiles arises when climatological ocean- and land-surface temperatures (water vapor mixing ratios) are independently perturbed by +/- 1.0 K (+/- 5 %) and +/- 5.0 K (+/- 15 %), respectively. At a given tropospheric level, such perturbations can cause a +/- 25 % variation of total ALH over ocean, and a factor-of-two sensitivity over land. This sensitivity is reduced substantially if perturbations of surface thermodynamic variables do not change surface relative humidity, or are not extended throughout the entire model evaporation layer. The ALH profiles retrieved in this study agree qualitatively with tropical total diabatic heating profiles deduced in earlier studies. Also, from January and July 1999 ALH-profile climatologies generated separately with TRMM Microwave Imager and Precipitation Radar rain statistics, it is shown that ALH profiles can be retrieved utilizing diverse satellite-derived rain products that offer convective and stratiform discrimination. Therefore, the ALH retrieval model developed in this study can be used to make regional estimates of total diabatic heating profiles in the future Global Precipitation Measurement mission, and to assimilate these profiles into numerical weather forecast and climate models.

[Phylogeny of gas exchange systems].

PubMed

Jürgens, K D; Gros, G

2002-04-01

Several systems of gas transport have developed during evolution, all of which are able to sufficiently supply oxygen to the tissues and eliminate the CO2 produced by the metabolism, in spite of great distances between the environment and the individual cells of the tissues. Almost all these systems utilize a combination of convection and diffusion steps. Convection achieves an efficient transport of gas over large distances, but requires energy and cannot occur across tissue barriers. Diffusion, on the other hand, achieves gas transport across barriers, but requires optimization of diffusion paths and diffusion areas. When two convectional gas flows are linked via a diffusional barrier (gas/fluid in the case of the avian lung, fluid/fluid in the case of gills), the directions in which the respective convectional movements pass each other are important determinants of gas exchange efficiency (concurrent, countercurrent and cross-current systems). The tracheal respiration found in insects has the advantage of circumventing the convective gas transport step in the blood, thereby avoiding the high energy expenditure of circulatory systems. This is made possible by a system of tracheae, ending in tracheoles, that reaches from the body surface to every cell within the body. The last step of gas transfer in these animals occurs by diffusion from the tracheoles ("air capillaries") to the mitochondria of cells. The disadvantage is that the tracheal system occupies a substantial fraction of body volume and that, due to limited mechanical stability of tracheal walls, this system would not be able to operate under conditions of high hydrostatic pressures, i. e. in large animals. Respiration in an "open" system, i. e. direct exposure of the diffusional barrier to the environmental air, eliminates the problem of bringing the oxygen to the barrier by convection, as is necessary in the avian and mammalian lung, in the insects' tracheal system and in the gills. An open system is found in the respiration via the skin, which is of significance in some amphibians, but is limited by the thickness of the skin that constitutes a substantial diffusion path for O2 and CO2. The thick skin, on the other hand, provides mechanical protection as well as flexibility for the animals' body and helps avoid massive water loss via the body surface. The gills of fishes, in contrast, exhibit rather short diffusion distances, are located in a mechanically protected space, and the problem of water loss does not exist. The flows of blood and water occur in opposite direction (countercurrent flow) and this situation makes an arterial PO2 approaching the environmental PO2 possible. A major disadvantage is constituted by the environmental medium since water contains little O2 compared to air and, to compensate this, much energy is expended to maintain a high flow rate of water through the gills. In the mammalian lung ("pool system"), the presence of a dead space and the rhythmic ventilation that replaces only a small fraction of the gas volume of the lung per breath, are responsible for an arterial PO2 (2/3 of the atmospheric PO2) that cannot reach the expiratory PO2. However, an advantage of this feature is the constantly high alveolar and arterial PCO2, which provides a highly effective H(+) buffer system in the entire body. The apparent disadvantage of the mammalian lung is avoided by the avian lung, which uses an extended system of airways to establish continuous equilibration of a part of the capillary blood with fresh air (cross current system), during inspiration as well as during expiration. In this system, arterial PO2 can significantly exceed expiratory PO2. A disadvantage here is the enormous amount of space taken up by the avian lung, in animals of 1 kg body weight three times as much as taken up by the mammalian lung. All respiratory exchange systems considered here exhibit high degrees of optimization - yet follow highly diverse construction principles. There is no such thing as an ideal gas exchange system. The system that has evolved in each species depends to an impressive extent on environmental conditions, on body build and size, on the animal's patterns of movement and on its energy consumption.

Magnetic resonance imaging of convection in laser-polarized xenon

NASA Technical Reports Server (NTRS)

Mair, R. W.; Tseng, C. H.; Wong, G. P.; Cory, D. G.; Walsworth, R. L.

2000-01-01

We demonstrate nuclear magnetic resonance (NMR) imaging of the flow and diffusion of laser-polarized xenon (129Xe) gas undergoing convection above evaporating laser-polarized liquid xenon. The large xenon NMR signal provided by the laser-polarization technique allows more rapid imaging than one can achieve with thermally polarized gas-liquid systems, permitting shorter time-scale events such as rapid gas flow and gas-liquid dynamics to be observed. Two-dimensional velocity-encoded imaging shows convective gas flow above the evaporating liquid xenon, and also permits the measurement of enhanced gas diffusion near regions of large velocity variation.

Gradient zone boundary control in salt gradient solar ponds

DOEpatents

Hull, John R.

1984-01-01

A method and apparatus for suppressing zone boundary migration in a salt gradient solar pond includes extending perforated membranes across the pond at the boundaries, between the convective and non-convective zones, the perforations being small enough in size to prevent individual turbulence disturbances from penetrating the hole, but being large enough to allow easy molecular diffusion of salt thereby preventing the formation of convective zones in the gradient layer. The total area of the perforations is a sizable fraction of the membrane area to allow sufficient salt diffusion while preventing turbulent entrainment into the gradient zone.

Gradient zone-boundary control in salt-gradient solar ponds

DOEpatents

Hull, J.R.

1982-09-29

A method and apparatus for suppressing zone boundary migration in a salt gradient solar pond includes extending perforated membranes across the pond at the boundaries, between the convective and non-convective zones, the perforations being small enough in size to prevent individual turbulence disturbances from penetrating the hole, but being large enough to allow easy molecular diffusion of salt thereby preventing the formation of convective zones in the gradient layer. The total area of the perforations is a sizeable fraction of the membrane area to allow sufficient salt diffusion while preventing turbulent entrainment into the gradient zone.

Control strategy on the double-diffusive convection in a nanofluid layer with internal heat generation

NASA Astrophysics Data System (ADS)

Mokhtar, N. F. M.; Khalid, I. K.; Siri, Z.; Ibrahim, Z. B.; Gani, S. S. A.

2017-10-01

The influences of feedback control and internal heat source on the onset of Rayleigh-Bénard convection in a horizontal nanofluid layer is studied analytically due to Soret and Dufour parameters. The confining boundaries of the nanofluid layer (bottom boundary-top boundary) are assumed to be free-free, rigid-free, and rigid-rigid, with a source of heat from below. Linear stability theory is applied, and the eigenvalue solution is obtained numerically using the Galerkin technique. Focusing on the stationary convection, it is shown that there is a positive thermal resistance in the presence of feedback control on the onset of double-diffusive convection, while there is a positive thermal efficiency in the existence of internal heat generation. The possibilities of suppress or augment of the Rayleigh-Bénard convection in a nanofluid layer are also discussed in detail.

Frequency modulation indicator, Arnold’s web and diffusion in the Stark Quadratic-Zeeman problem

NASA Astrophysics Data System (ADS)

Cordani, Bruno

2008-11-01

We notice that the fundamental frequencies of a slightly perturbed integrable Hamiltonian system are not time-constant inside a resonance but frequency modulated, as is evident from pendulum models and wavelet analysis. Exploiting an intrinsic imprecision inherent to the numerical frequency analysis algorithm itself, hence transforming a drawback into an opportunity, we define the Frequency Modulation Indicator, a very sensitive tool in detecting where fundamental frequencies are modulated, localizing so the resonances without having to resort, as in other methods, to the integration of variational equations. For the Kepler problem, the space of the orbits with a fixed energy has the topology of the product of two 2-spheres. The perturbation Hamiltonian, averaged over the mean anomaly, has surely a maximum and a minimum, to which correspond two periodic orbits in physical space. Studying the neighbourhood of these two elliptic stable points, we are able to define adapted action-angle variables, for example, the usual but “SO(4)-rotated” Delaunay variables. The procedure, implemented in the program KEPLER, is performed transparently for the user, providing a general scheme suited for generic perturbation. The method is then applied to the Stark-Quadratic-Zeeman problem, displaying very clearly the Arnold web of the resonances. Sectioning transversely one of the resonance strips so highlighted and performing a numerical frequency analysis, one is able to locate with great precision the thin stochastic layer surrounding a separatrix. Another very long (10 8 revolutions) frequency analysis on an orbit starting here reveals, as expected, a well defined pattern, which ensures that the integration errors do not eject the point out of the layer, and moreover a very slow drift in the frequency values, clearly due to Arnold diffusion.

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes.

PubMed

Barrenechea, Gabriel R; Burman, Erik; Karakatsani, Fotini

2017-01-01

For the case of approximation of convection-diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.

The Last Minutes of Oxygen Shell Burning in a Massive Star

NASA Astrophysics Data System (ADS)

Müller, Bernhard; Viallet, Maxime; Heger, Alexander; Janka, Hans-Thomas

2016-12-01

We present the first 4π-three-dimensional (3D) simulation of the last minutes of oxygen shell burning in an 18 M ⊙ supernova progenitor up to the onset of core collapse. A moving inner boundary is used to accurately model the contraction of the silicon and iron core according to a one-dimensional stellar evolution model with a self-consistent treatment of core deleptonization and nuclear quasi-equilibrium. The simulation covers the full solid angle to allow the emergence of large-scale convective modes. Due to core contraction and the concomitant acceleration of nuclear burning, the convective Mach number increases to ˜0.1 at collapse, and an ℓ = 2 mode emerges shortly before the end of the simulation. Aside from a growth of the oxygen shell from 0.51 M ⊙ to 0.56 M ⊙ due to entrainment from the carbon shell, the convective flow is reasonably well described by mixing-length theory, and the dominant scales are compatible with estimates from linear stability analysis. We deduce that artificial changes in the physics, such as accelerated core contraction, can have precarious consequences for the state of convection at collapse. We argue that scaling laws for the convective velocities and eddy sizes furnish good estimates for the state of shell convection at collapse and develop a simple analytic theory for the impact of convective seed perturbations on shock revival in the ensuing supernova. We predict a reduction of the critical luminosity for explosion by 12%-24% due to seed asphericities for our 3D progenitor model relative to the case without large seed perturbations.

On the implementation of an accurate and efficient solver for convection-diffusion equations

NASA Astrophysics Data System (ADS)

Wu, Chin-Tien

In this dissertation, we examine several different aspects of computing the numerical solution of the convection-diffusion equation. The solution of this equation often exhibits sharp gradients due to Dirichlet outflow boundaries or discontinuities in boundary conditions. Because of the singular-perturbed nature of the equation, numerical solutions often have severe oscillations when grid sizes are not small enough to resolve sharp gradients. To overcome such difficulties, the streamline diffusion discretization method can be used to obtain an accurate approximate solution in regions where the solution is smooth. To increase accuracy of the solution in the regions containing layers, adaptive mesh refinement and mesh movement based on a posteriori error estimations can be employed. An error-adapted mesh refinement strategy based on a posteriori error estimations is also proposed to resolve layers. For solving the sparse linear systems that arise from discretization, goemetric multigrid (MG) and algebraic multigrid (AMG) are compared. In addition, both methods are also used as preconditioners for Krylov subspace methods. We derive some convergence results for MG with line Gauss-Seidel smoothers and bilinear interpolation. Finally, while considering adaptive mesh refinement as an integral part of the solution process, it is natural to set a stopping tolerance for the iterative linear solvers on each mesh stage so that the difference between the approximate solution obtained from iterative methods and the finite element solution is bounded by an a posteriori error bound. Here, we present two stopping criteria. The first is based on a residual-type a posteriori error estimator developed by Verfurth. The second is based on an a posteriori error estimator, using local solutions, developed by Kay and Silvester. Our numerical results show the refined mesh obtained from the iterative solution which satisfies the second criteria is similar to the refined mesh obtained from the finite element solution.

A numerical study of the steady scalar convective diffusion equation for small viscosity

NASA Technical Reports Server (NTRS)

Giles, M. B.; Rose, M. E.

1983-01-01

A time-independent convection diffusion equation is studied by means of a compact finite difference scheme and numerical solutions are compared to the analytic inviscid solutions. The correct internal and external boundary layer behavior is observed, due to an inherent feature of the scheme which automatically produces upwind differencing in inviscid regions and the correct viscous behavior in viscous regions.

Thermosolutal convection in high-aspect-ratio enclosures

NASA Technical Reports Server (NTRS)

Wang, L. W.; Chen, C. T.

1988-01-01

Convection in high-aspect-ratio rectangular enclosures with combined horizontal temperature and concentration gradients is studied experimentally. An electrochemical system is employed to impose the concentration gradients. The solutal buoyancy force either opposes or augments the thermal buoyancy force. Due to a large difference between the thermal and solutal diffusion rates the flow possesses double-diffusive characteristics. Various complex flow patterns are observed with different experimental conditions.

Hydrodynamically induced fluid transfer and non-convective double-diffusion in microgravity sliding solvent diffusion cells

NASA Technical Reports Server (NTRS)

Pollmann, Konrad W.; Stodieck, Louis S.; Luttges, Marvin W.

1994-01-01

Microgravity can provide a diffusion-dominated environment for double-diffusion and diffusion-reaction experiments otherwise disrupted by buoyant convection or sedimentation. In sliding solvent diffusion cells, a diffusion interface between two liquid columns is achieved by aligning two offset sliding wells. Fluid in contact with the sliding lid of the cavities is subjected to an applied shear stress. The momentum change by the start/stop action of the well creates an additional hydrodynamical force. In microgravity, these viscous and inertial forces are sufficiently large to deform the diffusion interface and induce hydrodynamic transfer between the wells. A series of KC-135 parabolic flight experiments were conducted to characterize these effects and establish baseline data for microgravity diffusion experiments. Flow visualizations show the diffusion interface to be deformed in a sinusoidal fashion following well alignment. After the wells were separated again in a second sliding movement, the total induced liquid transfer was determined and normalized by the well aspect ratio. The normalized transfer decreased linearly with Reynolds number from 3.3 to 4.0% (w/v) for Re = 0.4 (Stokes flow) to a minimum of 1.0% for Re = 23 to 30. Reynolds numbers that provide minimum induced transfers are characterized by an interface that is highly deformed and unsuitable for diffusion measurements. Flat diffusion interfaces acceptable for diffusion measurements are obtained with Reynolds numbers on the order of 7 to 10. Microgravity experiments aboard a sounding rocket flight verified counterdiffusion of different solutes to be diffusion dominated. Ground control experiments showed enhanced mixing by double-diffusive convection. Careful selection of experimental parameters improves initial conditions and minimizes induced transfer rates.

Determination of drying kinetics and convective heat transfer coefficients of ginger slices

NASA Astrophysics Data System (ADS)

Akpinar, Ebru Kavak; Toraman, Seda

2016-10-01

In the present work, the effects of some parametric values on convective heat transfer coefficients and the thin layer drying process of ginger slices were investigated. Drying was done in the laboratory by using cyclone type convective dryer. The drying air temperature was varied as 40, 50, 60 and 70 °C and the air velocity is 0.8, 1.5 and 3 m/s. All drying experiments had only falling rate period. The drying data were fitted to the twelve mathematical models and performance of these models was investigated by comparing the determination of coefficient ( R 2), reduced Chi-square ( χ 2) and root mean square error between the observed and predicted moisture ratios. The effective moisture diffusivity and activation energy were calculated using an infinite series solution of Fick's diffusion equation. The average effective moisture diffusivity values and activation energy values varied from 2.807 × 10-10 to 6.977 × 10-10 m2/s and 19.313-22.722 kJ/mol over the drying air temperature and velocity range, respectively. Experimental data was used to evaluate the values of constants in Nusselt number expression by using linear regression analysis and consequently, convective heat transfer coefficients were determined in forced convection mode. Convective heat transfer coefficient of ginger slices showed changes in ranges 0.33-2.11 W/m2 °C.

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Double-diffusive translation of Earth's inner core

NASA Astrophysics Data System (ADS)

Deguen, R.; Alboussiére, T.; Labrosse, S.

2018-03-01

The hemispherical asymmetry of the inner core has been interpreted as resulting form a high-viscosity mode of inner core convection, consisting in a translation of the inner core. A thermally driven translation, as originally proposed, is unlikely if the currently favoured high values of the thermal conductivity of iron at core conditions are correct. We consider here the possibility that inner core translation results from an unstable compositional gradient, which would develop either because the light elements present in the core become increasingly incompatible as the inner core grows, or because of a possibly positive feedback of the development of the F-layer on inner core convection. Though the magnitude of the destabilising effect of the compositional field is predicted to be similar to or smaller than the stabilising effect of the thermal field, the huge difference between thermal and chemical diffusivities implies that double-diffusive instabilities can still arise even if the net buoyancy increases upward. Using linear stability analysis and numerical simulations, we demonstrate that a translation mode can indeed exist if the compositional field is destabilising, even if the temperature profile is subadiabatic, and irrespectively of the relative magnitudes of the composition and potential temperature gradients. The existence of this double diffusive mode of translation requires that the following conditions are met: (i) the compositional profile within the inner core is destabilising, and remains so for a duration longer than the destabilisation timescale (on the order of 200 My, but strongly dependent on the magnitude of the initial perturbation); and (ii) the inner core viscosity is sufficiently large, the required value being a strongly increasing function of the inner core size (e.g. 1017 Pa.s when the inner core was 200 km in radius, and ≃ 3 × 1021 Pa.s at the current inner core size). If these conditions are met, the predicted inner core translation rate is found to be similar to the inner core growth rate, which is more consistent with inferences from the geomagnetic field morphology and secular variation than the higher translation rate predicted for a thermally driven translation.

Constraints on the Longevity of the 2010 Eyjaföll Eruption Cloud From Analog Experiments and Modeling

NASA Astrophysics Data System (ADS)

Carazzo, G.; Jellinek, M.

2010-12-01

The prolonged disruption of global air travel as a result of the 2010 Eyjafjöll eruption in Iceland underscores the value of discerning the dynamics of volcanic ash-clouds in the atmosphere. Understanding the longevity of these clouds is a particularly long standing problem that bears not only on volcanic hazards to humans but also on the nature and time scale of volcanic forcings on climate change. Since early work on the subject, the common practice to tackle the problem of cloud longevity has been to account for the dynamics of sedimentation by individual particle settling. We use 1D modeling and analog experiments of a turbulent particle-laden umbrella cloud to show that this classical view can be misleading and that the residence times of these ash-clouds in the atmosphere depends strongly on the collective behavior of the solid fraction. Diffusive convection driven by the differential diffusion of constituents altering the cloud density (ash, temperature, sulfur dioxide) may enhance particle scavenging and extend the cloud longevity over time scales orders of magnitude longer than currently expected (i.e., years rather than days for powerful eruptions). Records of this behavior can be found in real-time measurements of stratospheric post-volcanic aerosols following the 1974 Fuego, the 1982 El Chichon, the 1991 Hudson and Pinatubo events, and more recently, from the 14 April 2010 Eyjafjöll eruption. The importance of diffusive convection in volcanic ash-clouds depends strongly on particle size distribution and concentration. For the 2010 Eyjafjöll eruption, we predict that particles larger than 10 microns should settle individually as commonly assumed, but particles smaller than 1 micron should diffuse slowly in layers extending the cloud longevity to several weeks rather than days. These predictions are found to be in good agreement with a number of satellite and ground-based lidar data on ash size and mass estimates performed at different locations across Europe.

Analysis of X-Ray Microradiographs of Al-Au Interface Quench Profile using Modeling of Solidification Including Double-Diffusion and Convection in the Melt

NASA Technical Reports Server (NTRS)

Bune, Andris V.; Kaukler, William

1999-01-01

Experimental data on Al-0.8Au horizontal solidification of a 1 mm thick specimen in a BN crucible shows the effect of growth rate on the solidification interface shape. For translation rates below 0.5 micron/s the interface maintains a plain and flat shape. When the translation rate is 3 to 5 micron/s or more, the interface appearance changes to two planar zones, with the zone closer to the bottom having higher inclination. The interface shapes were measured by first quenching in place during growth. X-ray microscopy shows the interface shape within the quenched sample by viewing through the side of the specimen. In order to provide theoretical explanation of the phenomena, numerical modeling was undertaken using finite element code FIDAP. Double diffusion convection in Al-0.8Au melt and crystal-melt interface curvature during directional solidification was analyzed numerically. Actual thermophysical properties of Al-0.8Au including the binary Al-Au phase diagram were used. Although convection in the sample is weak, for the slower translation rate convection and diffusion is sufficient for the redistribution of initial compositional stratification caused by gravity. When translation rate is raised, neither convection nor diffusion can provide proper mixing so that solidification temperatures differ significantly near the bottom within the bulk of the sample. As a result, the solid-liquid interface appears to have two planar zones with different inclination.

A Minimum-Residual Finite Element Method for the Convection-Diffusion Equation

DTIC Science & Technology

2013-05-01

4p . We note that these two choices of discretization for V are not mutually exclusive, and that novel choices for Vh are likely the key to yielding...the inside with the positive- definite operator A, which is precisely the discrete system that arises under the optimal test function framework of DPG...converts the fine-scale problem into a symmetric-positive definite one, allowing for a well-behaved subgrid model of fine scale behavior. We begin again

Regularization of moving boundaries in a laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results.

PubMed

Meulenbroek, Bernard; Ebert, Ute; Schäfer, Lothar

2005-11-04

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions. For some parameter value, this equation can be solved analytically, which shows rigorously that the uniformly propagating solution is linearly convectively stable and that the asymptotic relaxation is universal and exponential in time.

Managing evaporation for more robust microscale assays. Part 2. Characterization of convection and diffusion for cell biology.

PubMed

Berthier, Erwin; Warrick, Jay; Yu, Hongmeiy; Beebe, David J

2008-06-01

Cell based microassays allow the screening of a multitude of culture conditions in parallel, which can be used for various applications from drug screening to fundamental cell biology research. Tubeless microfluidic devices based on passive pumping are a step towards accessible high throughput microassays, however they are vulnerable to evaporation. In addition to volume loss, evaporation can lead to the generation of small flows. Here, we focus on issues of convection and diffusion for cell culture in microchannels and particularly the transport of soluble factors secreted by cells. We find that even for humidity levels as high as 95%, convection in a passive pumping channel can significantly alter distributions of these factors and that appropriate system design can prevent convection.

Convective instabilities in a ternary alloy mushy layer

NASA Astrophysics Data System (ADS)

Anderson, Daniel; Guba, Peter

2014-11-01

We investigate a mathematical model of convection, thermal and solutal diffusion in a primary mushy layer during the solidification of a ternary alloy. In particular, we explore the influence of phase-change effects, such as solute rejection, latent heat and background solidification, in a linear stability analysis of a non-convecting base state solution. We identify how different rates of diffusion (e.g. double diffusion) as well as how different rates of solute rejection (double solute rejection) play a role in this system. Novel modes of instability that can be present under statically stable conditions are identified. Parcel arguments are proposed to explain the physical mechanisms that give rise to the instabilities. This work was supported in part by the U.S. National Science Foundation, DMS-1107848 (D.M.A.) and by the Slovak Scientific Grant Agency, VEGA 1/0711/12 (P.G.).

Highly Unstable Double-Diffusive Finger Convection in a Hele-Shaw Cell: Baseline Experimental Data for Evaluation of Numerical Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

PRINGLE,SCOTT E.; COOPER,CLAY A.; GLASS JR.,ROBERT J.

An experimental investigation was conducted to study double-diffusive finger convection in a Hele-Shaw cell by layering a sucrose solution over a more-dense sodium chloride (NaCl) solution. The solutal Rayleigh numbers were on the order of 60,000, based upon the height of the cell (25 cm), and the buoyancy ratio was 1.2. A full-field light transmission technique was used to measure a dye tracer dissolved in the NaCl solution. They analyze the concentration fields to yield the temporal evolution of length scales associated with the vertical and horizontal finger structure as well as the mass flux. These measures show a rapidmore » progression through two early stages to a mature stage and finally a rundown period where mass flux decays rapidly. The data are useful for the development and evaluation of numerical simulators designed to model diffusion and convection of multiple components in porous media. The results are useful for correct formulation at both the process scale (the scale of the experiment) and effective scale (where the lab-scale processes are averaged-up to produce averaged parameters). A fundamental understanding of the fine-scale dynamics of double-diffusive finger convection is necessary in order to successfully parameterize large-scale systems.« less

Discrete effect on the halfway bounce-back boundary condition of multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations.

PubMed

Cui, Shuqi; Hong, Ning; Shi, Baochang; Chai, Zhenhua

2016-04-01

In this paper, we will focus on the multiple-relaxation-time (MRT) lattice Boltzmann model for two-dimensional convection-diffusion equations (CDEs), and analyze the discrete effect on the halfway bounce-back (HBB) boundary condition (or sometimes called bounce-back boundary condition) of the MRT model where three different discrete velocity models are considered. We first present a theoretical analysis on the discrete effect of the HBB boundary condition for the simple problems with a parabolic distribution in the x or y direction, and a numerical slip proportional to the second-order of lattice spacing is observed at the boundary, which means that the MRT model has a second-order convergence rate in space. The theoretical analysis also shows that the numerical slip can be eliminated in the MRT model through tuning the free relaxation parameter corresponding to the second-order moment, while it cannot be removed in the single-relaxation-time model or the Bhatnagar-Gross-Krook model unless the relaxation parameter related to the diffusion coefficient is set to be a special value. We then perform some simulations to confirm our theoretical results, and find that the numerical results are consistent with our theoretical analysis. Finally, we would also like to point out the present analysis can be extended to other boundary conditions of lattice Boltzmann models for CDEs.

Convection in a colloidal suspension in a closed horizontal cell

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smorodin, B. L., E-mail: bsmorodin@yandex.ru; Cherepanov, I. N.

2015-02-15

The experimentally detected [1] oscillatory regimes of convection in a colloidal suspension of nanoparticles with a large anomalous thermal diffusivity in a closed horizontal cell heated from below have been simulated numerically. The concentration inhomogeneity near the vertical cavity boundaries arising from the interaction of thermal-diffusion separation and convective mixing has been proven to serve as a source of oscillatory regimes (traveling waves). The dependence of the Rayleigh number at the boundary of existence of the traveling-wave regime on the aspect ratio of the closed cavity has been established. The spatial characteristics of the emerging traveling waves have been determined.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stephen W. Feldberg; Lewis, Ernie R.

In this study, the principle of unchanging total concentration as described by Oldham and Feldberg [J. Phys. Chem. B, 103, 1699 (1999)] is invoked to analyze systems comprising a redox pair (X z1 1 and X z2 2) plus one or more non-electroactive species (X z3 3,X z4 4...X zjmax jmax) where X zj j is the j th species with charge z j and concentration; c j. The principle states that if the diffusion coefficients for all species are identical and mass transport is governed by the Nernst-Planck expression, the total concentration does not change during any electrochemical perturbation,more » i.e.: Σ jmax j=1[X zj j]=Σ jmax j=1 c j = S P With this principle we deduce the electrochemically induced difference between the surface and bulk concentrations for each species. Those concentration differences are translated into density differences which are a function of the density of the solvent and of the concentration differences, molecular masses and the standard partial molar volumes of all species. Those density differences in turn can induce convection that will ultimately modify the observed current. However, we did not attempt to quantify details of the natural convection and current modification produced by those density differences.« less

A two-dimensional ocean model for long-term climatic simulations: Stability and coupling to atmospheric and sea ice models

NASA Astrophysics Data System (ADS)

Harvey, L. D. Danny

1992-06-01

A two-dimensional (latitude-depth) deep ocean model is presented which is coupled to a sea ice model and an Energy Balance Climate Model (EBCM), the latter having land-sea and surface-air resolution. The processes which occur in the ocean model are thermohaline overturning driven by the horizontal density gradient, shallow wind-driven overturning cells, convective overturning, and vertical and horizontal diffusion of heat and salt. The density field is determined from the temperature and salinity fields using a nonlinear equation of state. Mixed layer salinity is affected by evaporation, precipitation, runoff from continents, and sea ice freezing and melting, as well as by advective, convective, and diffusive exchanges with the deep ocean. The ocean model is first tested in an uncoupled mode, in which hemispherically symmetric mixed layer temperature and salinity, or salinity flux, are specified as upper boundary conditions. An experiment performed with previous models is repeated in which a mixed layer salinity perturbation is introduced in the polar half of one hemisphere after switching from a fixed salinity to a fixed salinity flux boundary condition. For small values of the vertical diffusion coefficient KV, the model undergoes self-sustained oscillations with a period of about 1500 years. With larger values of KV, the model locks into either an asymmetric mode with a single overturning cell spanning both hemispheres, or a symmetric quiescent state with downwelling near the equator, upwelling at high latitudes, and a warm deep ocean (depending on the value of KV). When the ocean model is forced with observed mixed layer temperature and salinity, no oscillations occur. The model successfully simulates the very weak meridional overturning and strong Antarctic Circumpolar Current at the latitudes of the Drake Passage. The coupled EBCM-deep ocean model displays internal oscillations with a period of 3000 years if the ocean fraction is uniform with latitude and KV and the horizontal diffusion coefficient in the mixed layer are not too large. Globally averaged atmospheric temperature changes of 2 K are driven by oscillations in the heat flux into or out of the deep ocean, with the sudden onset of a heat flux out of the deep ocean associated with the rapid onset of thermohaline overturning after a quiescent period, and the sudden onset of a heat flux into the deep ocean associated with the collapse of thermohaline overturning. When the coupled model is run with prescribed parameters (such as land-sea fraction and precipitation) varying with latitude based on observations, the model does not oscillate and produces a reasonable deep ocean temperature field but a completely unrealistic salinity field. Resetting the mixed layer salinity to observations on each time step (equivalent to the "flux correction" method used in atmosphere-ocean general circulation models) is sufficient to give a realistic salinity field throughout the ocean depth, but dramatically alters the flow field and associated heat transport. Although the model is highly idealized, the finding that the maximum perturbation in globally averaged heat flux from the deep ocean to the surface over a 100-year period is 1.4 W m-2 suggests that effect of continuing greenhouse gas increases, which could result in a heating perturbation of 10 W m-2 by the end of the next century, will swamp possible surface heating perturbations due to changes in oceanic circulation. On the other hand, the extreme sensitivity of the oceanic flow field to variations in precipitation and evaporation suggests that it will not be possible to produce accurate projections of regional climatic change in the near term, if at all.

Effects of Structure and Hydrodynamics on the Sooting Behavior of Spherical Microgravity Diffusion Flames

NASA Technical Reports Server (NTRS)

Sunderland, P. B.; Axelbaum, Richard L.; Urban, D. L.

2000-01-01

We have examined the sooting behavior of spherical microgravity diffusion flames burning ethylene at atmospheric pressure in the NASA Glenn 2.2-second drop tower. In a novel application of microgravity, spherical flames allowed convection across the flame to be either from fuel to oxidizer or from oxidizer to fuel. Thus, microgravity flames are uniquely capable of allowing independent variation of convection direction across the flame and stoichiometric mixture fraction, Z(sub st). This allowed us to determine the dominant mechanism responsible for the phenomenon of permanently-blue diffusion flames -- flames that remain blue as strain rate approaches zero. Stoichiometric mixture fraction was varied by changing inert concentrations such that adiabatic flame temperature did not change. At low and high Z(sub st) nitrogen was supplied with the oxidizer and the fuel, respectively. For the present flames, structure (Z(sub st)) was found to have a profound effect on soot production. Soot-free conditions were observed at high Z(sub st) (Z(sub st) = 0.78) and sooting conditions were observed at low Z(sub st) (Z(sub st) = 0.064) regardless of the direction of convection. Convection direction was found to have a lesser impact on soot inception, with formation being suppressed when convection at the flame sheet was directed towards the oxidizer.

Internal density waves of shock type induced by chemoconvection in miscible reacting liquids

NASA Astrophysics Data System (ADS)

Bratsun, D. A.

2017-10-01

A theoretical explanation of the phenomenon of spontaneous emergence of density waves experimentally observed recently in bilayered systems of miscible liquids placed in a narrow vertical gap of the Hele-Shaw cell in the gravitational field is provided. Upper and lower layers represent aqueous solutions of acids and bases, respectively, whose contact leads to the beginning of a neutralization reaction. The process is accompanied by a strong dependence of the reagent's diffusion coefficients on their concentrations, giving rise to the generation of local density pockets, in which convection develops. The cavities collapse under certain conditions, causing a density jump, which moves faster than typical perturbations in a medium and takes the form of a shock wave. A mathematical model of the phenomenon is proposed, which can be formally reduced to equations of motion of a compressible gas under certain assumptions. Numerical calculations are given and compared with the experimental data.

Electro-convective versus electroosmotic instability in concentration polarization.

PubMed

Rubinstein, Isaak; Zaltzman, Boris

2007-10-31

Electro-convection is reviewed as a mechanism of mixing in the diffusion layer of a strong electrolyte adjacent to a charge-selective solid, such as an ion exchange (electrodialysis) membrane or an electrode. Two types of electro-convection in strong electrolytes may be distinguished: bulk electro-convection, due to the action of the electric field upon the residual space charge of a quasi-electro-neutral bulk solution, and convection induced by electroosmotic slip, due to electric forces acting in the thin electric double layer of either quasi-equilibrium or non-equilibrium type near the solid/liquid interface. According to recent studies, the latter appears to be the likely source of mixing in the diffusion layer, leading to 'over-limiting' conductance in electrodialysis. Electro-convection near a planar uniform charge selective solid/liquid interface sets on as a result of hydrodynamic instability of one-dimensional steady state electric conduction through such an interface. We compare the results of linear stability analysis obtained for instabilities of this kind appearing in the full electro-convective and limiting non-equilibrium electroosmotic formulations. The short- and long-wave aspects of these instabilities are discussed along with the wave number selection principles.

Magnetically Driven Flows of Suspensions of Rods to Deliver Clot-Busting Drugs to Dead-End Arteries

NASA Astrophysics Data System (ADS)

Bonnecaze, Roger; Clements, Michael

2014-11-01

Suspensions of iron particles in the presence of a magnetic field create flows that could significantly increase the delivery of drugs to dissolve clots in stroke victims. An explanation of this flow rests on the foundation of the seminal works by Prof. Acrivos and his students on effective magnetic permittivity of suspensions of rods, hydrodynamic diffusion of particles, and the flow of suspensions. Intravenous administration of the clot dissolving tissue plasminogen activator (tPA) is the most used therapy for stroke. This therapy is often unsuccessful because the tPA delivery is diffusion-limited and too slow to be effective. Observations show that added iron particles in a rotating magnetic field form rotating rods along the wall of the occluded vessel, creating a convective flow that can carry tPA much faster than diffusion. We present a proposed mechanism for this magnetically driven flow in the form of coupled particle-scale and vessel-scale flow models. At the particle-scale, particles chain up to form rods that rotate, diffuse and translate in the presence of the flow and magnetic fields. Localized vorticity created by the rotating particles drives a macroscopic convective flow in the vessel. Suspension transport equations describe the flow at the vessel-scale. The flow affects the convection and diffusion of the suspension of particles, linking the two scales. The model equations are solved asymptotically and numerically to understand how to create convective flows in dead-end or blocked vessels.

The fluid mechanics of thrombus formation

NASA Technical Reports Server (NTRS)

1972-01-01

Experimental data are presented for the growth of thrombi (blood clots) in a stagnation point flow of fresh blood. Thrombus shape, size and structure are shown to depend on local flow conditions. The evolution of a thrombus is described in terms of a physical model that includes platelet diffusion, a platelet aggregation mechanism, and diffusion and convection of the chemical species responsible for aggregation. Diffusion-controlled and convection-controlled regimes are defined by flow parameters and thrombus location, and the characteristic growth pattern in each regime is explained. Quantitative comparisons with an approximate theoretical model are presented, and a more general model is formulated.

Climatology of summer midtropospheric perturbations in the U.S. northern plains. Part I: Influence on northwest flow severe weather outbreaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Shih-Yu; Chen, Tsing-Chang; Correia, James

Northwest flow severe weather outbreaks (NWF outbreaks) describe a type of summer convective storm that occurs in areas of mid-level NWF in the central United States. Convective storms associated with NWF outbreaks are often progressive (i.e. traveling a long distance) along systematic, northwestsoutheast oriented tracks throughout the northern plains. Previous studies have observed that progressive convective storms under NWF are often coupled with subsynoptic-scale midtropospheric perturbations (MPs) coming from the Rocky Mountains. This study traces such MPs for the decade of 1997-2006 using the North American Regional Reanalysis to examine their climatology and possible influence on NWF outbreaks. MPs initiatedmore » over the Rocky Mountains have a maximum frequency in July when the North American anticyclone fully develops and forms prevailing NWF over the northern plains. MPs developed under this anticyclone appear restricted in their vertical extension. Nevertheless, persistent upward motion is apparent in the leading edge (east) of MPs soon after their genesis subsequently inducing or intensifying convective storms. MPs propagate along systematic tracks similar to those of NWF outbreaks. The propagation of MPs also synchronizes with the progressive behavior of the associated convective storms. When encountering strong low-level jets (LLJs), upward motion and convergence of water vapor flux associated with MPs intensify substantially, resulting in strongly enhanced convection and precipitation. Convective wind and hail frequencies associated with MPs in strong LLJs reveal a pattern and magnitude very similar to that of NWF outbreaks. While about 60% of summer rainfall in the northern plains is linked to MPs, 75% of these instances occur in strong LLJs.« less

THE LAST MINUTES OF OXYGEN SHELL BURNING IN A MASSIVE STAR

DOE Office of Scientific and Technical Information (OSTI.GOV)

Müller, Bernhard; Viallet, Maxime; Janka, Hans-Thomas

We present the first  4 π– three-dimensional (3D) simulation of the last minutes of oxygen shell burning in an 18 M {sub ⊙} supernova progenitor up to the onset of core collapse. A moving inner boundary is used to accurately model the contraction of the silicon and iron core according to a one-dimensional stellar evolution model with a self-consistent treatment of core deleptonization and nuclear quasi-equilibrium. The simulation covers the full solid angle to allow the emergence of large-scale convective modes. Due to core contraction and the concomitant acceleration of nuclear burning, the convective Mach number increases to ∼0.1 at collapse,more » and an ℓ  = 2 mode emerges shortly before the end of the simulation. Aside from a growth of the oxygen shell from 0.51 M {sub ⊙} to 0.56 M {sub ⊙} due to entrainment from the carbon shell, the convective flow is reasonably well described by mixing-length theory, and the dominant scales are compatible with estimates from linear stability analysis. We deduce that artificial changes in the physics, such as accelerated core contraction, can have precarious consequences for the state of convection at collapse. We argue that scaling laws for the convective velocities and eddy sizes furnish good estimates for the state of shell convection at collapse and develop a simple analytic theory for the impact of convective seed perturbations on shock revival in the ensuing supernova. We predict a reduction of the critical luminosity for explosion by 12% – 24% due to seed asphericities for our 3D progenitor model relative to the case without large seed perturbations.« less

A microphysical pathway analysis to investigate aerosol effects on convective clouds

NASA Astrophysics Data System (ADS)

Heikenfeld, Max; White, Bethan; Labbouz, Laurent; Stier, Philip

2017-04-01

The impact of aerosols on ice- and mixed-phase processes in convective clouds remains highly uncertain, which has strong implications for estimates of the role of aerosol-cloud interactions in the climate system. The wide range of interacting microphysical processes are still poorly understood and generally not resolved in global climate models. To understand and visualise these processes and to conduct a detailed pathway analysis, we have added diagnostic output of all individual process rates for number and mass mixing ratios to two commonly-used cloud microphysics schemes (Thompson and Morrison) in WRF. This allows us to investigate the response of individual processes to changes in aerosol conditions and the propagation of perturbations throughout the development of convective clouds. Aerosol effects on cloud microphysics could strongly depend on the representation of these interactions in the model. We use different model complexities with regard to aerosol-cloud interactions ranging from simulations with different levels of fixed cloud droplet number concentration (CDNC) as a proxy for aerosol, to prognostic CDNC with fixed modal aerosol distributions. Furthermore, we have implemented the HAM aerosol model in WRF-chem to also perform simulations with a fully interactive aerosol scheme. We employ a hierarchy of simulation types to understand the evolution of cloud microphysical perturbations in atmospheric convection. Idealised supercell simulations are chosen to present and test the analysis methods for a strongly confined and well-studied case. We then extend the analysis to large case study simulations of tropical convection over the Amazon rainforest. For both cases we apply our analyses to individually tracked convective cells. Our results show the impact of model uncertainties on the understanding of aerosol-convection interactions and have implications for improving process representation in models.

Microfluidic diffusion diluter: bulging of PDMS microchannels under pressure-driven flow

NASA Astrophysics Data System (ADS)

Holden, Matthew A.; Kumar, Saurabh; Beskok, Ali; Cremer, Paul S.

2003-05-01

The bulging of microfluidic systems during pressure-driven flow is potentially a major consideration for polydimethylsiloxane (PDMS)-based devices. Microchannel cross-sectional areas can change drastically as a function of flow rate and downstream microchannel position. Such geometrical flexibility leads to difficulties in predicting convective/diffusive transport for these systems. We have previously introduced a non-dimensional parameter, kappa, for characterizing convection and diffusion behavior for pressure-driven flow in rigid all-glass systems. This paper describes a modification of that concept for application to non-rigid systems, which is accomplished by incorporating an experimental step to account for the bulging in PDMS/glass microsystems. Specifically, an experimental measurement of channel height by fluorescence microscopy is combined with the aforementioned theory to characterize convective/diffusive behavior at a single location in the device. This allowed the parameter kappa to be determined at that point and applied to predict fluid flow in the subsequent portion of the PDMS microsystem. This procedure was applied to a PDMS/glass microfluidic diffusion dilution (muDD) device designed for generating concentration gradients. Theoretically predicted and experimentally measured distributions of concentrations within the microsystem matched well.

Transepithelial ultrafiltration and fractal power diffusion of D-glucose in the perfused rat intestine.

PubMed

Kochak, Gregory M; Mangat, Surinder

2002-12-23

Despite an enormous body of research investigating the mass transfer of D-glucose through biological membranes, carrier-mediated and first-order models have remained the prevalent models describing glucose's quantitative behavior even though they have proven to be inadequate over extended concentration ranges. Recent evidence from GLUT2 knockout studies further questions our understanding of molecular models, especially those employing Michaelis-Menten (MM)-type kinetic models. In this report, evidence is provided that D-glucose is absorbed by rat intestinal epithelium by a combination of convective ultrafiltration and nonlinear diffusion. The diffusive component of mass transfer is described by a concentration-dependent permeability coefficient, modeled as a fractal power function. Glucose and sodium chloride-dependent-induced aqueous convection currents are the result of prevailing oncotic and osmotic pressure effects, and a direct effect of glucose and sodium chloride on intestinal epithelium resulting in enhanced glucose, sodium ion, and water mobility. The fractal power model of glucose diffusion was superior to the conventional MM description. A convection-diffusion model of mass transfer adequately characterized glucose mass transfer over a 105-fold glucose concentration range in the presence and absence of sodium ion.

Experimental investigation of the stability boundary for double-diffusive finger convection in a Hele-Shaw cell

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cooper, Clay A.; Glass, Robert J.; Tyler, Scott W.

OAK - B135 We apply high resolution, full field light transmission techniques to study the onset and development of convection in simulated porous media (Hele-Shaw cells) and fractures. The light transmission technique allows quantitative measurement of the solute concentration fields in time thus allowing direct measurements of the mass flux of components. Experiments are first designed to test theoretical stability relations as a function of the solute concentrations, solute diffusivities and the medium's permeability. Structural evolution and convective transport as a function of dimensionless control parameters is then determined across the full range of parameter space. We also consider themore » application of lattice gas automata techniques to numerically model the onset and development of convection. (Gary Drew notified on 3/25/03 of copyrighted Material)« less

Oceanic Uptake of Oxygen During Deep Convection Events Through Diffusive and Bubble-Mediated Gas Exchange

NASA Astrophysics Data System (ADS)

Sun, Daoxun; Ito, Takamitsu; Bracco, Annalisa

2017-10-01

The concentration of dissolved oxygen (O2) plays fundamental roles in diverse chemical and biological processes throughout the oceans. The balance between the physical supply and the biological consumption controls the O2 level of the interior ocean, and the O2 supply to the deep waters can only occur through deep convection in the polar oceans. We develop a theoretical framework describing the oceanic O2 uptake during open-ocean deep convection events and test it against a suite of numerical sensitivity experiments. Our framework allows for two predictions, confirmed by the numerical simulations. First, both the duration and the intensity of the wintertime cooling contribute to the total O2 uptake for a given buoyancy loss. Stronger cooling leads to deeper convection and the oxygenation can reach down to deeper depths. Longer duration of the cooling period increases the total amount of O2 uptake over the convective season. Second, the bubble-mediated influx of O2 tends to weaken the diffusive influx by shifting the air-sea disequilibrium of O2 toward supersaturation. The degree of compensation between the diffusive and bubble-mediated gas exchange depends on the dimensionless number measuring the relative strength of oceanic vertical mixing and the gas transfer velocity. Strong convective mixing, which may occur under strong cooling, reduces the degree of compensation so that the two components of gas exchange together drive exceptionally strong oceanic O2 uptake.

The solution of non-linear hyperbolic equation systems by the finite element method

NASA Technical Reports Server (NTRS)

Loehner, R.; Morgan, K.; Zienkiewicz, O. C.

1984-01-01

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

On the Effective Thermal Conductivity of Frost Considering Mass Diffusion and Eddy Convection

NASA Technical Reports Server (NTRS)

Kandula, Max

2010-01-01

A physical model for the effective thermal conductivity of water frost is proposed for application to the full range of frost density. The proposed model builds on the Zehner-Schlunder one-dimensional formulation for porous media appropriate for solid-to-fluid thermal conductivity ratios less than about 1000. By superposing the effects of mass diffusion and eddy convection on stagnant conduction in the fluid, the total effective thermal conductivity of frost is shown to be satisfactorily described. It is shown that the effects of vapor diffusion and eddy convection on the frost conductivity are of the same order. The results also point out that idealization of the frost structure by cylindrical inclusions offers a better representation of the effective conductivity of frost as compared to spherical inclusions. Satisfactory agreement between the theory and the measurements for the effective thermal conductivity of frost is demonstrated for a wide range of frost density and frost temperature.

Physical effects at the cellular level under altered gravity conditions

NASA Technical Reports Server (NTRS)

Todd, Paul

1992-01-01

Several modifications of differentiated functions of animal cells cultivated in vitro have been reported when cultures have been exposed to increased or decreased inertial acceleration fields by centrifugation, clinorotation, and orbital space flight. Variables modified by clinorotation conditions include inertial acceleration, convection, hydrostatic pressure, sedimentation, and shear stress, which also affect transport processes in the extracellular chemical environment. Autocrine, paracrine and endocrine substances, to which cells are responsive via specific receptors, are usually transported in vitro (and possibly in certain embryos) by convection and in vivo by a circulatory system or ciliary action. Increased inertial acceleration increases convective flow, while microgravity nearly abolishes it. In the latter case the extracellular transport of macromolecules is governed by diffusion. By making certain assumptions it is possible to calculate the Peclet number, the ratio of convective transport to diffusive transport. Some, but not all, responses of cells in vitro to modified inertial environments could be manifestations of modified extracellular convective flow.

Experimental Control of Thermocapillary Convection in a Liquid Bridge

NASA Technical Reports Server (NTRS)

Petrov, Valery; Schatz, Michael F.; Muehlner, Kurt A.; VanHook, Stephen J.; McCormick, W. D.; Swift, Jack B.; Swinney, Harry L.

1996-01-01

We demonstrate the stabilization of an isolated unstable periodic orbit in a liquid bridge convection experiment. A model independent, nonlinear control algorithm uses temperature measurements near the liquid interface to compute control perturbations which are applied by a thermoelectric element. The algorithm employs a time series reconstruction of a nonlinear control surface in a high dimensional phase space to alter the system dynamics.

Simulations of Convection Zone Flows and Measurements from Multiple Viewing Angles

NASA Technical Reports Server (NTRS)

Duvall, Thomas L.; Hanasoge, Shravan

2011-01-01

A deep-focusing time-distance measurement technique has been applied to linear acoustic simulations of a solar interior perturbed by convective flows. The simulations are for the full sphere for r/R greater than 0.2. From these it is straightforward to simulate the observations from different viewing angles and to test how multiple viewing angles enhance detectibility. Some initial results will be presented.

Flagella-Driven Flows Circumvent Diffusive Bottlenecks that Inhibit Metabolite Exchange

NASA Astrophysics Data System (ADS)

Short, Martin; Solari, Cristian; Ganguly, Sujoy; Kessler, John; Goldstein, Raymond; Powers, Thomas

2006-03-01

The evolution of single cells to large and multicellular organisms requires matching the organisms' needs to the rate of exchange of metabolites with the environment. This logistic problem can be a severe constraint on development. For organisms with a body plan that approximates a spherical shell, such as colonies of the volvocine green algae, the required current of metabolites grows quadratically with colony radius whereas the rate at which diffusion can exchange metabolites grows only linearly with radius. Hence, there is a bottleneck radius beyond which the diffusive current cannot keep up with metabolic demands. Using Volvox carteri as a model organism, we examine experimentally and theoretically the role that advection of fluid by surface-mounted flagella plays in enhancing nutrient uptake. We show that fluid flow driven by the coordinated beating of flagella produces a convective boundary layer in the concentration of a diffusing solute which in turn renders the metabolite exchange rate quadratic in the colony radius. This enhanced transport circumvents the diffusive bottleneck, allowing increase in size and thus evolutionary transitions to multicellularity in the Volvocales.

Macroscopic modeling of heat and water vapor transfer with phase change in dry snow based on an upscaling method: Influence of air convection

NASA Astrophysics Data System (ADS)

Calonne, N.; Geindreau, C.; Flin, F.

2015-12-01

At the microscopic scale, i.e., pore scale, dry snow metamorphism is mainly driven by the heat and water vapor transfer and the sublimation-deposition process at the ice-air interface. Up to now, the description of these phenomena at the macroscopic scale, i.e., snow layer scale, in the snowpack models has been proposed in a phenomenological way. Here we used an upscaling method, namely, the homogenization of multiple-scale expansions, to derive theoretically the macroscopic equivalent modeling of heat and vapor transfer through a snow layer from the physics at the pore scale. The physical phenomena under consideration are steady state air flow, heat transfer by conduction and convection, water vapor transfer by diffusion and convection, and phase change (sublimation and deposition). We derived three different macroscopic models depending on the intensity of the air flow considered at the pore scale, i.e., on the order of magnitude of the pore Reynolds number and the Péclet numbers: (A) pure diffusion, (B) diffusion and moderate convection (Darcy's law), and (C) strong convection (nonlinear flow). The formulation of the models includes the exact expression of the macroscopic properties (effective thermal conductivity, effective vapor diffusion coefficient, and intrinsic permeability) and of the macroscopic source terms of heat and vapor arising from the phase change at the pore scale. Such definitions can be used to compute macroscopic snow properties from 3-D descriptions of snow microstructures. Finally, we illustrated the precision and the robustness of the proposed macroscopic models through 2-D numerical simulations.

Physical Mechanisms for the Maintenance of GCM-Simulated Madden-Julian Oscillation over the Indian Ocean and Pacific

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deng, Liping; Wu, Xiaoqing

2011-05-05

The kinetic energy budget is conducted to analyze the physical processes responsible for the improved Madden-Julian Oscillation (MJO) simulated by the Iowa State University general circulation models (ISUGCM). The modified deep convection scheme that includes the revised convection closure, convection trigger condition and convective momentum transport (CMT) enhances the equatorial (10oS-10oN) MJO-related perturbation kinetic energy (PKE) in the upper troposphere and leads to more robust and coherent eastward propagating MJO signal. In the MJO source region-the Indian Ocean (45oE-120oE), the upper-tropospheric MJO PKE is maintained by the vertical convergence of wave energy flux and the barotropic conversion through the horizontalmore » shear of mean flow. In the convectively active region-the western Pacific (120oE-180o), the upper-tropospheric MJO PKE is supported by the convergence of horizontal and vertical wave energy fluxes. Over the central-eastern Pacific (180o-120oW), where convection is suppressed, the upper-tropospheric MJO PKE is mainly due to the horizontal convergence of wave energy flux. The deep convection trigger condition produces stronger convective heating which enhances the perturbation available potential energy (PAPE) production and the upward wave energy fluxes, and leads to the increased MJO PKE over the Indian Ocean and western Pacific. The trigger condition also enhances the MJO PKE over the central-eastern Pacific through the increased convergence of meridional wave energy flux from the subtropical latitudes of both hemispheres. The revised convection closure affects the response of mean zonal wind shear to the convective heating over the Indian Ocean and leads to the enhanced upper-tropospheric MJO PKE through the barotropic conversion. The stronger eastward wave energy flux due to the increase of convective heating over the Indian Ocean and western Pacific by the revised closure is favorable to the eastward propagation of MJO and the convergence of horizontal wave energy flux over the central-eastern Pacific. The convection-induced momentum tendency tends to decelerate the upper-tropospheric wind which results in a negative work to the PKE budget in the upper troposphere. However, the convection momentum tendency accelerates the westerly wind below 800 hPa over the western Pacific, which is partially responsible for the improved MJO simulation.« less

Evaporation enhancement in soils: a critical review

NASA Astrophysics Data System (ADS)

Rutten, Martine; van de Giesen, Nick

2015-04-01

Temperature gradients in the top layer of the soil are, especially during the daytime, steeper than would be expected if thermal conduction was the primary heat transfer mechanism. Evaporation seems to have significant influence on the soil heat budget. Only part of the surface soil heat flux is conducted downwards, increasing the soil temperatures, and part is used for evaporation, acting as a sink to the soil heat budget. For moist soils, the evaporation is limited by the transport of water molecules to the surface. The classical view is that water vapor is transported from the evaporation front to the surface by diffusion. Diffusion is mixing due to the random movement of molecules resulting in flattening concentration gradients. In soil, the diffusive vapor flux and the resulting latent heat flux are generally small. We found that transport enhancement is necessary in order to sustain vapor fluxes that are large enough to sustain latent heat fluxes, as well as being large enough to explain the observed temperature gradients. Enhancement of vapor diffusion is a known phenomenon, subject to debate on the explanations of underlying mechanism. In an extensive literature review on vapor enhancement in soils, the plausibility of various mechanisms was assessed. We reviewed mechanisms based on (combinations of) diffusive, viscous, buoyant, capillary and external pressure forces including: thermodiffusion, dispersion, Stefan's flow, Knudsen diffusion, liquid island effect, hydraulic lift, free convection, double diffusive convection and forced convection. The analysis of the order of magnitude of the mechanisms based on first principles clearly distinguished between plausible and implausible mechanisms. Thermodiffusion, Stefan's flow, Knudsen effects, liquid islands do not significantly contribute to enhanced evaporation. Double diffusive convection seemed unlikely due to lack of experimental evidence, but could not be completely excluded from the list of potential mechanisms. Hydraulic lift, the mechanism that small capillaries lift liquid water to the surface where it evaporates, does significantly contribute to enhanced evaporation from soils, also from dryer soils. The experimental evidence for and the theoretical underpinnings of this mechanism are convincing. However, we sought mechanisms that both explain enhanced evaporation and steep temperature gradients in the soil during the daytime. These often observed gradients consist of a sharp decrease of temperature with a depth up to the depth of the evaporation front. Hydraulic lift cannot explain this because the evaporation front is located at the surface. One remaining mechanism is forced convection due to atmospheric pressure fluctuations, also referred to as wind pumping. Wind pumping causes displacement and flow velocities too small for significant convective and too small for significant dispersive transport, when steady state dispersion formulations are used. However, experiments do indicate significant dispersive transport that can be explained by dispersion under unsteady flow conditions. Forced convection due to pressure fluctuations seems to be the only mechanism that can explain both enhanced evaporation and the steep temperature gradients.

A global ocean climatological atlas of the Turner angle: implications for double-diffusion and water-mass structure

NASA Astrophysics Data System (ADS)

You, Yuzhu

2002-11-01

The 1994 Levitus climatological atlas is used to calculate the Turner angle (named after J. Stewart Turner) to examine which oceanic water masses are favorable for double-diffusion in the form of diffusive convection or salt-fingering and which are doubly stable. This atlas complements the Levitus climatology. It reveals the major double-diffusive signals associated with large-scale water-mass structure. In total, about 44% of the oceans display double-diffusion, of which 30% is salt-fingering and 14% is diffusive double-diffusion. Results show that various central and deep waters are favorable for salt-fingering. The former is due to positive evaporation minus precipitation, and the latter is due to thermohaline circulation, i.e. the southward spreading of relatively warm, salty North Atlantic Deep Water (NADW) overlying cold, fresh Antarctic Bottom Water. In the northern Indian Ocean and eastern North Atlantic, favorable conditions for salt-fingering are found throughout the water column. The Red Sea (including the Persian Gulf) and Mediterranean Sea are the sources of warm, salty water for the ocean. As consequence, temperature and salinity in these outflow regions both decrease from the sea surface to the bottom. On the other hand, ocean currents are in general sluggish in these regions. In the polar and subpolar regions of Arctic and Antarctic, Okhotsk Sea, Gulf of Alaska, the subpolar gyre of the North Pacific, the Labrador Sea, and the Norwegian Sea, the upper layer water is favorable for diffusive convection because of high latitude surface cooling and ice melting. Weak and shallow diffusive convection is also found throughout tropical regions and the Bay of Bengal. The former is due to excessive precipitation over evaporation and rain cooling, and the latter is due to both precipitation and river runoff. Diffusive convection in the ocean's interior is unique to the South Atlantic between Antarctic Intermediate Water and upper NADW (uNADW). It is the consequence of the intrusive equatorward flow of upper Circumpolar Deep Water, which carries with it the minimum temperature and very low salinity overlying warm, salty uNADW.

Calculation of periodic flows in a continuously stratified fluid

NASA Astrophysics Data System (ADS)

Vasiliev, A.

2012-04-01

Analytic theory of disturbances generated by an oscillating compact source in a viscous continuously stratified fluid was constructed. Exact solution of the internal waves generation problem was constructed taking into account diffusivity effects. This analysis is based on set of fundamental equations of incompressible flows. The linearized problem of periodic flows in a continuously stratified fluid, generated by an oscillating part of the inclined plane was solved by methods of singular perturbation theory. A rectangular or disc placed on a sloping plane and oscillating linearly in an arbitrary direction was selected as a source of disturbances. The solutions include regularly perturbed on dissipative component functions describing internal waves and a family of singularly perturbed functions. One of the functions from the singular components family has an analogue in a homogeneous fluid that is a periodic or Stokes' flow. Its thickness is defined by a universal micro scale depending on kinematics viscosity coefficient and a buoyancy frequency with a factor depending on the wave slope. Other singular perturbed functions are specific for stratified flows. Their thickness are defined the diffusion coefficient, kinematic viscosity and additional factor depending on geometry of the problem. Fields of fluid density, velocity, vorticity, pressure, energy density and flux as well as forces acting on the source are calculated for different types of the sources. It is shown that most effective source of waves is the bi-piston. Complete 3D problem is transformed in various limiting cases that are into 2D problem for source in stratified or homogeneous fluid and the Stokes problem for an oscillating infinite plane. The case of the "critical" angle that is equality of the emitting surface and the wave cone slope angles needs in separate investigations. In this case, the number of singular component is saved. Patterns of velocity and density fields were constructed and analyzed by methods of computational mathematics. Singular components of the solution affect the flow pattern of the inhomogeneous stratified fluid, not only near the source of the waves, but at a large distance. Analytical calculations of the structure of wave beams are matched with laboratory experiments. Some deviations at large distances from the source are formed due to the contribution of background wave field associated with seiches in the laboratory tank. In number of the experiments vortices with closed contours were observed on some distances from the disk. The work was supported by Ministry of Education and Science RF (Goscontract No. 16.518.11.7059), experiments were performed on set up USU "HPC IPMec RAS".

Generalization of one-dimensional solute transport: A stochastic-convective flow conceptualization

NASA Astrophysics Data System (ADS)

Simmons, C. S.

1986-04-01

A stochastic-convective representation of one-dimensional solute transport is derived. It is shown to conceptually encompass solutions of the conventional convection-dispersion equation. This stochastic approach, however, does not rely on the assumption that dispersive flux satisfies Fick's diffusion law. Observable values of solute concentration and flux, which together satisfy a conservation equation, are expressed as expectations over a flow velocity ensemble, representing the inherent random processess that govern dispersion. Solute concentration is determined by a Lagrangian pdf for random spatial displacements, while flux is determined by an equivalent Eulerian pdf for random travel times. A condition for such equivalence is derived for steady nonuniform flow, and it is proven that both Lagrangian and Eulerian pdfs are required to account for specified initial and boundary conditions on a global scale. Furthermore, simplified modeling of transport is justified by proving that an ensemble of effectively constant velocities always exists that constitutes an equivalent representation. An example of how a two-dimensional transport problem can be reduced to a single-dimensional stochastic viewpoint is also presented to further clarify concepts.

Absolute versus convective helical magnetorotational instability in a Taylor-Couette flow.

PubMed

Priede, Jānis; Gerbeth, Gunter

2009-04-01

We analyze numerically the magnetorotational instability of a Taylor-Couette flow in a helical magnetic field [helical magnetorotational instability (HMRI)] using the inductionless approximation defined by a zero magnetic Prandtl number (Pr_{m}=0) . The Chebyshev collocation method is used to calculate the eigenvalue spectrum for small-amplitude perturbations. First, we carry out a detailed conventional linear stability analysis with respect to perturbations in the form of Fourier modes that corresponds to the convective instability which is not in general self-sustained. The helical magnetic field is found to extend the instability to a relatively narrow range beyond its purely hydrodynamic limit defined by the Rayleigh line. There is not only a lower critical threshold at which HMRI appears but also an upper one at which it disappears again. The latter distinguishes the HMRI from a magnetically modified Taylor vortex flow. Second, we find an absolute instability threshold as well. In the hydrodynamically unstable regime before the Rayleigh line, the threshold of absolute instability is just slightly above the convective one although the critical wavelength of the former is noticeably shorter than that of the latter. Beyond the Rayleigh line the lower threshold of absolute instability rises significantly above the corresponding convective one while the upper one descends significantly below its convective counterpart. As a result, the extension of the absolute HMRI beyond the Rayleigh line is considerably shorter than that of the convective instability. The absolute HMRI is supposed to be self-sustained and, thus, experimentally observable without any external excitation in a system of sufficiently large axial extension.

The Solar Dynamo

NASA Technical Reports Server (NTRS)

Hathaway, David H.

1998-01-01

The solar dynamo is the process by which the Sun's magnetic field is generated through the interaction of the field with convection and rotation. In this, it is kin to planetary dynamos and other stellar dynamos. Although the precise mechanism by which the Sun generates its field remains poorly understood despite decades of theoretical and observational work, recent advances suggest that solutions to this solar dynamo problem may be forthcoming. Two basic processes are involved in dynamo activity. When the fluid stresses dominate the magnetic stresses (high plasma beta = 8(pi)rho/B(sup 2)), shear flows can stretch magnetic field lines in the direction of the shear (the "alpha effect") and helical flows can lift and twist field lines into orthogonal planes (the "alpha effect"). These two processes can be active anywhere in the solar convection zone but with different results depending upon their relative strengths and signs. Little is known about how and where these processes occur. Other processes, such as magnetic diffusion and the effects of the fine scale structure of the solar magnetic field, pose additional problems.

The Effect of Pickling on Blue Borscht Gelatin and Other Interesting Diffusive Phenomena.

ERIC Educational Resources Information Center

Davis, Lawrence C.; Chou, Nancy C.

1998-01-01

Presents some simple demonstrations that students can construct for themselves in class to learn the difference between diffusion and convection rates. Uses cabbage leaves and gelatin and focuses on diffusion in ungelified media, a quantitative diffusion estimate with hydroxyl ions, and a quantitative diffusion estimate with photons. (DDR)

Global Distribution and Parameter Dependences of Gravity Wave Activity in the Martian Upper Thermosphere Derived from MAVEN NGIMS Observations

NASA Technical Reports Server (NTRS)

Terada, Naoki; Leblanc, Francois; Nakagawa, Hiromu; Medvedev, Alexander S.; Yigit, Erdal; Kuroda, Takeshi; Hara, Takuya; England, Scott L.; Fujiwara, Hitoshi; Terada, Kaori;

Large-scale parallel lattice Boltzmann-cellular automaton model of two-dimensional dendritic growth

NASA Astrophysics Data System (ADS)

Jelinek, Bohumir; Eshraghi, Mohsen; Felicelli, Sergio; Peters, John F.

2014-03-01

An extremely scalable lattice Boltzmann (LB)-cellular automaton (CA) model for simulations of two-dimensional (2D) dendritic solidification under forced convection is presented. The model incorporates effects of phase change, solute diffusion, melt convection, and heat transport. The LB model represents the diffusion, convection, and heat transfer phenomena. The dendrite growth is driven by a difference between actual and equilibrium liquid composition at the solid-liquid interface. The CA technique is deployed to track the new interface cells. The computer program was parallelized using the Message Passing Interface (MPI) technique. Parallel scaling of the algorithm was studied and major scalability bottlenecks were identified. Efficiency loss attributable to the high memory bandwidth requirement of the algorithm was observed when using multiple cores per processor. Parallel writing of the output variables of interest was implemented in the binary Hierarchical Data Format 5 (HDF5) to improve the output performance, and to simplify visualization. Calculations were carried out in single precision arithmetic without significant loss in accuracy, resulting in 50% reduction of memory and computational time requirements. The presented solidification model shows a very good scalability up to centimeter size domains, including more than ten million of dendrites. Catalogue identifier: AEQZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEQZ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 29,767 No. of bytes in distributed program, including test data, etc.: 3131,367 Distribution format: tar.gz Programming language: Fortran 90. Computer: Linux PC and clusters. Operating system: Linux. Has the code been vectorized or parallelized?: Yes. Program is parallelized using MPI. Number of processors used: 1-50,000 RAM: Memory requirements depend on the grid size Classification: 6.5, 7.7. External routines: MPI (http://www.mcs.anl.gov/research/projects/mpi/), HDF5 (http://www.hdfgroup.org/HDF5/) Nature of problem: Dendritic growth in undercooled Al-3 wt% Cu alloy melt under forced convection. Solution method: The lattice Boltzmann model solves the diffusion, convection, and heat transfer phenomena. The cellular automaton technique is deployed to track the solid/liquid interface. Restrictions: Heat transfer is calculated uncoupled from the fluid flow. Thermal diffusivity is constant. Unusual features: Novel technique, utilizing periodic duplication of a pre-grown “incubation” domain, is applied for the scaleup test. Running time: Running time varies from minutes to days depending on the domain size and number of computational cores.

The Cool Flames Experiment

NASA Technical Reports Server (NTRS)

Pearlman, Howard; Chapek, Richard; Neville, Donna; Sheredy, William; Wu, Ming-Shin; Tornabene, Robert

2001-01-01

A space-based experiment is currently under development to study diffusion-controlled, gas-phase, low temperature oxidation reactions, cool flames and auto-ignition in an unstirred, static reactor. At Earth's gravity (1g), natural convection due to self-heating during the course of slow reaction dominates diffusive transport and produces spatio-temporal variations in the thermal and thus species concentration profiles via the Arrhenius temperature dependence of the reaction rates. Natural convection is important in all terrestrial cool flame and auto-ignition studies, except for select low pressure, highly dilute (small temperature excess) studies in small vessels (i.e., small Rayleigh number). On Earth, natural convection occurs when the Rayleigh number (Ra) exceeds a critical value of approximately 600. Typical values of the Ra, associated with cool flames and auto-ignitions, range from 104-105 (or larger), a regime where both natural convection and conduction heat transport are important. When natural convection occurs, it alters the temperature, hydrodynamic, and species concentration fields, thus generating a multi-dimensional field that is extremely difficult, if not impossible, to be modeled analytically. This point has been emphasized recently by Kagan and co-workers who have shown that explosion limits can shift depending on the characteristic length scale associated with the natural convection. Moreover, natural convection in unstirred reactors is never "sufficiently strong to generate a spatially uniform temperature distribution throughout the reacting gas." Thus, an unstirred, nonisothermal reaction on Earth does not reduce to that generated in a mechanically, well-stirred system. Interestingly, however, thermal ignition theories and thermokinetic models neglect natural convection and assume a heat transfer correlation of the form: q=h(S/V)(T(bar) - Tw) where q is the heat loss per unit volume, h is the heat transfer coefficient, S/V is the surface to volume ratio, and (T(bar) - Tw ) is the spatially averaged temperature excess. This Newtonian form has been validated in spatially-uniform, well-stirred reactors, provided the effective heat transfer coefficient associated with the unsteady process is properly evaluated. Unfortunately, it is not a valid assumption for spatially-nonuniform temperature distributions induced by natural convection in unstirred reactors. "This is why the analysis of such a system is so difficult." Historically, the complexities associated with natural convection were perhaps recognized as early as 1938 when thermal ignition theory was first developed. In the 1955 text "Diffusion and Heat Exchange in Chemical Kinetics", Frank-Kamenetskii recognized that "the purely conductive theory can be applied at sufficiently low pressure and small dimensions of the vessel when the influence of natural convection can be disregarded." This was reiterated by Tyler in 1966 and further emphasized by Barnard and Harwood in 1974. Specifically, they state: "It is generally assumed that heat losses are purely conductive. While this may be valid for certain low pressure slow combustion regimes, it is unlikely to be true for the cool flame and ignition regimes." While this statement is true for terrestrial experiments, the purely conductive heat transport assumption is valid at microgravity (mu-g). Specifically, buoyant complexities are suppressed at mu-g and the reaction-diffusion structure associated with low temperature oxidation reactions, cool flames and auto-ignitions can be studied. Without natural convection, the system is simpler, does not require determination of the effective heat transfer coefficient, and is a testbed for analytic and numerical models that assume pure diffusive transport. In addition, mu-g experiments will provide baseline data that will improve our understanding of the effects of natural convection on Earth.

Space Particle Hazard Measurement and Modeling

DTIC Science & Technology

2007-11-30

the spacecraft and perturbations of the environment generated by the spacecraft. Koons et al. (1999) compiled and studied all spacecraft anomalies...unrealistic for D12 than for Dα0p). However, unlike the stability problems associated with the original cross diffusion terms, they are quite manageable ...E), to mono-energetic beams of charged particles of known energies which enables one, in principle , to unfold the space environment spectrum, j(E

Millimeter wave generation by relativistic electron beams

NASA Astrophysics Data System (ADS)

Kuo, S. S.; Cheo, B. R.; Tiong, K. K.; Whang, M. H.

1985-11-01

The classical technique of transformation and characteristics is employed to analyze the problem of strong turbulence in unmagnetized plasmas. The effects of resonance broadening and perturbation expansion are treated simultaneously without time securities. The renormalization procedure is used in the transformed Vlasov equation to analyze the turbulence and to derive explicitly a diffusion equation. Analyses are extended to imhomogeneous plasma and the relationship between the transformation and ponderomotive force is obtained.

Existence and exponential stability of traveling waves for delayed reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Hsu, Cheng-Hsiung; Yang, Tzi-Sheng; Yu, Zhixian

2018-03-01

The purpose of this work is to investigate the existence and exponential stability of traveling wave solutions for general delayed multi-component reaction-diffusion systems. Following the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, we first obtain the existence of monostable traveling wave solutions connecting two different equilibria. Then, applying the techniques of weighted energy method and comparison principle, we show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave solutions provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.

Model of convection mass transfer in titanium alloy at low energy high current electron beam action

NASA Astrophysics Data System (ADS)

Sarychev, V. D.; Granovskii, A. Yu; Nevskii, S. A.; Konovalov, S. V.; Gromov, V. E.

2017-01-01

The convection mixing model is proposed for low-energy high-current electron beam treatment of titanium alloys, pre-processed by heterogeneous plasma flows generated via explosion of carbon tape and powder TiB2. The model is based on the assumption vortices in the molten layer are formed due to the treatment by concentrated energy flows. These vortices evolve as the result of thermocapillary convection, arising because of the temperature gradient. The calculation of temperature gradient and penetration depth required solution of the heat problem with taking into account the surface evaporation. However, instead of the direct heat source the boundary conditions in phase transitions were changed in the thermal conductivity equation, assuming the evaporated material takes part in the heat exchange. The data on the penetration depth and temperature distribution are used for the thermocapillary model. The thermocapillary model embraces Navier-Stocks and convection heat transfer equations, as well as the boundary conditions with the outflow of evaporated material included. The solution of these equations by finite elements methods pointed at formation of a multi-vortices structure when electron-beam treatment and its expansion over new zones of material. As the result, strengthening particles are found at the depth exceeding manifold their penetration depth in terms of the diffusion mechanism.

Notes on hyperscaling violating Lifshitz and shear diffusion

NASA Astrophysics Data System (ADS)

Kolekar, Kedar S.; Mukherjee, Debangshu; Narayan, K.

2017-07-01

We explore in greater detail our investigations of shear diffusion in hyperscaling violating Lifshitz theories in Phys. Lett. B 760, 86 (2016), 10.1016/j.physletb.2016.06.046. This adapts and generalizes the membrane-paradigm-like analysis of Kovtun, Son, and Starinets for shear gravitational perturbations in the near horizon region given certain self-consistent approximations, leading to the shear diffusion constant on an appropriately defined stretched horizon. In theories containing a gauge field, some of the metric perturbations mix with some of the gauge field perturbations and the above analysis is somewhat more complicated. We find a similar near-horizon analysis can be obtained in terms of new field variables involving a linear combination of the metric and the gauge field perturbation resulting in a corresponding diffusion equation. Thereby as before, for theories with Lifshitz and hyperscaling violating exponents z , θ satisfying z <4 -θ in four bulk dimensions, our analysis here results in a similar expression for the shear diffusion constant with power-law scaling with temperature suggesting universal behavior in relation to the viscosity bound. For z =4 -θ , we find logarithmic behavior.

On the asymptotic behavior of a subcritical convection-diffusion equation with nonlocal diffusion

NASA Astrophysics Data System (ADS)

Cazacu, Cristian M.; Ignat, Liviu I.; Pazoto, Ademir F.

2017-08-01

In this paper we consider a subcritical model that involves nonlocal diffusion and a classical convective term. In spite of the nonlocal diffusion, we obtain an Oleinik type estimate similar to the case when the diffusion is local. First we prove that the entropy solution can be obtained by adding a small viscous term μ uxx and letting μ\\to 0 . Then, by using uniform Oleinik estimates for the viscous approximation we are able to prove the well-posedness of the entropy solutions with L 1-initial data. Using a scaling argument and hyperbolic estimates given by Oleinik’s inequality, we obtain the first term in the asymptotic behavior of the nonnegative solutions. Finally, the large time behavior of changing sign solutions is proved using the classical flux-entropy method and estimates for the nonlocal operator.

Analysis and design of numerical schemes for gas dynamics. 2: Artificial diffusion and discrete shock structure

NASA Technical Reports Server (NTRS)

Jameson, Antony

1994-01-01

The effect of artificial diffusion on discrete shock structures is examined for a family of schemes which includes scalar diffusion, convective upwind and split pressure (CUSP) schemes, and upwind schemes with characteristics splitting. The analysis leads to conditions on the diffusive flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a CUSP scheme in which the coefficients of the pressure differences is fully determined by the coefficient of convective diffusion. It is also shown how both the characteristic and CUSP schemes can be modified to preserve constant stagnation enthalpy in steady flow, leading to four variants, the E and H-characteristic schemes, and the E and H-CUSP schemes. Numerical results are presented which confirm the properties of these schemes.

Free Thermal Convection Inside a Stably Stratified FLUID:A Study by Means of Three Dimensional Particle Tracking Velocimetry

NASA Astrophysics Data System (ADS)

Cenedese, A.; Dore, V.; Moroni, M.

2009-05-01

Free thermal convection refers to the motion of vertical turbulent plumes or domes, which can occur when, an initially in-rest stratified fluid, is submitted to buoyancy forces, caused by a permanent perturbation associated to a heat transfer mechanism. When a fluid, in equilibrium, is stably stratified the external forcing can produce an unstable configuration ensuing the increasing in amplitude of internal waves, and, if it has strength enough, it can definitely erode the stratification, involving an increasing thickness of fluid volume. The entrainment phenomenon justifies the penetrative feature of convection and causes the growth of a convective boundary layer of well mixed fluid (Convective Mixing Layer) against the adjacent stable stratified layer. The non-steady phenomenon of penetrative convection in a stably stratified fluid has been reproduced in laboratory employing a tank filled with water and subjected to heating from below. The goal in the experiment is predicting the convective boundary layer growth as a function of initial and boundary conditions and describing the fate of a tracer dissolved in the fluid phase. The motivations of the research are mostly related to its connections to environmental topics. In nature the dynamics of penetrative convection influences the transport and mixing features of stratified fluids, playing a fundamental role in characterizing and forecasting the distribution of chemical species, with implication for water or air quality in the upper oceans and lakes or in the lower troposphere. When studying turbulent convective phenomenon, dispersion is mostly due to transport by large organized structures while molecular diffusion can be neglected. The knowledge of the horizontal and vertical extension of the structures dominating the flow field appears to be mandatory. In order to better understanding and likely describing the evolution of turbulent structures inside the convective layer, a fully three dimensional experimental technique is required. The equipment employed is suitable for simultaneously providing temperatures inside the domain through thermocouples and Lagrangian particle trajectories obtained by using a 3D-PTV technique. The combined use of a vertical array of thermocouples and 3D-PTV allows, simultaneously, profiling temperature and the 3D velocity components. A properly calibrated stereoscopic system of three monochrome 25 fps CCD cameras has been employed. The combination of image and object space based information is applied to establish the spatio-temporal correspondences between particle position of consecutive time steps, resulting in the reconstruction of 3D trajectories. The vertical dimension of convective structures is associated to the mixing layer height, detected both employing temperature data and statistics of the velocity field. On the other hand, the spatial correlation of the velocity field, providing the plume horizontal dimension, allows the horizontal extension of the mixing region to be determined. This information coupled to the knowledge of the mixing layer height allows the spatial extension of the convective region to be fully described.

Final Report of the Project "From the finite element method to the virtual element method"

DOE Office of Scientific and Technical Information (OSTI.GOV)

Manzini, Gianmarco; Gyrya, Vitaliy

The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for themore » numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.« less

Convective-diffusion-based fluorescence correlation spectroscopy for detection of a trace amount of E. coli in water.

PubMed

Qing, De-Kui; Mengüç, M Pinar; Payne, Fred A; Danao, Mary-Grace C

2003-06-01

Fluorescence correlation spectroscopy (FCS) is adapted for a new procedure to detect trace amounts of Escherichia coli in water. The present concept is based on convective diffusion rather than Brownian diffusion and employs confocal microscopy as in traditional FCS. With this system it is possible to detect concentrations as small as 1.5 x 10(5) E. coli per milliliter (2.5 x 10(-16) M). This concentration corresponds to an approximately 1.0-nM level of Rhodamine 6G dyes. A detailed analysis of the optical system is presented, and further improvements for the procedure are discussed.

The chemistry and diffusion of aircraft exhausts in the lower stratosphere during the first few hours after fly-by. [with attention to ozone depletion by SST exhaust plumes

NASA Technical Reports Server (NTRS)

Hilst, G. R.

1974-01-01

An analysis of the hydrogen-nitrogen-oxygen reaction systems in the lower stratosphere as they are initially perturbed by individual aircraft engine exhaust plumes was conducted in order to determine whether any significant chemical reactions occur, either among exhaust chemical species, or between these species and the environmental ozone, while the exhaust products are confined to intact plume segments at relatively high concentrations. The joint effects of diffusive mixing and chemical kinetics on the reactions were also studied, using the techniques of second-order closure diffusion/chemistry models. The focus of the study was on the larger problem of the potential depletion of ozone by supersonic transport aircraft exhaust materials emitted into the lower stratosphere.

Higher order reconstruction for MRI in the presence of spatiotemporal field perturbations.

PubMed

Wilm, Bertram J; Barmet, Christoph; Pavan, Matteo; Pruessmann, Klaas P

2011-06-01

Despite continuous hardware advances, MRI is frequently subject to field perturbations that are of higher than first order in space and thus violate the traditional k-space picture of spatial encoding. Sources of higher order perturbations include eddy currents, concomitant fields, thermal drifts, and imperfections of higher order shim systems. In conventional MRI with Fourier reconstruction, they give rise to geometric distortions, blurring, artifacts, and error in quantitative data. This work describes an alternative approach in which the entire field evolution, including higher order effects, is accounted for by viewing image reconstruction as a generic inverse problem. The relevant field evolutions are measured with a third-order NMR field camera. Algebraic reconstruction is then formulated such as to jointly minimize artifacts and noise in the resulting image. It is solved by an iterative conjugate-gradient algorithm that uses explicit matrix-vector multiplication to accommodate arbitrary net encoding. The feasibility and benefits of this approach are demonstrated by examples of diffusion imaging. In a phantom study, it is shown that higher order reconstruction largely overcomes variable image distortions that diffusion gradients induce in EPI data. In vivo experiments then demonstrate that the resulting geometric consistency permits straightforward tensor analysis without coregistration. Copyright © 2011 Wiley-Liss, Inc.

Diapycnal Transport and Pattern Formation in Double-Diffusive Convection

DTIC Science & Technology

2015-12-01

of knowledge. The effects of turbulent-dominated and purely double-diffusive regimes are compared to dual turbulent/double-diffusive systems and...is presented to remedy this dearth of knowledge. The effects of turbulent-dominated and purely double-diffusive regimes are compared to dual...8 2. Double-Diffusion: The Constant Flux Ratio Model ..........................9 3. The Combined Effects of

Enhanced heat transport during phase separation of liquid binary mixtures

NASA Astrophysics Data System (ADS)

Molin, Dafne; Mauri, Roberto

2007-07-01

We show that heat transfer in regular binary fluids is enhanced by induced convection during phase separation. The motion of binary mixtures is simulated using the diffuse interface model, where convection and diffusion are coupled via a nonequilibrium, reversible Korteweg body force. Assuming that the mixture is regular, i.e., its components are van der Waals fluids, we show that the two parameters that describe the mixture, namely the Margules constant and the interfacial thickness, depend on temperature as T-1 and T-1/2, respectively. Two quantities are used to measure heat transfer, namely the heat flux at the walls and the characteristic cooling time. Comparing these quantities with those of very viscous mixtures, where diffusion prevails over convection, we saw that the ratio between heat fluxes, which defines the Nusselt number, NNu, equals that between cooling times and remains almost constant in time. The Nusselt number depends on the following: the Peclet number, NPe, expressing the ratio between convective and diffusive mass fluxes; the Lewis number, NLe, expressing the ratio between thermal and mass diffusivities; the specific heat of the mixture, as it determines how the heat generated by mixing can be stored within the system; and the quenching depth, defined as the distance of the temperature at the wall from its critical value. In particular, the following results were obtained: (a) The Nusselt number grows monotonically with the Peclet number until it reaches an asymptotic value at NNu≈2 when NPe≈106; (b) the Nusselt number increases with NLe when NLe<1, remains constant at 11; (c) the Nusselt number is hardly influenced by the specific heat; (d) the Nusselt number decreases as the quenching rate increases. All these results can be explained by physical considerations. Predictably, considering that convection is within the creeping flow regime, the Nusselt number is always of o(10).

Analysis and design of numerical schemes for gas dynamics 1: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence

NASA Technical Reports Server (NTRS)

Jameson, Antony

1994-01-01

The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multi-dimensional problems on both structured and unstructured meshes, while it is equivalent to the total variation diminishing (TVD) principle for one-dimensional problems. A new formulation of symmetric limited positive (SLIP) schemes is presented, which can be generalized to produce schemes with arbitrary high order of accuracy in regions where the solution contains no extrema, and which can also be implemented on multi-dimensional unstructured meshes. Systems of equations lead to waves traveling with distinct speeds and possibly in opposite directions. Alternative treatments using characteristic splitting and scalar diffusive fluxes are examined, together with modification of the scalar diffusion through the addition of pressure differences to the momentum equations to produce full upwinding in supersonic flow. This convective upwind and split pressure (CUSP) scheme exhibits very rapid convergence in multigrid calculations of transonic flow, and provides excellent shock resolution at very high Mach numbers.

Prediction of oxygen distribution in aortic valve leaflet considering diffusion and convection.

PubMed

Wang, Ling; Korossis, Sotirios; Fisher, John; Ingham, Eileen; Jin, Zhongmin

2011-07-01

Oxygen supply and transport is an important consideration in the development of tissue engineered constructs. Previous studies from our group have focused on the effect of tissue thickness on the oxygen diffusion within a three-dimensional aortic valve leaflet model, and highlighted the necessity for additional transport mechanisms such as oxygen convection. The aims of this study were to investigate the effect of interstitial fluid flow within the aortic valve leaflet, induced by the cyclic loading of the leaflet, on oxygen transport. Indentation testing and finite element modelings were employed to derive the biphasic properties of the leaflet tissue. The biphasic properties were subsequently used in the computational modeling of oxygen convection in the leaflet, which was based on the effective interstitial fluid velocity and the tissue deformation. Subsequently, the oxygen profile was predicted within the valve leaflet model by solving the diffusion and convection equation simultaneously utilizing the finite difference method. The compression modulus (E) and hydraulic permeability were determined by adapting a finite element model to the experimental indentation test on valvular tissue, E = 0.05MPa, and k =2.0 mm4/Ns. Finite element model of oxygen convection in valvular tissue incorporating the predicted biphasic properties was developed and the interstitial fluid flow rate was calculated falling in range of 0.025-0.25 mm/s depending on the tissue depth. Oxygen distribution within valvular tissue was predicted using one-dimensional oxygen diffusion model taking into consider the interstitial fluid effect. It was found that convection did enhance the oxygen transport in valvular tissue by up to 68% increase in the minimum oxygen tension within the tissue, depending on the strain level of the tissue as reaction of the magnitude and frequencies of the cardiac loading. The effective interstitial fluid velocity was found to play an important role in enhancing the oxygen transport within the valve leaflet. Such an understanding is important in the development of valvular tissue engineered constructs.

Magnetic Damping of g-Jitter Induced Double-Diffusive Convection

NASA Technical Reports Server (NTRS)

Shu, Y.; Li, B. Q.; deGroh, H. C.

2001-01-01

This paper describes a numerical study of the g-jitter driven double diffusive convective flows, thermal and concentration distributions in binary alloy melt systems subject to an external magnetic field. The study is based on the finite element solution of transient magnetohydrodynamic equations governing the momentum, thermal and solutal transport in the melt pool. Numerical simulations are conducted using the synthesized single- and multi- frequency g-jitter as well as the real g-jitter data taken during space flights with or without an applied magnetic field. It is found that for the conditions studied, the main melt flow follows approximately a lineal- superposition of velocity components induced by individual g-jitter components, regardless of whether a magnetic field exists or not. The flow field is characterized by a recirculating double diffusive convection loop oscillating in time with a defined frequency equal to that of the driving g-jitter force. An applied magnetic field has little effect on the oscillating recirculating pattern, except around the moment in time when the flow reverses its direction. The field has no effect on the oscillation period, but it changes the phase angle. It is very effective in suppressing the flow intensity and produces a notable reduction of the solutal striation and time fluctuations in the melt. For a given magnetic field strength, the magnetic damping effect is more pronounced on the velocity associated with the largest g-jitter component present and/or the g-jitter spiking peaks. A stronger magnetic field is more effective in suppressing the melt convection and also is more helpful in bringing the convection in phase with the g-jitter driving force. The applied field is particularly useful in suppressing the effect of real g-jitter spikes on both flow and solutal distributions. With appropriately selected magnetic fields, the convective flows caused by g-jitter can be reduced sufficiently and diffusion dominant. solutal transport in the melt is possible.

Mixed convection peristaltic flow of third order nanofluid with an induced magnetic field.

PubMed

Noreen, Saima

2013-01-01

This research is concerned with the peristaltic flow of third order nanofluid in an asymmetric channel. The governing equations of third order nanofluid are modelled in wave frame of reference. Effect of induced magnetic field is considered. Long wavelength and low Reynolds number situation is tackled. Numerical solutions of the governing problem are computed and analyzed. The effects of Brownian motion and thermophoretic diffusion of nano particles are particularly emphasized. Physical quantities such as velocity, pressure rise, temperature, induced magnetic field and concentration distributions are discussed.

Investigation of parabolic computational techniques for internal high-speed viscous flows

NASA Technical Reports Server (NTRS)

Anderson, O. L.; Power, G. D.

1985-01-01

A feasibility study was conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves were present. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required.

Critical spaces for quasilinear parabolic evolution equations and applications

NASA Astrophysics Data System (ADS)

Prüss, Jan; Simonett, Gieri; Wilke, Mathias

2018-02-01

We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.

Taylor dispersion of colloidal particles in narrow channels

NASA Astrophysics Data System (ADS)

Sané, Jimaan; Padding, Johan T.; Louis, Ard A.

2015-09-01

We use a mesoscopic particle-based simulation technique to study the classic convection-diffusion problem of Taylor dispersion for colloidal discs in confined flow. When the disc diameter becomes non-negligible compared to the diameter of the pipe, there are important corrections to the original Taylor picture. For example, the colloids can flow more rapidly than the underlying fluid, and their Taylor dispersion coefficient is decreased. For narrow pipes, there are also further hydrodynamic wall effects. The long-time tails in the velocity autocorrelation functions are altered by the Poiseuille flow.

Chlorine dioxide-induced and Congo red-inhibited Marangoni effect on the chlorite-trithionate reaction front

NASA Astrophysics Data System (ADS)

Liu, Yang; Ren, Xingfeng; Pan, Changwei; Zheng, Ting; Yuan, Ling; Zheng, Juhua; Gao, Qingyu

2017-10-01

Hydrodynamic flows can exert multiple effects on an exothermal autocatalytic reaction, such as buoyancy and the Marangoni convection, which can change the structure and velocity of chemical waves. Here we report that in the chlorite-trithionate reaction, the production and consumption of chlorine dioxide can induce and inhibit Marangoni flow, respectively, leading to different chemo-hydrodynamic patterns. The horizontal propagation of a reaction-diffusion-convection front was investigated with the upper surface open to the air. The Marangoni convection, induced by gaseous chlorine dioxide on the surface, produced from chlorite disproportionation after the proton autocatalysis, has the same effect as the heat convection. When the Marangoni effect is removed by the reaction of chlorine dioxide with the Congo red (CR) indicator, an oscillatory propagation of the front tip is observed under suitable conditions. Replacing CR with bromophenol blue (BPB) distinctly enhanced the floating, resulting in multiple vortexes, owing to the coexistence between BPB and chlorine dioxide. Using the incompressible Navier-Stokes equations coupled with reaction-diffusion and heat conduction equations, we numerically obtain various experimental scenarios of front instability for the exothermic autocatalytic reaction coupled with buoyancy-driven convection and Marangoni convection.

Modified Laser Flash Method for Thermal Properties Measurements and the Influence of Heat Convection

NASA Technical Reports Server (NTRS)

Lin, Bochuan; Zhu, Shen; Ban, Heng; Li, Chao; Scripa, Rosalia N.; Su, Ching-Hua; Lehoczky, Sandor L.

2003-01-01

The study examined the effect of natural convection in applying the modified laser flash method to measure thermal properties of semiconductor melts. Common laser flash method uses a laser pulse to heat one side of a thin circular sample and measures the temperature response of the other side. Thermal diffusivity can be calculations based on a heat conduction analysis. For semiconductor melt, the sample is contained in a specially designed quartz cell with optical windows on both sides. When laser heats the vertical melt surface, the resulting natural convection can introduce errors in calculation based on heat conduction model alone. The effect of natural convection was studied by CFD simulations with experimental verification by temperature measurement. The CFD results indicated that natural convection would decrease the time needed for the rear side to reach its peak temperature, and also decrease the peak temperature slightly in our experimental configuration. Using the experimental data, the calculation using only heat conduction model resulted in a thermal diffusivity value is about 7.7% lower than that from the model with natural convection. Specific heat capacity was about the same, and the difference is within 1.6%, regardless of heat transfer models.

Convective drying of osmo-dehydrated apple slices: kinetics and spatial behavior of effective mass diffusivity and moisture content

NASA Astrophysics Data System (ADS)

de Farias Aires, Juarez Everton; da Silva, Wilton Pereira; de Almeida Farias Aires, Kalina Lígia Cavalcante; da Silva Júnior, Aluízio Freire; da Silva e Silva, Cleide Maria Diniz Pereira

2018-04-01

The main objective of this study is the presentation of a numerical model of liquid diffusion for the description of the convective drying of apple slices submitted to pretreatment of osmotic dehydration able of predicting the spatial distribution of effective mass diffusivity values in apple slabs. Two models that use numerical solutions of the two-dimensional diffusion equation in Cartesian coordinates with the boundary condition of third kind were proposed to describe drying. The first one does not consider the shrinkage of the product and assumes that the process parameters remain constant along the convective drying. The second one considers the shrinkage of the product and assumes that the effective mass diffusivity of water varies according to the local value of the water content in the apple samples. Process parameters were estimated from experimental data through an optimizer coupled to the numerical solutions. The osmotic pretreatment did not reduce the drying time in relation to the fresh fruits when the drying temperature was equal to 40 °C. The use of the temperature of 60 °C led to a reduction in the drying time. The model that considers the variations in the dimensions of the product and the variation in the effective mass diffusivity proved to be more adequate to describe the process.

Numerical modeling of Bridgman growth of PbSnTe in a magnetic field

NASA Technical Reports Server (NTRS)

Yao, Minwu; Chait, Arnon; Fripp, Archibald L.; Debnam, William J.

1995-01-01

In this work we study heat and mass transport, fluid motion, and solid/liquid phase change in the process of steady Bridgman growth of Pb(.8)Sn(.2)Te (LTT) in an axially-imposed uniform magnetic field under terrestrial and microgravity conditions. In particular, this research is concerned with the interrelationships among segregation, buoyancy-driven convection, and magnetic damping in the LTT melt. The main objectives are to provide a quantitative understanding of the complex transport phenomena during solidification of the nondilute binary of LTT, to provide estimates of the strength of magnetic field required to achieve the desired diffusion-dominated growth, and to assess the role of magnetic damping for space and earth based control of the buoyancy-induced convection. The problem was solved by using FIDAP and numerical results for both vertical and horizontal growth configurations with respect to the acceleration of gravity vector are presented.

THE SPECTRAL AMPLITUDE OF STELLAR CONVECTION AND ITS SCALING IN THE HIGH-RAYLEIGH-NUMBER REGIME

DOE Office of Scientific and Technical Information (OSTI.GOV)

Featherstone, Nicholas A.; Hindman, Bradley W., E-mail: feathern@colorado.edu

2016-02-10

Convection plays a central role in the dynamics of any stellar interior, and yet its operation remains largely hidden from direct observation. As a result, much of our understanding concerning stellar convection necessarily derives from theoretical and computational models. The Sun is, however, exceptional in that regard. The wealth of observational data afforded by its proximity provides a unique test bed for comparing convection models against observations. When such comparisons are carried out, surprising inconsistencies between those models and observations become apparent. Both photospheric and helioseismic measurements suggest that convection simulations may overestimate convective flow speeds on large spatial scales.more » Moreover, many solar convection simulations have difficulty reproducing the observed solar differential rotation owing to this apparent overestimation. We present a series of three-dimensional stellar convection simulations designed to examine how the amplitude and spectral distribution of convective flows are established within a star’s interior. While these simulations are nonmagnetic and nonrotating in nature, they demonstrate two robust phenomena. When run with sufficiently high Rayleigh number, the integrated kinetic energy of the convection becomes effectively independent of thermal diffusion, but the spectral distribution of that kinetic energy remains sensitive to both of these quantities. A simulation that has converged to a diffusion-independent value of kinetic energy will divide that energy between spatial scales such that low-wavenumber power is overestimated and high-wavenumber power is underestimated relative to a comparable system possessing higher Rayleigh number. We discuss the implications of these results in light of the current inconsistencies between models and observations.« less

Unsteady magnetohydrodynamics mixed convection flow in a rotating medium with double diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiann, Lim Yeou; Ismail, Zulkhibri; Khan, Ilyas

2015-05-15

Exact solutions of an unsteady Magnetohydrodynamics (MHD) flow over an impulsively started vertical plate in a rotating medium are presented. The effects of thermal radiative and thermal diffusion on the fluid flow are also considered. The governing equations are modelled and solved for velocity, temperature and concentration using Laplace transforms technique. Expressions of velocity, temperature and concentration profiles are obtained and their numerical results are presented graphically. Skin friction, Sherwood number and Nusselt number are also computed and presented in tabular forms. The determined solutions can generate a large class of solutions as special cases corresponding to different motions withmore » technical relevance. The results obtained herein may be used to verify the validation of obtained numerical solutions for more complicated fluid flow problems.« less

Influence of convection on the diffusive transport and sieving of water and small solutes across the peritoneal membrane.

PubMed

Asghar, Ramzana B; Diskin, Ann M; Spanel, Patrik; Smith, David; Davies, Simon J

2005-02-01

The three-pore model of peritoneal membrane physiology predicts sieving of small solutes as a result of the presence of a water-exclusive pathway. The purpose of this study was to measure the diffusive and convective components of small solute transport, including water, under differing convection. Triplicate studies were performed in eight stable individuals using 2-L exchanges of bicarbonate buffered 1.36 or 3.86% glucose and icodextrin. Diffusion of water was estimated by establishing an artificial gradient of deuterated water (HDO) between blood/body water and the dialysate. (125)RISA (radio-iodinated serum albumin) was used as an intraperitoneal volume marker to determine the net ultrafiltration and reabsorption of fluid. The mass transfer area coefficient (MTAC) for HDO and solutes was estimated using the Garred and Waniewski equations. The MTAC of HDO calculated for 1.36% glucose and icodextrin were similar (36.8 versus 39.7 ml/min; P = 0.3), whereas for other solutes, values obtained using icodextrin were consistently higher (P < 0.05). A significant increase in the MTAC of HDO was demonstrated with an increase in the convective flow of water when using 3.86% glucose (mean value, 49.5 ml/min; P < 0.05). MTAC for urea was also increased with 3.86% glucose. The identical MTAC for water using 1.36% glucose and icodextrin indicates that diffusion is predominantly through small pores, whereas the difference in MTAC for the remaining solutes is a reflection of their sieving. The increase in the MTAC of water and urea associated with an increase in convection is most likely due to increased mixing within the interstitium.

Clinopyroxene dissolution in basaltic melt

NASA Astrophysics Data System (ADS)

Chen, Yang; Zhang, Youxue

2009-10-01

The history of magmatic systems may be inferred from reactions between mantle xenoliths and host basalt if the thermodynamics and kinetics of the reactions are quantified. To study diffusive and convective clinopyroxene dissolution in silicate melts, diffusive clinopyroxene dissolution experiments were conducted at 0.47-1.90 GPa and 1509-1790 K in a piston-cylinder apparatus. Clinopyroxene saturation is found to be roughly determined by MgO and CaO content. The effective binary diffusivities, DMgO and DCaO, and the interface melt saturation condition, C0MgO×C0CaO, are extracted from the experiments. DMgO and DCaO show Arrhenian dependence on temperature. The pressure dependence is small and not resolved within 0.47-1.90 GPa. C0MgO×C0CaO in the interface melt increases with increasing temperature, but decreases with increasing pressure. Convective clinopyroxene dissolution, where the convection is driven by the density difference between the crystal and melt, is modeled using the diffusivities and interface melt saturation condition. Previous studies showed that the convective dissolution rate depends on the thermodynamics, kinetics and fluid dynamics of the system. Comparing our results for clinopyroxene dissolution to results from a previous study on convective olivine dissolution shows that the kinetic and fluid dynamic aspects of the two minerals are quite similar. However, the thermodynamics of clinopyroxene dissolution depends more strongly on the degree of superheating and composition of the host melt than that of olivine dissolution. The models for clinopyroxene and olivine dissolution are tested against literature experiments on mineral-melt interaction. They are then applied to previously proposed reactions between Hawaii basalts and mantle minerals, mid-ocean ridge basalts and mantle minerals, and xenoliths digestion in a basalt at Kuandian, Northeast China.

Hypoaigic influences on groundwater flux to a seasonally saline river

NASA Astrophysics Data System (ADS)

Trefry, M. G.; Svensson, T. J. A.; Davis, G. B.

2007-03-01

SummaryHypoaigic zones are aquifer volumes close to and beneath the shores of saline surface water bodies, and are characterized by the presence of time-dependent natural convection and chemical stratification. When transient and cyclic processes are involved there is significant potential for complex flow and reaction in the near-shore aquifer, presenting a unique challenge to pollutant risk assessment methodologies. This work considers the nature of some hypoaigic processes generated by the seasonally saline Canning River of Western Australia near a site contaminated by petroleum hydrocarbons. A dissolved hydrocarbon plume migrates within the shallow superficial aquifer to the nearby bank of the Canning River. Beneath the river bank a zone of complex fluid mixing is established by seasonal and tidal influences. Understanding this complexity and the subsequent ramifications for local biogeochemical conditions is critical to inferring the potential for degradation of advecting contaminants. A range of modelling approaches throws light on the overall topographic controls of discharge to the river, on the saline convection processes operating under the river bank, on the potential for fluid mixing, and on the various important time scales in the system. Saline distributions simulated within the aquifer hypoaigic zone are in at least qualitative agreement with previous field measurements at the site and are strongly affected by seasonal influences. Groundwater seepage velocities at the shoreline are found to be positively correlated with river salinity. Calculations of fluid age distributions throughout the system show sensitivity to dispersivity values; however, maximum fluid ages under the river appear to be diffusion limited to a few decades. The saline convection cell in the aquifer defines a zone of strong dispersive dilution of aged (many decades) deep aquifer fluids with relatively young (several months) riverine fluids. Seasonal recharge and river salinity cycles induce regular perturbations to the convection cell, yielding intra-annual variations of 50% in seepage velocity and almost 30% in wedge penetration distance at the plume location.

Role of dispersion on the onset of convection during CO2 sequestration

NASA Astrophysics Data System (ADS)

Hidalgo, J. J.; Carrera Ramirez, J.

2009-12-01

CO2 sequestration in geological formations containing saline water has been proposed as a solution to reduce gas emission to the atmosphere. Dissolution of CO2 takes place at the interphase with the brine as the CO2 migrates. The CO2-rich brine is denser than the resident one and tends to sink. This creates an unstable configuration that leads to a fingering sinking plume and convection to dominate diffusion. Understanding how instability fingers develop has received much attention because they accelerate dissolution trapping, which favors long term sequestration. The time for the onset of convection as the dominant transport mechanism has been traditionally studied by neglecting dispersion and treating the CO2 interface as a prescribed concentration boundary by analogy to a thermal convection problem. This work presents a more realistic representation of CO2 dissolution into brine. The proposed conceptual model acknowledges fluid and porous medium compressibility, hydrodynamic dispersion is included as a transport mechanism and the Boussinesq simplification is not assumed. Finally, boundary conditions include the CO2 mass flux across the top boundary. Results show that accounting for the CO2 mass flux across the prescribed concentration boundary has little effect on the onset of convection. However, accounting for dispersion causes a reduction of up to two orders of magnitude on the onset time. This implies that CO2 dissolution can be accelerated by activating dispersion as a transport mechanism, which can be achieved adopting a fluctuating injection scheme.

A simple method for finding explicit analytic transition densities of diffusion processes with general diploid selection.

PubMed

Song, Yun S; Steinrücken, Matthias

2012-03-01

The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.

A Simple Method for Finding Explicit Analytic Transition Densities of Diffusion Processes with General Diploid Selection

PubMed Central

Song, Yun S.; Steinrücken, Matthias

2012-01-01

The transition density function of the Wright–Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright–Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation–selection balance. PMID:22209899

3-D Modeling of Directional Solidification of a Non-Dilute Alloy with Temperature and Concentration Fields Coupling via Materials Properties Dependence and via Double Diffusive Convection

NASA Technical Reports Server (NTRS)

Bune, Andris V.; Gillies, Donald C.; Lehoczky, Sandor L.

1998-01-01

Numerical simulation of the HgCdTe growth by the vertical Bridgman method was performed using FIDAP finite element code. Double-diffusive melt convection is analyzed, as the primary factor at controls inhomogeneity of the solidified material. Temperature and concentration fields in the model are also coupled via material properties, such as thermal and solutal expansion coefficients with the dependence on both temperature and concentration, and melting temperature evaluation from pseudobinary CdTe-HgTe phase diagram. Experimental measurements were used to obtain temperature boundary conditions. Parametric study of the melt convection dependence on the gravity conditions was undertaken. It was found, that the maximum convection velocity in the melt can be reduced under certain conditions. Optimal conditions to obtain a near flat solidified interface are discussed. The predicted interface shape is in agreement with one obtained experimentally by quenching. The results of 3-D calculations are compared with previous 2- D findings. A video film featuring 3-D melt convection will be presented.

Numerical investigation of internal high-speed viscous flows using a parabolic technique

NASA Technical Reports Server (NTRS)

Anderson, O. L.; Power, G. D.

1985-01-01

A feasibility study has been conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves are present. A set of test problems with weak shock and expansion waves have been analyzed with this modified ADD method and stable and accurate solutions were demonstrated provided the streamwise step size was maintained at levels larger than the boundary layer displacement thickness. Calculations made with further reductions in step size encountered departure solutions consistent with strong interaction theory. Calculations were also performed for a flow field with a flame front in which a specific heat release was imposed to simulate a SCRAMJET combustor. In this case the flame front generated relatively thick shear layers which aggravated the departure solution problem. Qualitatively correct results were obtained for these cases using a marching technique with the convective terms in the normal momentum equation suppressed. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required.

Evaluation of AAFE apparatus to measure residual and transient convection in zero-gravity

NASA Technical Reports Server (NTRS)

Ruff, R. C.; Facemire, B. R.; Witherow, W. K.

1978-01-01

An evaluation apparatus which photographs convective and diffusive flows in crystal growth experiments is presented. Results in the following catagories are reported: (1) Human factors; (2) Electrical and mechanical; (3) Optical performance; and (4) Thermal performance.

Materials Science Laboratory - Columnar-to-Equiaxed Transition in Solidification Processing and Microstructure Formation in Casting of Technical Alloys under Diffusive and Magnetically Controlled Convective Conditions

NASA Technical Reports Server (NTRS)

Gandin, Charles-Andre; Ratke, Lorenz

2008-01-01

The Materials Science Laboratory - Columnar-to-Equiaxed Transition in Solidification Processing and Microstructure Formation in Casting of Technical Alloys under Diffusive and Magnetically Controlled Convective Conditions (MSL-CETSOL and MICAST) are two investigations which supports research into metallurgical solidification, semiconductor crystal growth (Bridgman and zone melting), and measurement of thermo-physical properties of materials. This is a cooperative investigation with the European Space Agency (ESA) and National Aeronautics and Space Administration (NASA) for accommodation and operation aboard the International Space Station (ISS). Research Summary: Materials Science Laboratory - Columnar-to-Equiaxed Transition in Solidification Processing (CETSOL) and Microstructure Formation in Casting of Technical Alloys under Diffusive and Magnetically Controlled Convective Conditions (MICAST) are two complementary investigations which will examine different growth patterns and evolution of microstructures during crystallization of metallic alloys in microgravity. The aim of these experiments is to deepen the quantitative understanding of the physical principles that govern solidification processes in cast alloys by directional solidification.

Convection Effects During Bulk Transparent Alloy Solidification in DECLIC-DSI and Phase-Field Simulations in Diffusive Conditions

NASA Astrophysics Data System (ADS)

Mota, F. L.; Song, Y.; Pereda, J.; Billia, B.; Tourret, D.; Debierre, J.-M.; Trivedi, R.; Karma, A.; Bergeon, N.

2017-08-01

To study the dynamical formation and evolution of cellular and dendritic arrays under diffusive growth conditions, three-dimensional (3D) directional solidification experiments were conducted in microgravity on a model transparent alloy onboard the International Space Station using the Directional Solidification Insert in the DEvice for the study of Critical LIquids and Crystallization. Selected experiments were repeated on Earth under gravity-driven fluid flow to evidence convection effects. Both radial and axial macrosegregation resulting from convection are observed in ground experiments, and primary spacings measured on Earth and microgravity experiments are noticeably different. The microgravity experiments provide unique benchmark data for numerical simulations of spatially extended pattern formation under diffusive growth conditions. The results of 3D phase-field simulations highlight the importance of accurately modeling thermal conditions that strongly influence the front recoil of the interface and the selection of the primary spacing. The modeling predictions are in good quantitative agreements with the microgravity experiments.

Mathematical modelling of the uptake and transport of salt in plant roots.

PubMed

Foster, Kylie J; Miklavcic, Stanley J

2013-11-07

In this paper, we present and discuss a mathematical model of ion uptake and transport in roots of plants. The underlying physical model of transport is based on the mechanisms of forced diffusion and convection. The model can take account of local variations in effective ion and water permeabilities across the major tissue regions of plant roots, represented through a discretized coupled system of governing equations including mass balance, forced diffusion, convection and electric potential. We present simulation results of an exploration of the consequent enormous parameter space. Among our findings we identify the electric potential as a major factor affecting ion transport across, and accumulation in, root tissues. We also find that under conditions of a constant but realistic level of bulk soil salt concentration and plant-soil hydraulic pressure, diffusion plays a significant role even when convection by the water transpiration stream is operating. Crown Copyright © 2013 Published by Elsevier Ltd. All rights reserved.

The Role of the Velocity Gradient in Laminar Convective Heat Transfer through a Tube with a Uniform Wall Heat Flux

ERIC Educational Resources Information Center

Wang, Liang-Bi; Zhang, Qiang; Li, Xiao-Xia

2009-01-01

This paper aims to contribute to a better understanding of convective heat transfer. For this purpose, the reason why thermal diffusivity should be placed before the Laplacian operator of the heat flux, and the role of the velocity gradient in convective heat transfer are analysed. The background to these analyses is that, when the energy…

On the Stability of Shocks with Particle Pressure

NASA Astrophysics Data System (ADS)

Finazzi, Stefano; Vietri, Mario

2008-11-01

We perform a linear stability analysis for corrugations of a Newtonian shock, with particle pressure included, for an arbitrary diffusion coefficient. We study first the dispersion relation for homogeneous media, showing that, besides the conventional pressure waves and entropy/vorticity disturbances, two new perturbation modes exist, dominated by the particles' pressure and damped by diffusion. We show that, due to particle diffusion into the upstream region, the fluid will be perturbed also upstream; we treat these perturbation in the short-wavelength (WKBJ) regime. We then show how to construct a corrugational mode for the shock itself, one, that is, where the shock executes free oscillations (possibly damped or growing) and sheds perturbations away from itself; this global mode requires the new modes. Then, using the perturbed Rankine-Hugoniot conditions, we show that this leads to the determination of the corrugational eigenfrequency. We solve numerically the equations for the eigenfrequency in the WKBJ regime for the models of Amato & Blasi, showing that they are stable. We then discuss the differences between our treatment and previous work.

Applying an economical scale-aware PDF-based turbulence closure model in NOAA NCEP GCMs.

NASA Astrophysics Data System (ADS)

Belochitski, A.; Krueger, S. K.; Moorthi, S.; Bogenschutz, P.; Cheng, A.

2017-12-01

A novel unified representation of sub-grid scale (SGS) turbulence, cloudiness, and shallow convection is being implemented into the NOAA NCEP Global Forecasting System (GFS) general circulation model. The approach, known as Simplified High Order Closure (SHOC), is based on predicting a joint PDF of SGS thermodynamic variables and vertical velocity, and using it to diagnose turbulent diffusion coefficients, SGS fluxes, condensation, and cloudiness. Unlike other similar methods, comparatively few new prognostic variables needs to be introduced, making the technique computationally efficient. In the base version of SHOC it is SGS turbulent kinetic energy (TKE), and in the developmental version — SGS TKE, and variances of total water and moist static energy (MSE). SHOC is now incorporated into a version of GFS that will become a part of the NOAA Next Generation Global Prediction System based around NOAA GFDL's FV3 dynamical core, NOAA Environmental Modeling System (NEMS) coupled modeling infrastructure software, and a set novel physical parameterizations. Turbulent diffusion coefficients computed by SHOC are now used in place of those produced by the boundary layer turbulence and shallow convection parameterizations. Large scale microphysics scheme is no longer used to calculate cloud fraction or the large-scale condensation/deposition. Instead, SHOC provides these quantities. Radiative transfer parameterization uses cloudiness computed by SHOC. An outstanding problem with implementation of SHOC in the NCEP global models is excessively large high level tropical cloudiness. Comparison of the moments of the SGS PDF diagnosed by SHOC to the moments calculated in a GigaLES simulation of tropical deep convection case (GATE), shows that SHOC diagnoses too narrow PDF distributions of total cloud water and MSE in the areas of deep convective detrainment. A subsequent sensitivity study of SHOC's diagnosed cloud fraction (CF) to higher order input moments of the SGS PDF demonstrated that CF is improved if SHOC is provided with correct variances of total water and MSE. Consequently, SHOC was modified to include two new prognostic equations for variances of total water and MSE, and coupled with the Chikira-Sugiyama parameterization of deep convection to include effects of detrainment on the prognostic variances.

Birch Lecture : The Deep Roots of Continents

NASA Astrophysics Data System (ADS)

Jaupart, C.

2006-12-01

The roots of Archean continents are made of depleted and buoyant mantle and may extend to depths larger than 250 km. Such distinctive characteristics have key dynamical and geological consequences that we are only beginning to address. Thick roots provide large volume repositories for chemical elements that do not mix with Earth's convecting interior. Their large diffusive relaxation time implies long-term thermal disequilibrium with their radioactive heat sources and with the cooling of the mantle. Their negative thermal buoyancy may drive convective instabilities with implications for intracontinental deformation and magmatism as well as for continental growth. The dynamical behaviour of continental roots depends on the buoyancy ratio B, the ratio of the intrinsic (chemical) buoyancy of depleted lithospheric mantle and the density difference due to thermal expansion. The lithosphere can be mechanically stable and in thermal equilibrium with heat supplied by small-scale convection at the top of the asthenosphere. Sufficient cooling may result in an oscillatory convective instability whereby perturbations to the base of the lithosphere rise and fall periodically. The lithosphere seems to have developed in a state near that of instability with different thicknesses depending on its intrinsic buoyancy. It may have grown not only by chemical differentiation during melting, but also by oscillatory convection entraining chemically denser material from the asthenosphere. Mantle plumes have different effects on lithospheres of different thicknesses and compositions. For B values larger than about 0.6, plume material does not really penetrate into the lithosphere and spreads beneath it. In this case, the buoyancy force that is applied to the base of the lithosphere drives moderate thinning and extension over large horizontal distances. It takes values of B less than 0.6 to achieve true plume penetration with a significant vertical velocity component. In this case, thinning and extension get localized above the rising plume. In both cases, heated lithosphere material becomes convectively unstable after some time and entrains asthenospheric material as it rises. Temperatures in thick continental lithosphere do not adjust rapidly to secular changes of mantle temperature. Analysis of (P,T) data from xenolith studies indicates that the Earth's mantle has cooled at a rate of 80 K Ga-1 or less. Thick continental roots preserve a record of Archean processes and of Earth's evolution through geological ages. Deciphering this record may well be our next challenge.

Non-kinematic Flux-transport Dynamos Including the Effects of Diffusivity Quenching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ichimura, Chiaki; Yokoyama, Takaaki

2017-04-10

Turbulent magnetic diffusivity is quenched when strong magnetic fields suppress turbulent motion in a phenomenon known as diffusivity quenching. Diffusivity quenching can provide a mechanism for amplifying magnetic field and influencing global velocity fields through Lorentz force feedback. To investigate this effect, we conducted mean field flux-transport dynamo simulations that included the effects of diffusivity quenching in a non-kinematic regime. We found that toroidal magnetic field strength is amplified by up to approximately 1.5 times in the convection zone as a result of diffusivity quenching. This amplification is much weaker than that in kinematic cases as a result of Lorentzmore » force feedback on the system’s differential rotation. While amplified toroidal fields lead to the suppression of equatorward meridional flow locally near the base of the convection zone, large-scale equatorward transport of magnetic flux via meridional flow, which is the essential process of the flux-transport dynamo, is sustainable in our calculations.« less

Unified path integral approach to theories of diffusion-influenced reactions

NASA Astrophysics Data System (ADS)

Prüstel, Thorsten; Meier-Schellersheim, Martin

2017-08-01

Building on mathematical similarities between quantum mechanics and theories of diffusion-influenced reactions, we develop a general approach for computational modeling of diffusion-influenced reactions that is capable of capturing not only the classical Smoluchowski picture but also alternative theories, as is here exemplified by a volume reactivity model. In particular, we prove the path decomposition expansion of various Green's functions describing the irreversible and reversible reaction of an isolated pair of molecules. To this end, we exploit a connection between boundary value and interaction potential problems with δ - and δ'-function perturbation. We employ a known path-integral-based summation of a perturbation series to derive a number of exact identities relating propagators and survival probabilities satisfying different boundary conditions in a unified and systematic manner. Furthermore, we show how the path decomposition expansion represents the propagator as a product of three factors in the Laplace domain that correspond to quantities figuring prominently in stochastic spatially resolved simulation algorithms. This analysis will thus be useful for the interpretation of current and the design of future algorithms. Finally, we discuss the relation between the general approach and the theory of Brownian functionals and calculate the mean residence time for the case of irreversible and reversible reactions.

Metal Accretion onto White Dwarfs. III. A Still Better Approach Based on the Coupling of Diffusion with Evolution

NASA Astrophysics Data System (ADS)

Brassard, Pierre; Fontaine, Gilles

2015-06-01

The accretion-diffusion picture is the model par excellence for describing the presence of planetary debris polluting the atmospheres of relatively cool white dwarfs. In the time-dependent approach used in Paper II of this series (Fontaine et al. 2014), the basic assumption is that the accreted metals are trace elements and do not influence the background structure, which may be considered static in time. Furthermore, the usual assumption of instantaneous mixing in the convection zone is made. As part of the continuing development of our local evolutionary code, diffusion in presence of stellar winds or accretion is now fully coupled to evolution. Convection is treated as a diffusion process, i.e., the assumption of instantaneous mixing is relaxed, and, furthermore, overshooting is included. This allows feedback on the evolving structure from the accreting metals. For instance, depending of its abundance, a given metal may contribute enough to the overall opacity (especially in a He background) to change the size of the convection zone as a function of time. Our better approach also allows to include in a natural way the mechanism of thermohaline convection, which we discuss at some length. Also, it is easy to consider sophisticated time-dependent models of accretion from circumstellar disks, such as those developed by Roman Rafikov at Princeton for instance. The current limitations of our approach are 1) the calculations are extremely computer-intensive, and 2) we have not yet developed detailed EOS megatables for metals beyond oxygen.

Analytical estimates of radial segregation in Bridgman growth from low-level steady and periodic accelerations

NASA Astrophysics Data System (ADS)

Naumann, Robert J.; Baugher, Charles

1992-08-01

Estimates of the convective flows driven by horizontal temperature gradients in the vertical Bridgman configuration are made for dilute systems subject to the low level accelerations typical of the residual accelerations experienced by a spacecraft in low Earth orbit. The estimates are made by solving the Navier-Stokes momentum equation in one dimension. The mass transport equation is then solved in two dimensions using a first-order perturbation method. This approach is valid provided the convective velocities are small compared to the growth velocity which generally requires a reduced gravity environment. If this condition is satisfied, there will be no circulating cells, and hence no convective transport along the vertical axis. However, the variations in the vertical velocity with radius will give rise to radial segregation. The approximate analytical model developed here can predict the degree of radial segregation for a variety of material and processing parameters to an accuracy well within a factor of two as compared against numerical computations of the full set of Navier-Stokes equations for steady accelerations. It has the advantage of providing more insight into the complex interplay of the processing parameters and how they affect the solute distribution in the grown crystal. This could be extremely valuable in the design of low-gravity experiments in which the intent is to control radial segregation. Also, the analysis can be extended to consider transient and periodic accelerations, which is difficult and costly to do numerically. Surprisingly, it was found that the relative radial segregation falls as the inverse cube of the frequency for periodic accelerations whose periods are short compared with the characteristic diffusion time.

A time fractional convection-diffusion equation to model gas transport through heterogeneous soil and gas reservoirs

NASA Astrophysics Data System (ADS)

Chang, Ailian; Sun, HongGuang; Zheng, Chunmiao; Lu, Bingqing; Lu, Chengpeng; Ma, Rui; Zhang, Yong

2018-07-01

Fractional-derivative models have been developed recently to interpret various hydrologic dynamics, such as dissolved contaminant transport in groundwater. However, they have not been applied to quantify other fluid dynamics, such as gas transport through complex geological media. This study reviewed previous gas transport experiments conducted in laboratory columns and real-world oil-gas reservoirs and found that gas dynamics exhibit typical sub-diffusive behavior characterized by heavy late-time tailing in the gas breakthrough curves (BTCs), which cannot be effectively captured by classical transport models. Numerical tests and field applications of the time fractional convection-diffusion equation (fCDE) have shown that the fCDE model can capture the observed gas BTCs including their apparent positive skewness. Sensitivity analysis further revealed that the three parameters used in the fCDE model, including the time index, the convection velocity, and the diffusion coefficient, play different roles in interpreting the delayed gas transport dynamics. In addition, the model comparison and analysis showed that the time fCDE model is efficient in application. Therefore, the time fractional-derivative models can be conveniently extended to quantify gas transport through natural geological media such as complex oil-gas reservoirs.

Numerical simulation of conservation laws

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; To, Wai-Ming

1992-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

Separation of acoustic waves in isentropic flow perturbations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Henke, Christian, E-mail: christian.henke@atlas-elektronik.com

2015-04-15

The present contribution investigates the mechanisms of sound generation and propagation in the case of highly-unsteady flows. Based on the linearisation of the isentropic Navier–Stokes equation around a new pathline-averaged base flow, it is demonstrated for the first time that flow perturbations of a non-uniform flow can be split into acoustic and vorticity modes, with the acoustic modes being independent of the vorticity modes. Therefore, we can propose this acoustic perturbation as a general definition of sound. As a consequence of the splitting result, we conclude that the present acoustic perturbation is propagated by the convective wave equation and fulfilsmore » Lighthill’s acoustic analogy. Moreover, we can define the deviations of the Navier–Stokes equation from the convective wave equation as “true” sound sources. In contrast to other authors, no assumptions on a slowly varying or irrotational flow are necessary. Using a symmetry argument for the conservation laws, an energy conservation result and a generalisation of the sound intensity are provided. - Highlights: • First splitting of non-uniform flows in acoustic and non-acoustic components. • These result leads to a generalisation of sound which is compatible with Lighthill’s acoustic analogy. • A closed equation for the generation and propagation of sound is given.« less

Concentration and density changes at an electrode surface and the principle of unchanging total concentration

DOE PAGES

Stephen W. Feldberg; Lewis, Ernie R.

2016-02-17

In this study, the principle of unchanging total concentration as described by Oldham and Feldberg [J. Phys. Chem. B, 103, 1699 (1999)] is invoked to analyze systems comprising a redox pair (X z1 1 and X z2 2) plus one or more non-electroactive species (X z3 3,X z4 4...X zjmax jmax) where X zj j is the j th species with charge z j and concentration; c j. The principle states that if the diffusion coefficients for all species are identical and mass transport is governed by the Nernst-Planck expression, the total concentration does not change during any electrochemical perturbation,more » i.e.: Σ jmax j=1[X zj j]=Σ jmax j=1 c j = S P With this principle we deduce the electrochemically induced difference between the surface and bulk concentrations for each species. Those concentration differences are translated into density differences which are a function of the density of the solvent and of the concentration differences, molecular masses and the standard partial molar volumes of all species. Those density differences in turn can induce convection that will ultimately modify the observed current. However, we did not attempt to quantify details of the natural convection and current modification produced by those density differences.« less

Quenching and anisotropy of hydromagnetic turbulent transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karak, Bidya Binay; Brandenburg, Axel; Rheinhardt, Matthias

2014-11-01

Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the α effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-field method, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the quenched flows, we obtain for themore » quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows, these quenching exponents become about 4, 1.5, and 2.3, respectively. For the α effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the Ω×J effect nearly the same quenching exponent is obtained as for α. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents.« less

On Improving 4-km Mesoscale Model Simulations

NASA Astrophysics Data System (ADS)

Deng, Aijun; Stauffer, David R.

2006-03-01

A previous study showed that use of analysis-nudging four-dimensional data assimilation (FDDA) and improved physics in the fifth-generation Pennsylvania State University National Center for Atmospheric Research Mesoscale Model (MM5) produced the best overall performance on a 12-km-domain simulation, based on the 18 19 September 1983 Cross-Appalachian Tracer Experiment (CAPTEX) case. However, reducing the simulated grid length to 4 km had detrimental effects. The primary cause was likely the explicit representation of convection accompanying a cold-frontal system. Because no convective parameterization scheme (CPS) was used, the convective updrafts were forced on coarser-than-realistic scales, and the rainfall and the atmospheric response to the convection were too strong. The evaporative cooling and downdrafts were too vigorous, causing widespread disruption of the low-level winds and spurious advection of the simulated tracer. In this study, a series of experiments was designed to address this general problem involving 4-km model precipitation and gridpoint storms and associated model sensitivities to the use of FDDA, planetary boundary layer (PBL) turbulence physics, grid-explicit microphysics, a CPS, and enhanced horizontal diffusion. Some of the conclusions include the following: 1) Enhanced parameterized vertical mixing in the turbulent kinetic energy (TKE) turbulence scheme has shown marked improvements in the simulated fields. 2) Use of a CPS on the 4-km grid improved the precipitation and low-level wind results. 3) Use of the Hong and Pan Medium-Range Forecast PBL scheme showed larger model errors within the PBL and a clear tendency to predict much deeper PBL heights than the TKE scheme. 4) Combining observation-nudging FDDA with a CPS produced the best overall simulations. 5) Finer horizontal resolution does not always produce better simulations, especially in convectively unstable environments, and a new CPS suitable for 4-km resolution is needed. 6) Although use of current CPSs may violate their underlying assumptions related to the size of the convective element relative to the grid size, the gridpoint storm problem was greatly reduced by applying a CPS to the 4-km grid.

General Solutions for Hydromagnetic Free Convection Flow over an Infinite Plate with Newtonian Heating, Mass Diffusion and Chemical Reaction

NASA Astrophysics Data System (ADS)

Fetecau, Constatin; Shah, Nehad Ali; Vieru, Dumitru

2017-12-01

The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined. Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration, three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution (the steady-state), for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.

Prandtl-number Effects in High-Rayleigh-number Spherical Convection

NASA Astrophysics Data System (ADS)

Orvedahl, Ryan J.; Calkins, Michael A.; Featherstone, Nicholas A.; Hindman, Bradley W.

2018-03-01

Convection is the predominant mechanism by which energy and angular momentum are transported in the outer portion of the Sun. The resulting overturning motions are also the primary energy source for the solar magnetic field. An accurate solar dynamo model therefore requires a complete description of the convective motions, but these motions remain poorly understood. Studying stellar convection numerically remains challenging; it occurs within a parameter regime that is extreme by computational standards. The fluid properties of the convection zone are characterized in part by the Prandtl number \\Pr = ν/κ, where ν is the kinematic viscosity and κ is the thermal diffusion; in stars, \\Pr is extremely low, \\Pr ≈ 10‑7. The influence of \\Pr on the convective motions at the heart of the dynamo is not well understood since most numerical studies are limited to using \\Pr ≈ 1. We systematically vary \\Pr and the degree of thermal forcing, characterized through a Rayleigh number, to explore its influence on the convective dynamics. For sufficiently large thermal driving, the simulations reach a so-called convective free-fall state where diffusion no longer plays an important role in the interior dynamics. Simulations with a lower \\Pr generate faster convective flows and broader ranges of scales for equivalent levels of thermal forcing. Characteristics of the spectral distribution of the velocity remain largely insensitive to changes in \\Pr . Importantly, we find that \\Pr plays a key role in determining when the free-fall regime is reached by controlling the thickness of the thermal boundary layer.

Theoretical study of the influence of chemical reactions and physical parameters on the convective dissolution of CO2 in aqueous solutions

NASA Astrophysics Data System (ADS)

Loodts, Vanessa; Rongy, Laurence; De Wit, Anne

2014-05-01

Subsurface carbon sequestration has emerged as a promising solution to the problem of increasing atmospheric carbon dioxide (CO2) levels. How does the efficiency of such a sequestration process depend on the physical and chemical characteristics of the storage site? This question is emblematic of the need to better understand the dynamics of CO2 in subsurface formations, and in particular, the properties of the convective dissolution of CO2 in the salt water of aquifers. This dissolution is known to improve the safety of the sequestration by reducing the risks of leaks of CO2 to the atmosphere. Buoyancy-driven convection makes this dissolution faster by transporting dissolved CO2 further away from the interface. Indeed, upon injection, the less dense CO2 phase rises above the aqueous layer where it starts to dissolve. The dissolved CO2 increases the density of the aqueous solution, thereby creating a layer of denser CO2-rich solution above less dense solution. This unstable density gradient in the gravity field is at the origin of convection. In this framework, we theoretically investigate the effect of CO2 pressure, salt concentration, temperature, and chemical reactions on the dissolution-driven convection of CO2 in aqueous solutions. On the basis of a linear stability analysis, we assess the stability of the time-dependent density profiles developing when CO2 dissolves in an aqueous layer below it. We predict that increasing CO2 pressure destabilizes the system with regard to buoyancy-driven convection, because it increases the density gradient at the origin of the instability. By contrast, increasing salt concentration or temperature stabilizes the system via effects on CO2 solubility, solutal expansion coefficient, diffusion coefficient and on the viscosity and density of the solution. We also show that a reaction of CO2 with chemical species dissolved in the aqueous solution can either enhance or decrease the amplitude of the convective dissolution compared to the non reactive one. On the basis of a reaction-diffusion-convection model, we classify the various possible cases and show that the difference between the solutal expansion coefficients of the reactant and of the product governs the type of density profile building up in the aqueous solution and thus the stability of the system. By contrast to non reactive density profiles, reactive density profiles can feature a minimum that induces a delay of the buoyancy-driven convection. This work identifies the parameters that could influence the dissolution-driven convection in the aquifers, and thus impact the safety of the sequestration. In other words, this theoretical study shows that it is crucial to analyse the composition and reactivity of potential storage sites to choose those that will be most efficient for long-term CO2 sequestration.

Stability of exact solutions describing two-layer flows with evaporation at the interface

NASA Astrophysics Data System (ADS)

Bekezhanova, V. B.; Goncharova, O. N.

2016-12-01

A new exact solution of the equations of free convection has been constructed in the framework of the Oberbeck-Boussinesq approximation of the Navier-Stokes equations. The solution describes the joint flow of an evaporating viscous heat-conducting liquid and gas-vapor mixture in a horizontal channel. In the gas phase the Dufour and Soret effects are taken into account. The consideration of the exact solution allows one to describe different classes of flows depending on the values of the problem parameters and boundary conditions for the vapor concentration. A classification of solutions and results of the solution analysis are presented. The effects of the external disturbing influences (of the liquid flow rates and longitudinal gradients of temperature on the channel walls) on the stability characteristics have been numerically studied for the system HFE7100-nitrogen in the common case, when the longitudinal temperature gradients on the boundaries of the channel are not equal. In the system both monotonic and oscillatory modes can be formed, which damp or grow depending on the values of the initial perturbations, flow rates and temperature gradients. Hydrodynamic perturbations are most dangerous under large gas flow rates. The increasing oscillatory perturbations are developed due to the thermocapillary effect under large longitudinal gradients of temperature. The typical forms of the disturbances are shown.

Vibration isolation technology: Sensitivity of selected classes of experiments to residual accelerations

NASA Technical Reports Server (NTRS)

Alexander, J. Iwan D.

1990-01-01

The solution was sought of a 2-D axisymmetric moving boundary problem for the sensitivity of isothermal and nonisothermal liquid columns and the sensitivity of thermo-capillary flows to buoyancy driven convection caused by residual accelerations. The sensitivity of a variety of space experiments to residual accelerations are examined. In all the cases discussed, the sensitivity is related to the dynamic response of a fluid. In some cases the sensitivity can be defined by the magnitude of the response of the velocity field. This response may involve motion of the fluid associated with internal density gradients, or the motion of a free liquid surface. For fluids with internal density gradients, the type of acceleration to which the experiment is sensitive will depend on whether buoyancy driven convection must be small in comparison to other types of fluid motion (such as thermocapillary flow), or fluid motion must be suppressed or eliminated (such as in diffusion studies, or directional solidification experiments). The effect of the velocity on the composition and temperature field must be considered, particularly in the vicinity of the melt crystal interface. As far as the response to transient disturbances is concerned the sensitivity is determined by both the magnitude and frequency the acceleration and the characteristic momentum and solute diffusion times.

Testing stellar evolution models with detached eclipsing binaries

NASA Astrophysics Data System (ADS)

Higl, J.; Weiss, A.

2017-12-01

Stellar evolution codes, as all other numerical tools, need to be verified. One of the standard stellar objects that allow stringent tests of stellar evolution theory and models, are detached eclipsing binaries. We have used 19 such objects to test our stellar evolution code, in order to see whether standard methods and assumptions suffice to reproduce the observed global properties. In this paper we concentrate on three effects that contain a specific uncertainty: atomic diffusion as used for standard solar model calculations, overshooting from convective regions, and a simple model for the effect of stellar spots on stellar radius, which is one of the possible solutions for the radius problem of M dwarfs. We find that in general old systems need diffusion to allow for, or at least improve, an acceptable fit, and that systems with convective cores indeed need overshooting. Only one system (AI Phe) requires the absence of it for a successful fit. To match stellar radii for very low-mass stars, the spot model proved to be an effective approach, but depending on model details, requires a high percentage of the surface being covered by spots. We briefly discuss improvements needed to further reduce the freedom in modelling and to allow an even more restrictive test by using these objects.

Three-dimensional convection of binary mixtures in porous media.

PubMed

Umla, R; Augustin, M; Huke, B; Lücke, M

2011-11-01

We investigate convection patterns of binary mixtures with a positive separation ratio in porous media. As setup, we choose the Rayleigh-Bénard system of a fluid layer heated from below. Results are obtained by a multimode Galerkin method. Using this method, we compute square and crossroll patterns, and we analyze their structural, bifurcation, and stability properties. Evidence is provided that, for a strong enough Soret effect, both structures exist as stable forms of convection. Some of their properties are found to be similar to square and crossroll convection in the system without porous medium. However, there are also qualitative differences. For example, squares can be destabilized by oscillatory perturbations with square symmetry in porous media, and their velocity isolines are deformed in the so-called Soret regime.

Double-diffusive layers in the Adriatic Sea

NASA Astrophysics Data System (ADS)

Carniel, Sandro; Sclavo, Mauro; Kantha, Lakshmi; Prandke, Hartmut

2008-01-01

A microstructure profiler was deployed to make turbulence measurements in the upper layers of the southern Adriatic Sea in the Mediterranean during the Naval Research Laboratory (NRL) DART06A (Dynamics of the Adriatic in Real Time) winter cruise in March 2006. Measurements in the Po river plume along the Italian coast near the Gargano promontory displayed classic double-diffusive layers and staircase structures resulting from the relatively colder and fresher wintertime Po river outflow water masses overlying warmer and more saline water masses from the Adriatic Sea. We report here on the water mass and turbulence structure measurements made both in the double-diffusive interfaces and the adjoining mixed layers in the water columns undergoing double-diffusive convection (DDC). This dataset augments the relatively sparse observations available hitherto on the diffusive layer type of DDC. Measured turbulence diffusivities are consistent with those from earlier theoretical and experimental formulations, suggesting that the wintertime Po river plume is a convenient and easily accessible place to study double diffusive convective processes of importance to mixing in the interior of many regions of the global oceans.

Convective Instability and Mass Transport of the Diffusion Layer in CO2 Sequestration

NASA Astrophysics Data System (ADS)

Backhaus, S.

2011-12-01

The long-term fate of supercritical (sc) CO2 in saline aquifers is critical to the security of carbon sequestration, an important option for eliminating or reducing the emissions of this most prevalent greenhouse gas. scCO2 is less dense than brine and floats to the top of the aquifer where it is trapped in a metastable state by a geologic feature such as a low permeability cap rock. Dissolution into the underlying brine creates a CO2-brine mixture that is denser than brine, eliminating buoyancy and removing the threat of CO2 escaping back to the atmosphere. If molecular diffusion were the only dissolution mechanism, the CO2 waste stream from a typical large coal-fired electrical power plant may take upward of 10,000 years to no longer pose a threat, however, a convective instability of the dense diffusion boundary layer between the scCO2 and the brine can dramatically increase the dissolution rates, shortening the lifetime of the scCO2 waste pool. We present results of 2D and 3D similitude-correct, laboratory-scale experiments using an analog fluid system. The experiments and flow visualization reveal the onset of the convective instability, the dynamics of the fluid flows during the convective processes, and the long-term mass transfer rates.

Buoyancy-driven instabilities around miscible A+B→C reaction fronts: a general classification.

PubMed

Trevelyan, P M J; Almarcha, C; De Wit, A

2015-02-01

Upon contact between miscible solutions of reactants A and B along a horizontal interface in the gravity field, various buoyancy-driven instabilities can develop when an A+B→C reaction takes place and the density varies with the concentrations of the various chemicals. To classify the possible convective instability scenarios, we analyze the spatial dependence of the large time asymptotic density profiles as a function of the key parameters of the problem, which are the ratios of diffusion coefficients and of solutal expansion coefficients of species A, B, and C. We find that 62 different density profiles can develop in the reactive problem, whereas only 6 of them can be obtained in the nonreactive one.

Thin Film Mediated Phase Change Phenomena: Crystallization, Evaporation and Wetting

NASA Technical Reports Server (NTRS)

Wettlaufer, John S.

1998-01-01

We focus on two distinct materials science problems that arise in two distinct microgravity environments: In space and within the space of a polymeric network. In the former environment, we consider a near eutectic alloy film in contact with its vapor which, when evaporating on earth, will experience compositionally induced buoyancy driven convection. The latter will significantly influence the morphology of the crystallized end member. In the absence of gravity, the morphology will be dominated by molecular diffusion and Marangoni driven viscous flow, and we study these phenomena theoretically and experimentally. The second microgravity environment exists in liquids, gels, and other soft materials where the small mass of individual molecules makes the effect of gravity negligible next to the relatively strong forces of intermolecular collisions. In such materials, an essential question concerns how to relate the molecular dynamics to the bulk rheological behavior. Here, we observe experimentally the diffusive motion of a single molecule in a single polymer filament, embedded within a polymer network and find anomalous diffusive behavior.

The Double ITCZ Syndrome in GCMs: A Coupled Problem among Convection, Atmospheric and Ocean Circulations

NASA Astrophysics Data System (ADS)

Zhang, G. J.; Song, X.

2017-12-01

The double ITCZ bias has been a long-standing problem in coupled atmosphere-ocean models. A previous study indicates that uncertainty in the projection of global warming due to doubling of CO2 is closely related to the double ITCZ biases in global climate models. Thus, reducing the double ITCZ biases is not only important to getting the current climate features right, but also important to narrowing the uncertainty in future climate projection. In this work, we will first review the possible factors contributing to the ITCZ problem. Then, we will focus on atmospheric convection, presenting recent progress in alleviating the double ITCZ problem and its sensitivity to details of convective parameterization, including trigger conditions for convection onset, convective memory, entrainment rate, updraft model and closure in the NCAR CESM1. These changes together can result in dramatic improvements in the simulation of ITCZ. Results based on both atmospheric only and coupled simulations with incremental changes of convection scheme will be shown to demonstrate the roles of convection parameterization and coupled interaction between convection, atmospheric circulation and ocean circulation in the simulation of ITCZ.

Convective diffusion in protein crystal growth

NASA Technical Reports Server (NTRS)

Baird, J. K.; Meehan, E. J., Jr.; Xidis, A. L.; Howard, S. B.

1986-01-01

A protein crystal modeled as a flat plate suspended in the parent solution, with the normal to the largest face perpendicular to gravity and the protein concentration in the solution adjacent to the plate taken to be the equilibrium solubility, is studied. The Navier-Stokes equation and the equation for convective diffusion in the boundary layer next to the plate are solved to calculate the flow velocity and the protein mass flux. The local rate of growth of the plate is shown to vary significantly with depth due to the convection. For an aqueous solution of lysozyme at a concentration of 40 mg/ml, the boundary layer at the top of a 1-mm-high crystal has a thickness of 80 microns at 1 g, and 2570 microns at 10 to the -6th g.

Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection at large Rayleigh numbers

NASA Astrophysics Data System (ADS)

Kozitskiy, Sergey

2018-06-01

Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection has been performed by using the previously derived system of complex Ginzburg-Landau type amplitude equations, valid in a neighborhood of Hopf bifurcation points. Simulation has shown that the state of spatiotemporal chaos develops in the system. It has the form of nonstationary structures that depend on the parameters of the system. The shape of structures does not depend on the initial conditions, and a limited number of spectral components participate in their formation.

Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection at large Rayleigh numbers

NASA Astrophysics Data System (ADS)

Kozitskiy, Sergey

2018-05-01

Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection has been performed by using the previously derived system of complex Ginzburg-Landau type amplitude equations, valid in a neighborhood of Hopf bifurcation points. Simulation has shown that the state of spatiotemporal chaos develops in the system. It has the form of nonstationary structures that depend on the parameters of the system. The shape of structures does not depend on the initial conditions, and a limited number of spectral components participate in their formation.

Convective stirring efficiency in strongly temperature-dependent, infinite Prandtl number fluids: application to planetary mantles.

NASA Astrophysics Data System (ADS)

Tosi, N.; Samuel, H.

2017-12-01

Many rocky planetary bodies currently exhibit solid-state convection, or have experienced this process during their histories.Such a style of convection is characterized by the negligible influence of inertia, and a rheology known to be strongly temperature-dependent. Convective motion within such planetary envelopes determine their ability to preserve or to homogenize compositional heterogeneities.Therefore, understanding the efficiency of convective stirring is key to the interpretation of petrological, geochemical, and cosmochemical data originating on the Earth from sampled erupted lava, or inferred from meteorite analysis (e.g., Mars). In order to study this problem we have conducted series of numerical experiments in 2D and 3D Cartesian domains heated from below and cooled from above. We varied systematically the Rayleigh number and the activation energy using a strongly temperature-dependent viscosity based on the Arrhenius law for diffusion creep. Given the large values of activation energy considered, all our experiments fall into the stagnant lid regime. Stirring efficiency is determined by computing the finite-time Lyapunov exponents, which provide a measure of the Lagrangian deformation.This systematic exploration allows the degree of heterogeneity and its spatial variability to be quantified, and yields mixing times for both 2D and 3D geometries.Our results indicate significant differences between geometries: 2D cases lead more frequently to steady solutions, for which stirring efficiency is spatially heterogeneous and mostly weak. On the other hand, 3D cases show more time dependence of the velocity field and generally yield more efficient convective stirring, even for cases with a weak time-dependence of the flow. Scaling laws for stirring efficiencies are derived, and will serve as a basis to discuss the application to planetary mantles.

Geochemistry of Dissolved Gases in the Hypersaline Orca Basin.

DTIC Science & Technology

1980-12-01

brine (",250%/o) is internally well mixed due to convective overturning, but transfer across the brine-sea water interface is controlled by- molecular ...diffusion. With a molecular diffusivity of l0-cm . sec- , it will take 10 years for all salts to diffuse fro’i-te-basin. Heat diffuses faster than salt...trolled by molecular diffusion. With a molecular diffusivity of 10 cm sec , it will take 10 years for all salts to diffuse from the basin. Heat diffuses

Extreme value statistics for two-dimensional convective penetration in a pre-main sequence star

NASA Astrophysics Data System (ADS)

Pratt, J.; Baraffe, I.; Goffrey, T.; Constantino, T.; Viallet, M.; Popov, M. V.; Walder, R.; Folini, D.

2017-08-01

Context. In the interior of stars, a convectively unstable zone typically borders a zone that is stable to convection. Convective motions can penetrate the boundary between these zones, creating a layer characterized by intermittent convective mixing, and gradual erosion of the density and temperature stratification. Aims: We examine a penetration layer formed between a central radiative zone and a large convection zone in the deep interior of a young low-mass star. Using the Multidimensional Stellar Implicit Code (MUSIC) to simulate two-dimensional compressible stellar convection in a spherical geometry over long times, we produce statistics that characterize the extent and impact of convective penetration in this layer. Methods: We apply extreme value theory to the maximal extent of convective penetration at any time. We compare statistical results from simulations which treat non-local convection, throughout a large portion of the stellar radius, with simulations designed to treat local convection in a small region surrounding the penetration layer. For each of these situations, we compare simulations of different resolution, which have different velocity magnitudes. We also compare statistical results between simulations that radiate energy at a constant rate to those that allow energy to radiate from the stellar surface according to the local surface temperature. Results: Based on the frequency and depth of penetrating convective structures, we observe two distinct layers that form between the convection zone and the stable radiative zone. We show that the probability density function of the maximal depth of convective penetration at any time corresponds closely in space with the radial position where internal waves are excited. We find that the maximal penetration depth can be modeled by a Weibull distribution with a small shape parameter. Using these results, and building on established scalings for diffusion enhanced by large-scale convective motions, we propose a new form for the diffusion coefficient that may be used for one-dimensional stellar evolution calculations in the large Péclet number regime. These results should contribute to the 321D link.

Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion

NASA Astrophysics Data System (ADS)

Lv, Yu; Ihme, Matthias

2014-08-01

This paper presents the development of a discontinuous Galerkin (DG) method for application to chemically reacting flows in subsonic and supersonic regimes under the consideration of variable thermo-viscous-diffusive transport properties, detailed and stiff reaction chemistry, and shock capturing. A hybrid-flux formulation is developed for treatment of the convective fluxes, combining a conservative Riemann-solver and an extended double-flux scheme. A computationally efficient splitting scheme is proposed, in which advection and diffusion operators are solved in the weak form, and the chemically stiff substep is advanced in the strong form using a time-implicit scheme. The discretization of the viscous-diffusive transport terms follows the second form of Bassi and Rebay, and the WENO-based limiter due to Zhong and Shu is extended to multicomponent systems. Boundary conditions are developed for subsonic and supersonic flow conditions, and the algorithm is coupled to thermochemical libraries to account for detailed reaction chemistry and complex transport. The resulting DG method is applied to a series of test cases of increasing physico-chemical complexity. Beginning with one- and two-dimensional multispecies advection and shock-fluid interaction problems, computational efficiency, convergence, and conservation properties are demonstrated. This study is followed by considering a series of detonation and supersonic combustion problems to investigate the convergence-rate and the shock-capturing capability in the presence of one- and multistep reaction chemistry. The DG algorithm is then applied to diffusion-controlled deflagration problems. By examining convergence properties for polynomial order and spatial resolution, and comparing these with second-order finite-volume solutions, it is shown that optimal convergence is achieved and that polynomial refinement provides advantages in better resolving the localized flame structure and complex flow-field features associated with multidimensional and hydrodynamic/thermo-diffusive instabilities in deflagration and detonation systems. Comparisons with standard third- and fifth-order WENO schemes are presented to illustrate the benefit of the DG scheme for application to detonation and multispecies flow/shock-interaction problems.

Convective diffusion of nanoparticles from the epithelial barrier toward regional lymph nodes.

PubMed

Dukhin, Stanislav S; Labib, Mohamed E

2013-11-01

Drug delivery using nanoparticles as drug carriers has recently attracted the attention of many investigators. Targeted delivery of nanoparticles to the lymph nodes is especially important to prevent cancer metastasis or infection, and to diagnose disease stage. However, systemic injection of nanoparticles often results in organ toxicity because they reach and accumulate in all the lymph nodes in the body. An attractive strategy would be to deliver the drug-loaded nanoparticles to a subset of draining lymph nodes corresponding to a specific site or organ to minimize systemic toxicity. In this respect, mucosal delivery of nanoparticles to regional draining lymph nodes of a selected site creates a new opportunity to accomplish this task with minimal toxicity. One example is the delivery of nanoparticles from the vaginal lumen to draining lymph nodes to prevent the transmission of HIV in women. Other known examples include mucosal delivery of vaccines to induce immunity. In all cases, molecular and particle transport by means of diffusion and convective diffusion play a major role. The corresponding transport processes have common inherent regularities and are addressed in this review. Here we use nanoparticle delivery from the vaginal lumen to the lymph nodes as an example to address the many aspects of associated transport processes. In this case, nanoparticles penetrate the epithelial barrier and move through the interstitium (tissue) to the initial lymphatics until they finally reach the lymph nodes. Since the movement of interstitial liquid near the epithelial barrier is retarded, nanoparticle transport was found to take place through special foci present in the epithelium. Immediately after nanoparticles emerge from the foci, they move through the interstitium due to diffusion affected by convection (convective diffusion). Specifically, the convective transport of nanoparticles occurs due to their convection together with interstitial fluid through the interstitium toward the initial lymph capillaries. Afterwards, nanoparticles move together with the lymph flow along the initial lymph capillaries and then enter the afferent lymphatics and ultimately reach the lymph node. As the liquid moves through the interstitium toward the initial lymph capillaries due to the axial movement of lymph along the lymphatics, the theory for coupling between lymph flow and concomitant flow through the interstitium is developed to describe this general case. The developed theory is applied to interpret the large uptake of Qdots by lymph nodes during inflammation, which is induced by pre-treating mouse vagina with the surfactant Nonoxynol-9 prior to instilling the Qdots. Inflammation is viewed here to cause broadening of the pores within the interstitium with the concomitant formation of transport channels which function as conduits to transport the nanoparticles to the initial lymph capillaries. We introduced the term "effective channels" to denote those channels which interconnect with foci present in the epithelial barrier and which function to transport nanoparticles to initial lymph capillaries. The time of transport toward the lymph node, predicated by the theory, increases rapidly with increasing the distance y0 between the epithelial barrier and the initial lymph capillaries. Transport time is only a few hours, when y0 is small, about some R (where R is the initial lymph capillary radius), due to the predomination of a rather rapid convection in this case. This transport time to the lymph nodes may be tens of hours (or longer) when y0 is essentially larger and the slow diffusion controls the transport rate in a zone not far from the epithelial barrier, where convection is weak at large y0. Accounting for transport by diffusion only, which is mainly considered in many relevant publications, is not sufficient to explain our nanoparticle uptake kinetics because the possibility of fast transport due to convection is overlooked. Our systematic investigations have revealed that the information about the main transport conditions, namely, y0 and the pore broadening up to the dimension of the interstitial transport channels, is necessary to create the quantitative model of enhanced transport during inflammation with the use of the proposed model as a prerequisite. The modeling for convective diffusion of nanoparticles from the epithelial barrier to the lymph node has been mainly accomplished here, while the diffusion only scenario is accounted for in other studies. This first modeling is a semi-quantitative one. A more rigorous mathematical approach is almost impossible at this stage because the transport properties of the model are introduced here for the first time. These properties include: discovery of foci in the epithelium, formation of transport channels, definition of channels interconnecting with foci (effective foci and channels), generation of flow in the interstitium toward the initial lymph capillaries due to axial flow within afferent lymphatics, deformation of this flow due to hydrodynamic impermeability of the squamous layer with the formation of the hydrodynamic stagnation zone near the epithelial barrier, predomination of slow diffusion transport within the above zone, and predomination of fast convection of nanoparticles near the initial lymph capillaries. Copyright © 2013 Elsevier B.V. All rights reserved.

Convective diffusion of nanoparticles from the epithelial barrier towards regional lymph nodes

PubMed Central

Dukhin, Stanislav S; Labib, Mohamed E.

2013-01-01

Drug delivery using nanoparticles as drug carriers has recently attracted the attention of many investigators. Targeted delivery of nanoparticles to lymph nodes is especially important to prevent cancer metastasis or infection, and to diagnose disease stage. However, systemic injection of nanoparticles often results in organ toxicity because they reach and accumulate in all the lymph nodes in the body. An attractive strategy would be to deliver the drug-loaded nanoparticles to a subset of draining lymph nodes corresponding to a specific site or organ to minimize systemic toxicity. In this respect, mucosal delivery of nanoparticles to regional draining lymph nodes of a selected site creates a new opportunity to accomplish this task with minimal toxicity. One example is the delivery of nanoparticles from the vaginal lumen to draining lymph nodes to prevent the transmission of HIV in women. Other known examples include mucosal delivery of vaccines to induce immunity. In all cases, molecular and particle transport by means of diffusion and convective diffusion play a major role. The corresponding transport processes have common inherent regularities and are addressed in this review. Here we use nanoparticles delivery from the vaginal lumen to lymph nodes as an example to address the many aspects of associated transport processes. In this case, nanoparticles penetrate the epithelial barrier and move through the interstitium (tissue) to the initial lymphatics until they finally reach the lymph nodes. Since the movement of interstitial liquid near the epithelial barrier is retarded, nanoparticles transport was found to take place through special foci present in the epithelium. Immediately after nanoparticles emerge from the foci, they move through the interstitium due to diffusion affected by convection (convective diffusion). Specifically, the convective transport of nanoparticles occurs due to their convection together with interstitial fluid through the interstitium towards the initial lymph capillaries. Afterwards, nanoparticles move together with the lymph flow along the initial lymph capillaries and then enter the afferent lymphatics and ultimately reach the lymph node. As the liquid moves through the interstitium towards the initial lymph capillaries due to the axial movement of lymph along the lymphatics, the theory for coupling between lymph flow and concomitant flow through the interstitium is developed to describe this general case. The developed theory is applied to interpret the large uptake of Qdots by lymph nodes during inflammation, which is induced by pre-treating mouse vagina with the surfactant Nonoxynol-9 prior to instilling the Qdots. Inflammation is viewed here to cause broadening of the pores within the interstitium with the concomitant formation of transport channels which function as conduits to transport the nanoparticles to the initial lymph capillaries. We introduced the term “effective channels” to denote those channels which interconnect with foci present in the epithelial barrier and which function to transport nanoparticles to initial lymph capillaries. The time of transport towards the lymph node, predicated by the theory, increases rapidly with increasing the distance y0 between the epithelial barrier and the initial lymph capillaries. Transport time is only a few hours, when y0 is small, about some R (where R is the initial lymph capillary radius), due to the predomination of a rather rapid convection in this case. This transport time to lymph nodes may be tens of hours (or longer) when y0 is essentially larger and the slow diffusion controls the transport rate in a zone not far from the epithelial barrier, where convection is weak at large y0. Accounting for transport by diffusion only, which is mainly considered in many relevant publications, is not sufficient to explain our nanoparticles uptake kinetics because the possibility of fast transport due to convection is overlooked. Our systematic investigations have revealed that the information about the main transport conditions, namely, y0 and the pore broadening up to the dimension of the interstitial transport channels, is necessary to create the quantitative model of enhanced transport during inflammation with the use of the proposed model as a prerequisite. The modeling for convective diffusion of nanoparticles from the epithelial barrier to the lymph node has been mainly accomplished here, while the diffusion only scenario is accounted for in other studies. This first modeling is a semi-quantitative one. A more rigorous mathematical approach is almost impossible at this stage because the transport properties of the model are introduced here for the first time. These properties include: discovery of foci in the epithelium, formation of transport channels, definition of channels interconnecting with foci (effective foci and channels), generation of flow in the interstitium towards the initial lymph capillaries due to axial flow within afferent lymphatics, deformation of this flow due to hydrodynamic impermeability of the squamous layer with the formation of the hydrodynamic stagnation zone near the epithelial barrier, predomination of slow diffusion transport within the above zone, and predomination of fast convection of nanoparticles near the initial lymph capillaries. PMID:23859221

Dependence of image quality on image operator and noise for optical diffusion tomography

NASA Astrophysics Data System (ADS)

Chang, Jenghwa; Graber, Harry L.; Barbour, Randall L.

1998-04-01

By applying linear perturbation theory to the radiation transport equation, the inverse problem of optical diffusion tomography can be reduced to a set of linear equations, W(mu) equals R, where W is the weight function, (mu) are the cross- section perturbations to be imaged, and R is the detector readings perturbations. We have studied the dependence of image quality on added systematic error and/or random noise in W and R. Tomographic data were collected from cylindrical phantoms, with and without added inclusions, using Monte Carlo methods. Image reconstruction was accomplished using a constrained conjugate gradient descent method. Result show that accurate images containing few artifacts are obtained when W is derived from a reference states whose optical thickness matches that of the unknown teste medium. Comparable image quality was also obtained for unmatched W, but the location of the target becomes more inaccurate as the mismatch increases. Results of the noise study show that image quality is much more sensitive to noise in W than in R, and the impact of noise increase with the number of iterations. Images reconstructed after pure noise was substituted for R consistently contain large peaks clustered about the cylinder axis, which was an initially unexpected structure. In other words, random input produces a non- random output. This finding suggests that algorithms sensitive to the evolution of this feature could be developed to suppress noise effects.

Lagrangian chaos in three- dimensional steady buoyancy-driven flows

NASA Astrophysics Data System (ADS)

Contreras, Sebastian; Speetjens, Michel; Clercx, Herman

2016-11-01

Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry. Buoyancy-driven flows are prototypical systems in the study of thermal instabilities and pattern formation. The differentially heated cavity problem has been widely studied for the investigation of buoyancy-induced oscillatory flow. However, far less attention has been devoted to the three-dimensional Lagrangian transport properties in such flows. This study seeks to address this by investigating Lagrangian transport in the steady flow inside a cubic cavity differentially-heated from the side. The theoretical and numerical analysis expands on previously reported similarities between the current flow and lid-driven flows. The Lagrangian dynamics are controlled by the Péclet number (Pe) and the Prandtl number (Pr). Pe controls the behaviour qualitatively in that growing Pe progressively perturbs the integable state (Pe =0), thus paving the way to chaotic dynamics. Pr plays an entirely quantitative role in that Pr<1 and Pr>1 amplifies and diminishes, respectively, the perturbative effect of non-zero Pe. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).

The study of the Boltzmann equation of solid-gas two-phase flow with three-dimensional BGK model

NASA Astrophysics Data System (ADS)

Liu, Chang-jiang; Pang, Song; Xu, Qiang; He, Ling; Yang, Shao-peng; Qing, Yun-jie

2018-06-01

The motion of many solid-gas two-phase flows can be described by the Boltzmann equation. In order to simplify the Boltzmann equation, the convective-diffusion term is reserved and the collision term is replaced by the three-dimensional Bharnagar-Gross-Krook (BGK) model. Then the simplified Boltzmann equation is solved by homotopy perturbation method (HPM), and its approximate analytical solution is obtained. Through the analyzing, it is proved that the analytical solution satisfies all the constraint conditions, and its formation is in accord with the formation of the solution that is obtained by traditional Chapman-Enskog method, and the solving process of HPM is much more simple and convenient. This preliminarily shows the effectiveness and rapidness of HPM to solve the Boltzmann equation. The results obtained herein provide some theoretical basis for the further study of dynamic model of solid-gas two-phase flows, such as the sturzstrom of high-speed distant landslide caused by microseism and the sand storm caused by strong breeze.

Influence of Mercury

NASA Astrophysics Data System (ADS)

Tackley, P. J.; Aurnou, J. M.; Aubert, J.

2009-04-01

Due to the absence of an atmosphere and proximity to the Sun, Mercury's surface temperature varies laterally by several 100s K, even when averaged over long time periods. The dominant variation in time-averaged surface T occurs from pole to equator (~225 K) [1]. The resonant relationship between Mercury's orbit and rotation results in a smaller longitudinal variation (~100 K) [1]. Here we demonstrate, using models of mantle convection in a 3-D spherical shell, that this stationary lateral variation in surface temperature has a small but significant influence on mantle convection and on the lateral variation of heat flux across the core-mantle boundary (CMB). We evaluate the possible observational signature of this laterally-varying convection in terms of boundary topography, stress distribution, gravity and moment of inertia tensor. We furthermore test whether the lateral variation in CMB flux is capable of driving a thermal wind dynamo, i.e., weak dynamo action with no internally-driven core convective motions. For Mercury's mantle we assume a dry olivine rheology including both diffusion creep and disclocation creep with rheological parameters such as activation energy and volume taken from the synthesis of [2]. We assume decaying radiogenic heat sources with the same concentration as in the bulk silicate Earth, and a parameterised model of core cooling. The models are run for 4.5 Ga from a relatively hot initial state with random initial perturbations. We use the code StagYY, which uses a finite-volume discretization on a spherical yin-yang grid and a multigrid solver [3]. Results in spherical axisymmetric geometry, compare a case with constant surface temperature to one with a latitude-dependent surface temperature. The system forms about 3 convection cells from pole to equator. Although the results look similar to first order, in the latitude-dependent case the convection is noticably more sluggish and colder towards the pole. In CMB flux, both cases display large oscillations due to convection cells. A pole-to-equator trend is superimposed on this for the case with laterally-varying surface temperature. Although the amplitude of this long-wavelength variation is smaller than that of the within-cell variation, its long-wavelength nature might be effective in driving thermal winds in the core. Results in a full 3-D spherical shell indicate that convection adopts a cellular structure with a polygonal network of downwellings and plume-like upwellings, as is usually obtained for stagnant lid convection, for example, in the recent 3-D spherical Mercury models of [4]. This is in notable contrast to the models of [5], in which linear upwellings were obtained. This difference could be because the initial perturbations used by [5] used a small number of low-order spherical harmonics, i.e., a long-wavelength pattern with particular symmetries, whereas our initial perturbations are random white noise. The origin of this difference requires further investigation. The pattern of CMB heat flux shows a strong l=2, m=0 pattern, again with superimposed small-scale variations due to convection cells. The surface geoid displays an very dominant (2,0) pattern, which would be a strong diagnostic of this behaviour. These models are being further analysed for boundary topography and stress distribution. Models of planetary dynamos have traditionally depended upon the concept that secular cooling and internal radioactive decay are responsible for genererating convective fluid motions within the core [e.g. 6]. Some models, of Earth's dynamo in particular, also include thermal winds --shear flows driven by heat flux variations along the core-mantle boundary -- that modify the dynamo process [e.g. 7]. We have now shown, following the work of [8], that thermal winds themselves are capable of driving dynamo action in planetary cores (Fig. 4). In fully self-consistent, three-dimensional models, we find that thermal wind dynamos do not require a net heat flux to emanate from the core and can operate even when the core fluid is neutrally stratified. In these models, the dynamo is powered externally by thermal energy stored in the mantle. This dynamo mechanism can occur on planetary bodies, such as Mercury, which are likely to have weak net heat fluxes from their cores but possess significant core-mantle boundary heat flux variations (Figures 1 - 3). We plan to use the pattern of CMB heat flux from the mantle models as a boundary condition for core models, in order to determine the feasibility of thermal wind dynamo action occurring in Mercury's core. References [1] Aharonson, O., et al. (2004) EPSL, 218, 261-268. [2] Karato, S. and Wu, P. (1993) Sci., 260, 771-778. [3] Tackley, P. J. (2008) PEPI, doi: 10.1016/j.pepi.2008.08.005.. [4] Breuer, D. et al. (2007) Sp. Sci. Rev., 132, 229-260. [5] King, S. D. (2008) Nature Geoscience, 1, 229-232. [5] Heimpel, M. H. et al. (2005) EPSL, 236, 542-557. [7] Willis, A., et al. (2007) PEPI, 165, 83-92. [8] Sarson, G., (2003) PRSL A, 459, 1241-1259. [9] Aubert, J., et al. (2008) GJI, 172, 945-956.

Simulation of moving flat plate with unsteady translational motion using vortex method

NASA Astrophysics Data System (ADS)

Widodo, A. F.; Zuhal, L. R.

2013-10-01

This paper presents simulation of moving flate plate with unsteady translational motion using Lagrangianmeshless numerical simulation named vortex method. The method solves Navier-Stokes equations in term of vorticity. The solving strategy is splitting the equation into diffusion and convection term to be solved separately. The diffusion term is modeled by particles strength exchange(PSE) which is the most accurate of diffusion modeling in vortex method. The convection term that represents transport of particles is calculated by time step integration of velocity. Velocity of particles is natively calculated using Biot-Savart relation but for acceleration, fastmultiple method(FMM) is employed. The simulation is validated experimentally using digital particle image velocimetry(DPIV) and the results give good agreement.

Monte Carlo PDF method for turbulent reacting flow in a jet-stirred reactor

NASA Astrophysics Data System (ADS)

Roekaerts, D.

1992-01-01

A stochastic algorithm for the solution of the modeled scalar probability density function (PDF) transport equation for single-phase turbulent reacting flow is described. Cylindrical symmetry is assumed. The PDF is represented by ensembles of N representative values of the thermochemical variables in each cell of a nonuniform finite-difference grid and operations on these elements representing convection, diffusion, mixing and reaction are derived. A simplified model and solution algorithm which neglects the influence of turbulent fluctuations on mean reaction rates is also described. Both algorithms are applied to a selectivity problem in a real reactor.

Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Soh, Woo Y.

1992-01-01

A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.

Decreases in maximal oxygen uptake following long-duration spaceflight: Role of convective and diffusive O2 transport mechanisms.

PubMed

Ade, C J; Broxterman, R M; Moore, A D; Barstow, T J

2017-04-01

We have previously predicted that the decrease in maximal oxygen uptake (V̇o 2max ) that accompanies time in microgravity reflects decrements in both convective and diffusive O 2 transport to the mitochondria of the contracting myocytes. The aim of this investigation was therefore to quantify the relative changes in convective O 2 transport (Q̇o 2 ) and O 2 diffusing capacity (Do 2 ) following long-duration spaceflight. In nine astronauts, resting hemoglobin concentration ([Hb]), V̇o 2max , maximal cardiac output (Q̇ Tmax ), and differences in arterial and venous O 2 contents ([Formula: see text]-[Formula: see text]) were obtained retrospectively for International Space Station Increments 19-33 (April 2009-November 2012). Q̇o 2 and Do 2 were calculated from these variables via integration of Fick's Principle of Mass Conservation and Fick's Law of Diffusion. V̇o 2max significantly decreased from pre- to postflight (-53.9 ± 45.5%, P = 0.008). The significant decrease in Q̇ Tmax (-7.8 ± 9.1%, P = 0.05), despite an unchanged [Hb], resulted in a significantly decreased Q̇o 2 (-11.4 ± 10.5%, P = 0.02). Do 2 significantly decreased from pre- to postflight by -27.5 ± 24.5% ( P = 0.04), as did the peak [Formula: see text]-[Formula: see text] (-9.2 ± 7.5%, P = 0.007). With the use of linear regression analysis, changes in V̇o 2max were significantly correlated with changes in Do 2 ( R 2  = 0.47; P = 0.04). These data suggest that spaceflight decreases both convective and diffusive O 2 transport. These results have practical implications for future long-duration space missions and highlight the need to resolve the specific mechanisms underlying these spaceflight-induced changes along the O 2 transport pathway. NEW & NOTEWORTHY Long-duration spaceflight elicited a significant decrease in maximal oxygen uptake. Given the adverse physiological adaptations to microgravity along the O 2 transport pathway that have been reported, an integrative approach to the determinants of postflight maximal oxygen uptake is needed. We demonstrate that both convective and diffusive oxygen transport are decreased following ~6 mo International Space Station missions. Copyright © 2017 the American Physiological Society.

Melt Stabilization of PbSnTe in a Magnetic Field

NASA Technical Reports Server (NTRS)

Fripp, Archibald L.; Debnam, William J.; Rosch, William; Chait, Arnon; Yao, Minwu; Szofran, Frank R.

1999-01-01

Both the experimental observation and numerical simulation indicate that the Bridgman growth of PbSnTe under the microgravity environment in space is still greatly influenced by buoyancy-induced convection. The application of a magnetic field during the semiconductor growth can dampen the convective flow in the metal-like melt. However, for Bridgman growth of PbSnTe on earth (with either vertical or horizontal configuration), both experimental observation and numerical modeling suggest that even with a strong magnetic furnace (5-Tesla constant axial magnetic field), the convective flow in the melt still cannot be sufficiently suppressed to reach the diffusion-controlled level. In order to completely dampen the buoyancy-induced convection on earth, estimates based on scaling analysis indicate that for common experimental conditions, an extremely high magnetic field is required, far beyond the capacity of the experimental apparatus currently available. Therefore, it is proposed that only the combination of microgravity environment and magnetic damping will produce the desired diffusion-controlled growth state for this particular material. The primary objectives of this study are to provide a quantitative understanding of the complex transport phenomena during solidification of non-dilute binarys, to furnish a numerical tool for furnace design and growth condition optimization, to provide estimates of the required magnetic field strength for low gravity growth, and to assess the role of magnetic damping for space and earth control of the double-diffusive convection. As an integral part of a NASA research program, our numerical simulation supports both the flight and ground-based experiments in an effort to bring together a complete picture of the complex physical phenomena involved in the crystal growth process. For Bridgman growth of PbSnTe under microgravity (with both vertical and horizontal configurations), the simulations suggest that a moderate axial magnetic field of only a few kilo-Gauss in strength could effectively eliminate buoyancy-induced convection in the melt and control solute segregation. Therefore, this work confirms the idea that the combination of microgravity environment and the magnetic damping will indeed be sufficient to produce the desired diffusion-controlled growth state for PbSnTe.

Establishing the diffuse correlation spectroscopy signal relationship with blood flow.

PubMed

Boas, David A; Sakadžić, Sava; Selb, Juliette; Farzam, Parisa; Franceschini, Maria Angela; Carp, Stefan A

2016-07-01

Diffuse correlation spectroscopy (DCS) measurements of blood flow rely on the sensitivity of the temporal autocorrelation function of diffusively scattered light to red blood cell (RBC) mean square displacement (MSD). For RBCs flowing with convective velocity [Formula: see text], the autocorrelation is expected to decay exponentially with [Formula: see text], where [Formula: see text] is the delay time. RBCs also experience shear-induced diffusion with a diffusion coefficient [Formula: see text] and an MSD of [Formula: see text]. Surprisingly, experimental data primarily reflect diffusive behavior. To provide quantitative estimates of the relative contributions of convective and diffusive movements, we performed Monte Carlo simulations of light scattering through tissue of varying vessel densities. We assumed laminar vessel flow profiles and accounted for shear-induced diffusion effects. In agreement with experimental data, we found that diffusive motion dominates the correlation decay for typical DCS measurement parameters. Furthermore, our model offers a quantitative relationship between the RBC diffusion coefficient and absolute tissue blood flow. We thus offer, for the first time, theoretical support for the empirically accepted ability of the DCS blood flow index ([Formula: see text]) to quantify tissue perfusion. We find [Formula: see text] to be linearly proportional to blood flow, but with a proportionality modulated by the hemoglobin concentration and the average blood vessel diameter.

Plasma convection and ion beam generation in the plasma sheet boundary layer

NASA Technical Reports Server (NTRS)

Moghaddam-Taaheri, E.; Goertz, C. K.; Smith, R. A.

1991-01-01

Because of the dawn-dusk electric field E(dd), plasma in the magnetotail convects from the lobe toward the central plasma sheet (CPS). In the absence of space or velocity diffusion due to plasma turbulence, convection would yield a steady state distribution function f = V exp (-2/3) g(v exp 2 V exp 2/3), where V is the flux tube volume. Starting with such a distribution function and a plasma beta which varies from beta greater than 1 in the CPS to beta much smaller than 1 in the lobe, the evolution of the ion distribution function was studied considering the combined effects of ion diffusion by kinetic Alfven waves (KAW) in the ULF frequency range (1-10 mHz) and convection due to E(dd) x B drift in the plasma sheet boundary layer (PSBL) and outer central plasma sheet (OCPS). The results show that, during the early stages after launching the KAWs, a beamlike ion distribution forms in the PSBL and at the same time the plasma density and temperature decrease in the OCPS. Following this stage, ions in the beams convect toward the CPS resulting in an increase of the plasma temperature in the OCPS.

Convection and reaction in a diffusive boundary layer in a porous medium: nonlinear dynamics.

PubMed

Andres, Jeanne Therese H; Cardoso, Silvana S S

2012-09-01

We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

ADOPT: A tool for automatic detection of tectonic plates at the surface of convection models

NASA Astrophysics Data System (ADS)

Mallard, C.; Jacquet, B.; Coltice, N.

2017-08-01

Mantle convection models with plate-like behavior produce surface structures comparable to Earth's plate boundaries. However, analyzing those structures is a difficult task, since convection models produce, as on Earth, diffuse deformation and elusive plate boundaries. Therefore we present here and share a quantitative tool to identify plate boundaries and produce plate polygon layouts from results of numerical models of convection: Automatic Detection Of Plate Tectonics (ADOPT). This digital tool operates within the free open-source visualization software Paraview. It is based on image segmentation techniques to detect objects. The fundamental algorithm used in ADOPT is the watershed transform. We transform the output of convection models into a topographic map, the crest lines being the regions of deformation (plate boundaries) and the catchment basins being the plate interiors. We propose two generic protocols (the field and the distance methods) that we test against an independent visual detection of plate polygons. We show that ADOPT is effective to identify the smaller plates and to close plate polygons in areas where boundaries are diffuse or elusive. ADOPT allows the export of plate polygons in the standard OGR-GMT format for visualization, modification, and analysis under generic softwares like GMT or GPlates.

Interactions between solidification and compositional convection in mushy layers

NASA Technical Reports Server (NTRS)

Worster, M. Grae

1994-01-01

Mushy layers are ubiquitous during the solidification of alloys. They are regions of mixed phase wherein solid crystals are bathed in the melt from which they grew. The matrix of crystals forms a porous medium through which the melt can flow, driven either by external forces or by its own buoyancy in a gravitational field. Buoyancy-driven convection of the melt depends both on temperature gradients, which are necessary for solidification, and on compositional gradients, which are generated as certain components of the alloy are preferentially incorporated in the solid phase and the remaining components are expelled into the melt. In fully liquid regions, the combined action of temperature and concentration on the density of the liquid can cause various forms of double-diffusive convection. However, in the interior of mushy regions the temperature and concentration are thermodynamically coupled so only single-diffusive convection can occur. Typically, the effect of composition on the buoyancy of the melt is much greater than the effect of temperature, and thus convection in mushy layers in driven primarily by the computational gradients within them. The rising interstitial liquid is relatively dilute, having come from colder regions of the mushy layer, where the liquidus concentration is lower, and can dissolve the crystal matrix through which it flows. This is the fundamental process by which chimneys are formed. It is a nonlinear process that requires the convective velocities to be sufficiently large, so fully fledged chimneys (narrow channels) might be avoided by means that weaken the flow. Better still would be to prevent convection altogether, since even weak convection will cause lateral, compositional inhomogeneities in castings. This report outlines three studies that examine the onset of convection within mushy layers.

Applying horizontal diffusion on pressure surface to mesoscale models on terrain-following coordinates

Treesearch

Hann-Ming Henry Juang; Ching-Teng Lee; Yongxin Zhang; Yucheng Song; Ming-Chin Wu; Yi-Leng Chen; Kevin Kodama; Shyh-Chin Chen

2005-01-01

The National Centers for Environmental Prediction regional spectral model and mesoscale spectral model (NCEP RSM/MSM) use a spectral computation on perturbation. The perturbation is defined as a deviation between RSM/MSM forecast value and their outer model or analysis value on model sigma-coordinate surfaces. The horizontal diffusion used in the models applies...

Implementation of a diffusion convection surface evolution model in WallDYN

NASA Astrophysics Data System (ADS)

Schmid, K.

2013-07-01

In thermonuclear fusion experiments with multiple plasma facing materials the formation of mixed materials is inevitable. The formation of these mixed material layers is a dynamic process driven the tight interaction between transport in the plasma scrape off layer and erosion/(re-) deposition at the surface. To track this global material erosion/deposition balance and the resulting formation of mixed material layers the WallDYN code has been developed which couples surface processes and plasma transport. The current surface model in WallDYN cannot fully handle the growth of layers nor does it include diffusion. However at elevated temperatures diffusion is a key process in the formation of mixed materials. To remedy this shortcoming a new surface model has been developed which, for the first time, describes both layer growth/recession and diffusion in a single continuous diffusion/convection equation. The paper will detail the derivation of the new surface model and compare it to TRIDYN calculations.

Turbulence in core-collapse supernovae

NASA Astrophysics Data System (ADS)

Radice, David; Abdikamalov, Ernazar; Ott, Christian D.; Mösta, Philipp; Couch, Sean M.; Roberts, Luke F.

2018-05-01

Multidimensional simulations show that non-radial, turbulent, fluid motion is a fundamental component of the core-collapse supernova explosion mechanism. Neutrino-driven convection, the standing accretion shock instability, and relic-perturbations from advanced nuclear burning stages can all impact the outcome of core collapse in a qualitative and quantitative way. Here, we review the current understanding of these phenomena and their role in the explosion of massive stars. We also discuss the role of protoneutron star convection and of magnetic fields in the context of the delayed neutrino mechanism.

Comment on "Electromagnetic convective cells in a nonuniform dusty plasma".

PubMed

Shukla, P K; Stenflo, L; Pokhotelov, O A; Onishchenko, O G

2001-04-01

Recently, Saleem and Haque [Phys. Rev. E 60, 7612 (1999)] concluded that in the presence of a perturbed electron current parallel to an external magnetic field, the dispersion relation of the electrostatic convective cell and the magnetostatic modes is not modified. In the present Comment, the properties of electromagnetic as well as electrostatic waves in a nonuniform dusty magnetoplasma are reexamined, to demonstrate that Eq. (13) of the paper by Saleem and Haque as well as their conclusions are erroneous.

Applying an economical scale-aware PDF-based turbulence closure model in NOAA NCEP GCMs

NASA Astrophysics Data System (ADS)

Belochitski, A.; Krueger, S. K.; Moorthi, S.; Bogenschutz, P.; Pincus, R.

2016-12-01

A novel unified representation of sub-grid scale (SGS) turbulence, cloudiness, and shallow convection is being implemented into the NOAA NCEP Global Forecasting System (GFS) general circulation model. The approach, known as Simplified High Order Closure (SHOC), is based on predicting a joint PDF of SGS thermodynamic variables and vertical velocity and using it to diagnose turbulent diffusion coefficients, SGS fluxes, condensation and cloudiness. Unlike other similar methods, only one new prognostic variable, turbulent kinetic energy (TKE), needs to be intoduced, making the technique computationally efficient.SHOC is now incorporated into a version of GFS, as well as into the next generation of the NCEP global model - NOAA Environmental Modeling System (NEMS). Turbulent diffusion coefficients computed by SHOC are now used in place of those produced by the boundary layer turbulence and shallow convection parameterizations. Large scale microphysics scheme is no longer used to calculate cloud fraction or the large-scale condensation/deposition. Instead, SHOC provides these variables. Radiative transfer parameterization uses cloudiness computed by SHOC.Outstanding problems include high level tropical cloud fraction being too high in SHOC runs, possibly related to the interaction of SHOC with condensate detrained from deep convection.Future work will consist of evaluating model performance and tuning the physics if necessary, by performing medium-range NWP forecasts with prescribed initial conditions, and AMIP-type climate tests with prescribed SSTs. Depending on the results, the model will be tuned or parameterizations modified. Next, SHOC will be implemented in the NCEP CFS, and tuned and evaluated for climate applications - seasonal prediction and long coupled climate runs. Impact of new physics on ENSO, MJO, ISO, monsoon variability, etc will be examined.

Convective dissolution of carbon dioxide in saline aquifers

NASA Astrophysics Data System (ADS)

Neufeld, Jerome A.; Hesse, Marc A.; Riaz, Amir; Hallworth, Mark A.; Tchelepi, Hamdi A.; Huppert, Herbert E.

2010-11-01

Geological carbon dioxide (CO2) storage is a means of reducing anthropogenic emissions. Dissolution of CO2 into the brine, resulting in stable stratification, increases storage security. The dissolution rate is determined by convection in the brine driven by the increase of brine density with CO2 saturation. We present a new analogue fluid system that reproduces the convective behaviour of CO2-enriched brine. Laboratory experiments and high-resolution numerical simulations show that the convective flux scales with the Rayleigh number to the 4/5 power, in contrast with a classical linear relationship. A scaling argument for the convective flux incorporating lateral diffusion from downwelling plumes explains this nonlinear relationship for the convective flux, provides a physical picture of high Rayleigh number convection in a porous medium, and predicts the CO2 dissolution rates in CO2 accumulations. These estimates of the dissolution rate show that convective dissolution can play an important role in enhancing storage security.

Self-propulsion of a planar electric or magnetic microbot immersed in a polar viscous fluid

NASA Astrophysics Data System (ADS)

Felderhof, B. U.

2011-05-01

A planar sheet immersed in an electrically polar liquid like water can propel itself by means of a plane wave charge density propagating in the sheet. The corresponding running electric wave polarizes the fluid and causes an electrical torque density to act on the fluid. The sheet is convected by the fluid motion resulting from the conversion of rotational particle motion, generated by the torque density, into translational fluid motion by the mechanism of friction and spin diffusion. Similarly, a planar sheet immersed in a magnetic ferrofluid can propel itself by means of a plane wave current density in the sheet and the torque density acting on the fluid corresponding to the running wave magnetic field and magnetization. The effect is studied on the basis of the micropolar fluid equations of motion and Maxwell’s equations of electrostatics or magnetostatics, respectively. An analytic expression is derived for the velocity of the sheet by perturbation theory to second order in powers of the amplitude of the driving charge or current density. Under the assumption that the equilibrium magnetic equation of state may be used in linearized form and that higher harmonics than the first may be neglected, a set of self-consistent integral equations is derived which can be solved numerically by iteration. In typical situations the second-order perturbation theory turns out to be quite accurate.

Fluid flow and convective transport of solutes within the intervertebral disc.

PubMed

Ferguson, Stephen J; Ito, Keita; Nolte, Lutz P

2004-02-01

Previous experimental and analytical studies of solute transport in the intervertebral disc have demonstrated that for small molecules diffusive transport alone fulfils the nutritional needs of disc cells. It has been often suggested that fluid flow into and within the disc may enhance the transport of larger molecules. The goal of the study was to predict the influence of load-induced interstitial fluid flow on mass transport in the intervertebral disc. An iterative procedure was used to predict the convective transport of physiologically relevant molecules within the disc. An axisymmetric, poroelastic finite-element structural model of the disc was developed. The diurnal loading was divided into discrete time steps. At each time step, the fluid flow within the disc due to compression or swelling was calculated. A sequentially coupled diffusion/convection model was then employed to calculate solute transport, with a constant concentration of solute being provided at the vascularised endplates and outer annulus. Loading was simulated for a complete diurnal cycle, and the relative convective and diffusive transport was compared for solutes with molecular weights ranging from 400 Da to 40 kDa. Consistent with previous studies, fluid flow did not enhance the transport of low-weight solutes. During swelling, interstitial fluid flow increased the unidirectional penetration of large solutes by approximately 100%. Due to the bi-directional temporal nature of disc loading, however, the net effect of convective transport over a full diurnal cycle was more limited (30% increase). Further study is required to determine the significance of large solutes and the timing of their delivery for disc physiology.

Mass transfer characteristics during convective, microwave and combined microwave-convective drying of lemon slices.

PubMed

Sadeghi, Morteza; Mirzabeigi Kesbi, Omid; Mireei, Seyed Ahmad

2013-02-01

The investigation of drying kinetics and mass transfer phenomena is important for selecting optimum operating conditions, and obtaining a high quality dried product. Two analytical models, conventional solution of the diffusion equation and the Dincer and Dost model, were used to investigate mass transfer characteristics during combined microwave-convective drying of lemon slices. Air temperatures of 50, 55 and 60 °C, and specific microwave powers of 0.97 and 2.04 W g(-1) were the process variables. Kinetics curves for drying indicated one constant rate period followed by one falling rate period in convective and microwave drying methods, and only one falling rate period with the exception of a very short accelerating period at the beginning of microwave-convective treatments. Applying the conventional method, the effective moisture diffusivity varied from 2.4 × 10(-11) to 1.2 × 10(-9) m(2) s(-1). The Biot number, the moisture transfer coefficient, and the moisture diffusivity, respectively in the ranges of 0.2 to 3.0 (indicating simultaneous internal and external mass transfer control), 3.7 × 10(-8) to 4.3 × 10(-6) m s(-1), and 2.2 × 10(-10) to 4.2 × 10(-9) m(2) s(-1) were also determined using the Dincer and Dost model. The higher degree of prediction accuracy was achieved by using the Dincer and Dost model for all treatments. Therefore, this model could be applied as an effective tool for predicting mass transfer characteristics during the drying of lemon slices. Copyright © 2012 Society of Chemical Industry.

Interacting Convective Processes in Kilauea Iki Lava Lake, Hawaii

NASA Astrophysics Data System (ADS)

Helz, R. T.

2007-12-01

Kilauea Iki lava lake formed in 1959 as a closed magma chamber of 40 million m3 of picritic magma. Repeated drilling and sampling of the lake allows recognition of processes of magmatic differentiation, and places time restrictions on the periods when they operated. Two processes, double-diffusive convection and finger diapirism, occurred because melt density decreases as olivine crystallization and re-equilibration proceeds, until after plagioclase begins to crystallize. Finger diapirism, described in previous work, occurred from 1961 to 1971 and affected most the lava lake between depths of 13 to 94 m. The period of inferred double- diffusive convection occurred between mid-1962 and 1964 and affected only the most olivine-poor part of the lava lake. Recent re-evaluation of petrographic and chemical data refine our understanding of this second process. The overall variation of bulk MgO content with depth in Kilauea Iki is an S-curve, consistent with gravitative redistribution of the abundant olivine phenocrysts present in the erupted lava. The olivine-poor zone (MgO <11 weight percent) is a sill-like volume found between depths of 21 to 43 m in the lake. This zone is bisected by a median layer containing more and slightly coarser olivine phenocrysts, which has an MgO content 2 weight percent higher than the minimum in the layers above and below. This configuration, not achievable by gravitative settling, suggests that the olivine-poor zone at some point contained a two-layer convective system. The upper and median layers of the olivine-poor zone contain a sparse population of augite microphenocrysts (0.2-0.4 mm in length), often in monomineralic clusters (1-3 mm in length), while the lower layer contains only olivine. Plagioclase and other phases occur only in the groundmass in all samples. If the layers developed before groundmass crystallization began, then the assemblage in the upper layer was olivine + augite, and was olivine-only in the lower. Because melt density decreases as temperature decreases in this part of the crystallization range and because the lava lake was strongly cooled from above, the conditions for double- diffusive convection, with splitting of the melt column into layers, were met. Core samples and temperature data obtained by drilling the lake in mid-1962 and late 1967 constrain the period of double-diffusive convection to the first half of that period. The process ceased without shifting the position of the median olivine-enriched layer downward, suggesting that it was very brief. Finger diapirism, already active in Kilauea Iki, was volumetrically more important, and passed through both layers. This overlapping process may have ended the broader convective process by reducing the thermal gradient that drove it. Although double- diffusive convection was a minor process in Kilauea Iki, it did occur in this closed magma system.

Ensemble superparameterization versus stochastic parameterization: A comparison of model uncertainty representation in tropical weather prediction

NASA Astrophysics Data System (ADS)

Subramanian, Aneesh C.; Palmer, Tim N.

2017-06-01

Stochastic schemes to represent model uncertainty in the European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble prediction system has helped improve its probabilistic forecast skill over the past decade by both improving its reliability and reducing the ensemble mean error. The largest uncertainties in the model arise from the model physics parameterizations. In the tropics, the parameterization of moist convection presents a major challenge for the accurate prediction of weather and climate. Superparameterization is a promising alternative strategy for including the effects of moist convection through explicit turbulent fluxes calculated from a cloud-resolving model (CRM) embedded within a global climate model (GCM). In this paper, we compare the impact of initial random perturbations in embedded CRMs, within the ECMWF ensemble prediction system, with stochastically perturbed physical tendency (SPPT) scheme as a way to represent model uncertainty in medium-range tropical weather forecasts. We especially focus on forecasts of tropical convection and dynamics during MJO events in October-November 2011. These are well-studied events for MJO dynamics as they were also heavily observed during the DYNAMO field campaign. We show that a multiscale ensemble modeling approach helps improve forecasts of certain aspects of tropical convection during the MJO events, while it also tends to deteriorate certain large-scale dynamic fields with respect to stochastically perturbed physical tendencies approach that is used operationally at ECMWF.