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Sample records for algebraic eddy viscosity

  1. Anisotropic eddy viscosity models

    NASA Technical Reports Server (NTRS)

    Carati, D.; Cabot, W.

    1996-01-01

    A general discussion on the structure of the eddy viscosity tensor in anisotropic flows is presented. The systematic use of tensor symmetries and flow symmetries is shown to reduce drastically the number of independent parameters needed to describe the rank 4 eddy viscosity tensor. The possibility of using Onsager symmetries for simplifying further the eddy viscosity is discussed explicitly for the axisymmetric geometry.

  2. Ekman Spiral in Horizontally Inhomogeneous Ocean with Varying Eddy Viscosity

    DTIC Science & Technology

    2015-01-01

    1 Ekman Spiral in Horizontally Inhomogeneous Ocean with Varying Eddy Viscosity ...in Horizontally Inhomogeneous Ocean with Varying Eddy Viscosity 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d...generated by surface wind stress with constant eddy viscosity in homogeneous ocean. In real oceans, the eddy viscosity varies due to turbulent mixing

  3. A dynamic subgrid-scale eddy viscosity model

    NASA Technical Reports Server (NTRS)

    Germano, Massimo; Piomelli, Ugo; Moin, Parviz; Cabot, William H.

    1990-01-01

    One major drawback of the eddy viscosity subgrid-scale stress models used in large-eddy simulations is their inability to represent correctly with a single universal constant different turbulent field in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work, a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity (Germano 1990) between the subgrid-scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid-scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The results of large-eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.

  4. A transport equation for eddy viscosity

    NASA Technical Reports Server (NTRS)

    Durbin, P. A.; Yang, Z.

    1992-01-01

    A transport equation for eddy viscosity is proposed for wall bounded turbulent flows. The proposed model reduces to a quasi-homogeneous form far from surfaces. Near to a surface, the nonhomogeneous effect of the wall is modeled by an elliptic relaxation model. All the model terms are expressed in local variables and are coordinate independent; the model is intended to be used in complex flows. Turbulent channel flow and turbulent boundary layer flows with/without pressure gradient are calculated using the present model. Comparisons between model calculations and direct numerical simulation or experimental data show good agreement.

  5. Solvable model in renormalization group analysis for effective eddy viscosity.

    PubMed

    Chang, Chien C; Lin, Bin-Shei; Wang, Chi-Tzung

    2003-04-01

    This study presents a solvable model in renormalization group analysis for the effective eddy viscosity. It is found fruitful to take a simple hypothesis that large-scale eddies are statistically independent of those of smaller scales. A limiting operation of renormalization group analysis yields an inhomogeneous ordinary differential equation for the invariant effective eddy viscosity. The closed-form solution of the equation facilitates derivations of an expression of the Kolmogorov constant C(K) and of the Smagorinsky model for large-eddy simulation of turbulent flow. The Smagorinsky constant C(S) is proportional to C(3/4)(K). In particular, we shall illustrate that the value of C(K) ranges from 1.35 to 2.06, which is in close agreement with the generally accepted experimental values (1.2 approximately 2.2).

  6. Effects of Eddy Viscosity on Time Correlations in Large Eddy Simulation

    NASA Technical Reports Server (NTRS)

    He, Guowei; Rubinstein, R.; Wang, Lian-Ping; Bushnell, Dennis M. (Technical Monitor)

    2001-01-01

    Subgrid-scale (SGS) models for large. eddy simulation (LES) have generally been evaluated by their ability to predict single-time statistics of turbulent flows such as kinetic energy and Reynolds stresses. Recent application- of large eddy simulation to the evaluation of sound sources in turbulent flows, a problem in which time, correlations determine the frequency distribution of acoustic radiation, suggest that subgrid models should also be evaluated by their ability to predict time correlations in turbulent flows. This paper compares the two-point, two-time Eulerian velocity correlation evaluated from direct numerical simulation (DNS) with that evaluated from LES, using a spectral eddy viscosity, for isotropic homogeneous turbulence. It is found that the LES fields are too coherent, in the sense that their time correlations decay more slowly than the corresponding time. correlations in the DNS fields. This observation is confirmed by theoretical estimates of time correlations using the Taylor expansion technique. Tile reason for the slower decay is that the eddy viscosity does not include the random backscatter, which decorrelates fluid motion at large scales. An effective eddy viscosity associated with time correlations is formulated, to which the eddy viscosity associated with energy transfer is a leading order approximation.

  7. Prediction of Transonic Vortex Flows Using Linear and Nonlinear Turbulent Eddy Viscosity Models

    NASA Technical Reports Server (NTRS)

    Bartels, Robert E.; Gatski, Thomas B.

    2000-01-01

    Three-dimensional transonic flow over a delta wing is investigated with a focus on the effect of transition and influence of turbulence stress anisotropies. The performance of linear eddy viscosity models and an explicit algebraic stress model is assessed at the start of vortex flow, and the results compared with experimental data. To assess the effect of transition location, computations that either fix transition or are fully turbulent are performed. To assess the effect of the turbulent stress anisotropy, comparisons are made between predictions from the algebraic stress model and the linear eddy viscosity models. Both transition location and turbulent stress anisotropy significantly affect the 3D flow field. The most significant effect is found to be the modeling of transition location. At a Mach number of 0.90, the computed solution changes character from steady to unsteady depending on transition onset. Accounting for the anisotropies in the turbulent stresses also considerably impacts the flow, most notably in the outboard region of flow separation.

  8. RAS one-equation turbulence model with non-singular eddy-viscosity coefficient

    NASA Astrophysics Data System (ADS)

    Rahman, M. M.; Agarwal, R. K.; Siikonen, T.

    2016-02-01

    A simplified consistency formulation for Pk/ε (production to dissipation ratio) is devised to obtain a non-singular Cμ (coefficient of eddy-viscosity) in the explicit algebraic Reynolds stress model of Gatski and Speziale. The coefficient Cμ depends non-linearly on both rotational/irrotational strains and is used in the framework of an improved RAS (Rahman-Agarwal-Siikonen) one-equation turbulence model to calculate a few well-documented turbulent flows, yielding predictions in good agreement with the direct numerical simulation and experimental data. The strain-dependent Cμ assists the RAS model in constructing the coefficients and functions such as to benefit complex flows with non-equilibrium turbulence. Comparisons with the Spalart-Allmaras one-equation model and the shear stress transport k-ω model demonstrate that Cμ improves the response of RAS model to non-equilibrium effects.

  9. A normal stress subgrid-scale eddy viscosity model in large eddy simulation

    NASA Technical Reports Server (NTRS)

    Horiuti, K.; Mansour, N. N.; Kim, John J.

    1993-01-01

    The Smagorinsky subgrid-scale eddy viscosity model (SGS-EVM) is commonly used in large eddy simulations (LES) to represent the effects of the unresolved scales on the resolved scales. This model is known to be limited because its constant must be optimized in different flows, and it must be modified with a damping function to account for near-wall effects. The recent dynamic model is designed to overcome these limitations but is compositionally intensive as compared to the traditional SGS-EVM. In a recent study using direct numerical simulation data, Horiuti has shown that these drawbacks are due mainly to the use of an improper velocity scale in the SGS-EVM. He also proposed the use of the subgrid-scale normal stress as a new velocity scale that was inspired by a high-order anisotropic representation model. The testing of Horiuti, however, was conducted using DNS data from a low Reynolds number channel flow simulation. It was felt that further testing at higher Reynolds numbers and also using different flows (other than wall-bounded shear flows) were necessary steps needed to establish the validity of the new model. This is the primary motivation of the present study. The objective is to test the new model using DNS databases of high Reynolds number channel and fully developed turbulent mixing layer flows. The use of both channel (wall-bounded) and mixing layer flows is important for the development of accurate LES models because these two flows encompass many characteristic features of complex turbulent flows.

  10. A kinematic eddy viscosity model including the influence of density variations and preturbulence

    NASA Technical Reports Server (NTRS)

    Cohen, L. S.

    1973-01-01

    A model for the kinematic eddy viscosity was developed which accounts for the turbulence produced as a result of jet interactions between adjacent streams as well as the turbulence initially present in the streams. In order to describe the turbulence contribution from jet interaction, the eddy viscosity suggested by Prandtl was adopted, and a modification was introduced to account for the effect of density variation through the mixing layer. The form of the modification was ascertained from a study of the compressible turbulent boundary layer on a flat plate. A kinematic eddy viscosity relation which corresponds to the initial turbulence contribution was derived by employing arguments used by Prandtl in his mixing length hypothesis. The resulting expression for self-preserving flow is similar to that which describes the mixing of a submerged jet. Application of the model has led to analytical predictions which are in good agreement with available turbulent mixing experimental data.

  11. Renormalization-group theory for the eddy viscosity in subgrid modeling

    NASA Technical Reports Server (NTRS)

    Zhou, YE; Vahala, George; Hossain, Murshed

    1988-01-01

    Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.

  12. The present state and the future direction of eddy viscosity models

    NASA Technical Reports Server (NTRS)

    Wilcox, David C.

    1992-01-01

    Information is given in viewgraph form on the present state and future direction of eddy viscosity models. Topics covered include the eddy viscosity dilemma, two-equation models, equations of motion, free shear flows, incompressible free shear flows, model-predicted boundary layer structure, defect layer analysis, the effects of pressure gradients, viscous sublayer structure, wall functions and viscous damping, viscous damping for kappa-omega, the effects of compressibility, perturbation analysis of the wall layer, an alternative compressibility term, unsteady boundary layers, incompressible separation, backstep results, and compressible separation.

  13. A new non-eddy viscosity subgrid-scale model and its application to channel flow

    NASA Technical Reports Server (NTRS)

    Shah, K. B.; Ferziger, J. H.

    1995-01-01

    To date, most large-eddy simulations (LES) have been carried out with eddy viscosity subgrid scale (SGS) models, with only a few exceptions that used the mixed model. Even though the assumptions behind Smagorinsky's model are rather stringent, it has been applied successfully to a variety of turbulent flows. This success is attributed to the ability of eddy viscosity models to drain energy from large scales, thus simulating the dissipative nature of turbulence. Most SGS models are absolutely dissipative, i.e. they remove energy from the large scales at every instant. However, SGS stresses may transfer energy back to the large scales intermittently; this reverse transfer or backscatter is especially important in geophysical flows and in transition. In a fully developed channel flow, there is reverse flow of energy from small to large scales near the walls, but eddy viscosity models are unable to account for this important feature. The dynamic localization eddy viscosity model of Ghosal et al. (1995) allows backscatter by co-evolving an auxiliary equation for the SGS energy; however, the computational cost is considerably larger than for conventional SGS models (Cabot 1994). In this report, a new non-eddy viscosity model based on local approximation of total quantities in terms of filtered ones is introduced; the scale similarity model of Bardina (1983) is a special case of this model. This procedure does not require the assumption of homogeneity, permits backscatter of energy from small to large scales, and is readily implemented in finite difference codes. The results of applying the proposed model to second order finite volume simulation of plane channel flow at high Reynolds numbers (Re(sub b) = 38,000) is described in this report. Greater emphasis is placed on the high Reynolds number flow since it provides a more rigorous test of the SGS model and its potential application. The results are compared to ones produced by the conventional and dynamic Smagorinsky

  14. Turbulent Eddy Viscosity and Large-Scale Convection in the Sun

    NASA Technical Reports Server (NTRS)

    Stothers, Richard B.

    2000-01-01

    It is suggested here that the laminar character of the large-scale deep convective flows appearing in numerical simulations of the Sun's convective envelope arises from the effect of turbulent eddy viscosity. Previously, M. Schwarzchild suggested the same idea to explain the observed surface granulation in the Sun.

  15. A New K-epsilon Eddy Viscosity Model for High Reynolds Number Turbulent Flows: Model Development and Validation

    NASA Technical Reports Server (NTRS)

    Shih, T.-H.; Liou, W. W.; Shabbir, A.; Yang, Z.; Zhu, J.

    1994-01-01

    A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model.

  16. Convection without eddy viscosity: An attempt to model the interiors of giant planets

    NASA Technical Reports Server (NTRS)

    Ingersoll, A. P.

    1986-01-01

    In the theory of hydrostatic quasi-geostrophic flow in the Earth's atmosphere the principal results do not depend on the eddy viscosity. This contrasts with published theories of convection in deep rotating fluid spheres, where the wavelength of the fastest growing disturbance varies as E sup 1/3, where E, the Ekman number, is proportional to the eddy viscosity. A new theory of quasi-columnar motions in stably stratified fluid spheres attempts to capture the luck of the meteorologists. The theory allows one to investigate the stability of barotropic and baroclinic zonal flows that extend into the planetary interior. It is hypothesized that the internal heat Jupiter and Saturn comes out not radially but on sloping surfaces defined by the internal entropy distribution. To test the hypothesis one searches for basic states in which the wavelength of the fastest-growing disturbance remains finite as E tends to zero, and is which the heat flux vector is radially outward and poleward.

  17. Structural Uncertainties in RANS Models: Reynolds Stress Transport contra Eddy Viscosity Frameworks

    NASA Astrophysics Data System (ADS)

    Mishra, Aashwin; Edeling, Wouter; Iaccarino, Gianluca

    2016-11-01

    A vast majority of turbulent flow studies, both in academia and industry, utilize Reynolds Averaged Navier Stokes based models. There are different RANS modeling frameworks to select from, depending on their complexity and computational requirements, such as eddy viscosity based models, second moment closures, etc. While the relative strengths and weaknesses of each modeling paradigm (vis-a-vis their predictive fidelity, realizability, etc) are roughly established for disparate flows, there are no extant comparative estimates on the relative uncertainty in their predictions. In this investigation, we estimate the structural uncertainty inherent to different RANS modeling approaches for select internal flows. This involves comparisons between models conforming to the same framework, and, across different modeling frameworks. We establish, compare, analyze and explicate the model inadequacy for flows such as in parallel, curved, converging and diverging channels for different models. One of the novel facets of this study involves the estimation of the structural uncertainties of established Reynolds Stress Transport models, and, contrasting these against simpler eddy viscosity models. This work was supported under the DARPA EQUiPS project(Technical Monitor: Fariba Fahroo).

  18. One-dimensional wave bottom boundary layer model comparison: specific eddy viscosity and turbulence closure models

    USGS Publications Warehouse

    Puleo, J.A.; Mouraenko, O.; Hanes, D.M.

    2004-01-01

    Six one-dimensional-vertical wave bottom boundary layer models are analyzed based on different methods for estimating the turbulent eddy viscosity: Laminar, linear, parabolic, k—one equation turbulence closure, k−ε—two equation turbulence closure, and k−ω—two equation turbulence closure. Resultant velocity profiles, bed shear stresses, and turbulent kinetic energy are compared to laboratory data of oscillatory flow over smooth and rough beds. Bed shear stress estimates for the smooth bed case were most closely predicted by the k−ω model. Normalized errors between model predictions and measurements of velocity profiles over the entire computational domain collected at 15° intervals for one-half a wave cycle show that overall the linear model was most accurate. The least accurate were the laminar and k−ε models. Normalized errors between model predictions and turbulence kinetic energy profiles showed that the k−ω model was most accurate. Based on these findings, when the smallest overall velocity profile prediction error is required, the processing requirements and error analysis suggest that the linear eddy viscosity model is adequate. However, if accurate estimates of bed shear stress and TKE are required then, of the models tested, the k−ω model should be used.

  19. Three-fluid, Three-dimensional Magnetohydrodynamic Solar Wind Model with Eddy Viscosity and Turbulent Resistivity

    NASA Astrophysics Data System (ADS)

    Usmanov, Arcadi V.; Goldstein, Melvyn L.; Matthaeus, William H.

    2014-06-01

    We have developed a three-fluid, three-dimensional magnetohydrodynamic solar wind model that incorporates turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating. The solar wind plasma is described as a system of co-moving solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Numerical steady-state solutions of Reynolds-averaged solar wind equations coupled with turbulence transport equations for turbulence energy, cross helicity, and correlation length are obtained by the time relaxation method in the corotating with the Sun frame of reference in the region from 0.3 to 100 AU (but still inside the termination shock). The model equations include the effects of electron heat conduction, Coulomb collisions, photoionization of interstellar hydrogen atoms and their charge exchange with the solar wind protons, turbulence energy generation by pickup protons, and turbulent heating of solar wind protons and electrons. The turbulence transport model is based on the Reynolds decomposition and turbulence phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. In addition to using separate energy equations for the solar wind protons and electrons, a significant improvement over our previous work is that the turbulence model now uses an eddy viscosity approximation for the Reynolds stress tensor and the mean turbulent electric field. The approximation allows the turbulence model to account for driving of turbulence by large-scale velocity gradients. Using either a dipole approximation for the solar magnetic field or synoptic solar magnetograms from the Wilcox Solar Observatory for assigning boundary conditions at the coronal base, we apply the model to study the global structure of the solar wind and its three-dimensional properties, including embedded turbulence, heating, and acceleration throughout the heliosphere. The model results are

  20. Three-fluid, three-dimensional magnetohydrodynamic solar wind model with eddy viscosity and turbulent resistivity

    SciTech Connect

    Usmanov, Arcadi V.; Matthaeus, William H.; Goldstein, Melvyn L.

    2014-06-10

    We have developed a three-fluid, three-dimensional magnetohydrodynamic solar wind model that incorporates turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating. The solar wind plasma is described as a system of co-moving solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Numerical steady-state solutions of Reynolds-averaged solar wind equations coupled with turbulence transport equations for turbulence energy, cross helicity, and correlation length are obtained by the time relaxation method in the corotating with the Sun frame of reference in the region from 0.3 to 100 AU (but still inside the termination shock). The model equations include the effects of electron heat conduction, Coulomb collisions, photoionization of interstellar hydrogen atoms and their charge exchange with the solar wind protons, turbulence energy generation by pickup protons, and turbulent heating of solar wind protons and electrons. The turbulence transport model is based on the Reynolds decomposition and turbulence phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. In addition to using separate energy equations for the solar wind protons and electrons, a significant improvement over our previous work is that the turbulence model now uses an eddy viscosity approximation for the Reynolds stress tensor and the mean turbulent electric field. The approximation allows the turbulence model to account for driving of turbulence by large-scale velocity gradients. Using either a dipole approximation for the solar magnetic field or synoptic solar magnetograms from the Wilcox Solar Observatory for assigning boundary conditions at the coronal base, we apply the model to study the global structure of the solar wind and its three-dimensional properties, including embedded turbulence, heating, and acceleration throughout the heliosphere. The model results are

  1. A simple eddy viscosity formulation for turbulent boundary layers near smooth walls

    NASA Astrophysics Data System (ADS)

    Absi, Rafik

    2009-03-01

    The aim of this study is to improve the prediction of near-wall mean streamwise velocity profile U by using a simple method. The U profile is obtained by solving the momentum equation which is written as an ordinary differential equation. An eddy viscosity formulation based on a near-wall turbulent kinetic energy k function [R. Absi, Analytical solutions for the modeled k-equation, ASME J. Appl. Mech. 75 (2008) 044501] and the van Driest mixing length equation [E.R. van Driest, On turbulent flow near a wall, J. Aero. Sci. 23 (1956) 1007] is used. The parameters obtained from the k profiles are used for the computation of U (variables with the superscript of + are those nondimensionalized by the wall friction velocity u and the kinematic viscosity ν). Comparisons with DNS data of fully-developed turbulent channel flows for 109

  2. Three-fluid, 3D MHD solar wind modeling with turbulence transport and eddy viscosity

    NASA Astrophysics Data System (ADS)

    Usmanov, A. V.; Goldstein, M. L.; Matthaeus, W. H.

    2014-12-01

    We present results from a three-fluid, fully three-dimensional MHD solar wind model that includes turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating. The solar wind plasma is described as a co-moving system of three species: the solar wind protons, electrons, and interstellar pickup protons. Separate energy equations are employed for each species. We obtain numerical solutions of Reynolds-averaged solar wind equations coupled with turbulence transport equations in the region from 0.3 to 100 AU. The integrated system of equations includes the effects of electron heat conduction, Coulomb collisions, photoionization of interstellar hydrogen atoms and their charge exchange with the solar wind protons, turbulence energy generation by pickup protons, and turbulent heating of solar wind protons and electrons. Using either a dipole approximation for the solar magnetic field or synoptic solar magnetograms from the Wilcox Solar Observatory for assigning boundary conditions at the coronal base, we apply the model to study the global structure of the solar wind and its three-dimensional properties, including turbulence parameters, throughout the heliosphere. The model results are compared with observations on WIND, Ulysses and Voyager 2 spacecraft. This work is partially supported by LWS and Heliophysics Grand Challenges programs.

  3. Calculation of eddy viscosity in a compressible turbulent boundary layer with mass injection and chemical reaction

    NASA Technical Reports Server (NTRS)

    Omori, S.; Gross, K. W.

    1973-01-01

    The turbulent kinetic energy equation is coupled with boundary layer equations to solve the characteristics of compressible turbulent boundary layers with mass injection and combustion. The Reynolds stress is related to the turbulent kinetic energy using the Prandtl-Wieghardt formulation. When a lean mixture of hydrogen and nitrogen is injected through a porous plate into the subsonic turbulent boundary layer of air flow and ignited by external means, the turbulent kinetic energy increases twice as much as that of noncombusting flow with the same mass injection rate of nitrogen. The magnitudes of eddy viscosity between combusting and noncombusting flows with injection, however, are almost the same due to temperature effects, while the distributions are different. The velocity profiles are significantly affected by combustion. If pure hydrogen as a transpiration coolant is injected into a rocket nozzle boundary layer flow of combustion products, the temperature drops significantly across the boundary layer due to the high heat capacity of hydrogen. At a certain distance from the wall hydrogen reacts with the combustion products, liberating an extensive amount of heat.

  4. Numerical simulation of turbulent free surface flow with two-equation k- eddy-viscosity models

    NASA Astrophysics Data System (ADS)

    Ferreira, V. G.; Mangiavacchi, N.; Tomé, M. F.; Castelo, A.; Cuminato, J. A.; McKee, S.

    2004-02-01

    This paper presents a finite difference technique for solving incompressible turbulent free surface fluid flow problems. The closure of the time-averaged Navier-Stokes equations is achieved by using the two-equation eddy-viscosity model: the high-Reynolds k- (standard) model, with a time scale proposed by Durbin; and a low-Reynolds number form of the standard k- model, similar to that proposed by Yang and Shih. In order to achieve an accurate discretization of the non-linear terms, a second/third-order upwinding technique is adopted. The computational method is validated by applying it to the flat plate boundary layer problem and to impinging jet flows. The method is then applied to a turbulent planar jet flow beneath and parallel to a free surface. Computations show that the high-Reynolds k- model yields favourable predictions both of the zero-pressure-gradient turbulent boundary layer on a flat plate and jet impingement flows. However, the results using the low-Reynolds number form of the k- model are somewhat unsatisfactory.

  5. Nonlinear eddy viscosity modeling and experimental study of jet spreading rates.

    PubMed

    Heschl, C; Inthavong, K; Sanz, W; Tu, J

    2014-02-01

    Indoor airflow pattern is strongly influenced by turbulent shear and turbulent normal stresses that are responsible for entrainment effects and turbulence-driven secondary motion. Therefore, an accurate prediction of room airflows requires reliable modeling of these turbulent quantities. The most widely used turbulence models include RANS-based models that provide quick solutions but are known to fail in turbulent free shear and wall-affected flows. In order to cope with this deficiency, this study presents a nonlinear k-ε turbulence model and evaluates it along with linear k-ε models for an indoor isothermal linear diffuser jet flow measured in two model rooms using PIV. The results show that the flow contains a free jet near the inlet region and a wall-affected region downstream where the jet is pushed toward the ceiling by entrainment through the well-known Coanda effect. The CFD results show that an accurate prediction of the entrainment process is very important and that the nonlinear eddy viscosity model is able to predict the turbulence-driven secondary motions. Furthermore, turbulence models that are calibrated for high Reynolds free shear layer flows were not able to reproduce the measured velocity distributions, and it is suggested that the model constants of turbulence models should be adjusted before they are used for room airflow simulations.

  6. Predictions of flow through an isothermal serpentine passage with linear eddy-viscosity Reynolds Averaged Navier Stokes models.

    SciTech Connect

    Laskowski, Gregory Michael

    2005-12-01

    Flows with strong curvature present a challenge for turbulence models, specifically eddy viscosity type models which assume isotropy and a linear and instantaneous equilibrium relation between stress and strain. Results obtained from three different codes and two different linear eddy viscosity turbulence models are compared to a DNS simulation in order to gain some perspective on the turbulence modeling capability of SIERRA/Fuego. The Fuego v2f results are superior to the more common two-layer k-e model results obtained with both a commercial and research code in terms of the concave near wall behavior predictions. However, near the convex wall, including the separated region, little improvement is gained using the v2f model and in general the turbulent kinetic energy prediction is fair at best.

  7. Modelling transverse turbulent mixing in a shallow flow by using an eddy viscosity approach

    NASA Astrophysics Data System (ADS)

    Gualtieri, C.

    2009-04-01

    The mixing of contaminants in streams and rivers is a significant problem in environmental fluid mechanics and rivers engineering since to understand the impact and the fate of pollutants in these water bodies is a primary goal of water quality management. Since most rivers have a high aspect ratio, that is the width to depth ratio, discharged pollutants become vertically mixed within a short distance from the source and vertical mixing is only important in the so-called near-field. As a rule of thumb, neutrally buoyant solute becomes fully mixed vertically within 50-75 depths from the source. Notably, vertical mixing analysis relies on well-known theoretical basis, that is Prandtl mixing length model, which assumes the hypothesis of plane turbulent shear flow and provides theoretical predictions of the vertical turbulent diffusivity which closely match experimental results. In the mid-field, the vertical concentration gradients are negligible and both subsequent transverse and longitudinal changes of the depth-averaged concentrations of the pollutants should be addressed. In the literature, for the application of one-dimensional water quality models the majority of research efforts were devoted to estimate the rate of longitudinal mixing of a contaminant, that is the development of a plume resulting from a temporally varying pollutant source once it has become cross-sectionally well-mixed, in the far-field. Although transverse mixing is a significant process in river engineering when dealing with the discharge of pollutants from point sources or the mixing of tributary inflows, no theoretical basis exists for the prediction of its rate, which is indeed based upon the results of experimental works carried on in laboratory channels or in streams and rivers. Turbulence models based on the eddy viscosity approach, such as the k-ɛ model, k-? and their variation are the most widely used turbulence models and this is largely due to their ease in implementation

  8. Calculation of eddy viscosity in a compressible turbulent boundary layer with mass injection and chemical reaction, volume 1. [theoretical analysis

    NASA Technical Reports Server (NTRS)

    Omori, S.

    1973-01-01

    The turbulent kinetic energy equation is coupled with boundary layer equations to solve the characteristics of compressible turbulent boundary layers with mass injection and combustion. The Reynolds stress is related to the turbulent kinetic energy using the Prandtl-Wieghardt formulation. When a lean mixture of hydrogen and nitrogen is injected through a porous plate into the subsonic turbulent boundary layer of air flow and ignited by external means, the turbulent kinetic energy increases twice as much as that of noncombusting flow with the same mass injection rate of nitrogen. The magnitudes of eddy viscosity between combusting and noncombusting flows with injection, however, are almost the same due to temperature effects, while the distributions are different. The velocity profiles are significantly affected by combustion; that is, combustion alters the velocity profile as if the mass injection rate is increased, reducing the skin-friction as a result of a smaller velocity gradient at the wall. If pure hydrogen as a transpiration coolant is injected into a rocket nozzle boundary layer flow of combustion products, the temperature drops significantly across the boundary layer due to the high heat capacity of hydrogen. At a certain distance from the wall, hydrogen reacts with the combustion products, liberating an extensive amount of heat. The resulting large increase in temperature reduces the eddy viscosity in this region.

  9. Calculation of eddy viscosity in a compressible turbulent boundary layer with mass injection and chemical reaction, volume 2. [computer programs

    NASA Technical Reports Server (NTRS)

    Omori, S.

    1973-01-01

    As described in Vol. 1, the eddy viscosity is calculated through the turbulent kinetic energy, in order to include the history of the flow and the effect of chemical reaction on boundary layer characteristics. Calculations can be performed for two different cooling concepts; that is, transpiration and regeneratively cooled wall cases. For the regenerative cooling option, coolant and gas side wall temperature and coolant bulk temperature in a rocket engine can be computed along the nozzle axis. Thus, this computer program is useful in designing coolant flow rate and cooling tube geometry, including the tube wall thickness as well as in predicting the effects of boundary layers along the gas side wall on thrust performances.

  10. A Dynamic Eddy Viscosity Model for the Shallow Water Equations Solved by Spectral Element and Discontinuous Galerkin Methods

    NASA Astrophysics Data System (ADS)

    Marras, Simone; Suckale, Jenny; Giraldo, Francis X.; Constantinescu, Emil

    2016-04-01

    We present the solution of the viscous shallow water equations where viscosity is built as a residual-based subgrid scale model originally designed for large eddy simulation of compressible [1] and stratified flows [2]. The necessity of viscosity for a shallow water model not only finds motivation from mathematical analysis [3], but is supported by physical reasoning as can be seen by an analysis of the energetics of the solution. We simulated the flow of an idealized wave as it hits a set of obstacles. The kinetic energy spectrum of this flow shows that, although the inviscid Galerkin solutions -by spectral elements and discontinuous Galerkin [4]- preserve numerical stability in spite of the spurious oscillations in the proximity of the wave fronts, the slope of the energy cascade deviates from the theoretically expected values. We show that only a sufficiently small amount of dynamically adaptive viscosity removes the unwanted high-frequency modes while preserving the overall sharpness of the solution. In addition, it yields a physically plausible energy decay. This work is motivated by a larger interest in the application of a shallow water model to the solution of tsunami triggered coastal flows. In particular, coastal flows in regions around the world where coastal parks made of mitigation hills of different sizes and configurations are considered as a means to deviate the power of the incoming wave. References [1] M. Nazarov and J. Hoffman (2013) "Residual-based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods" Int. J. Numer. Methods Fluids, 71:339-357 [2] S. Marras, M. Nazarov, F. X. Giraldo (2015) "Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES" J. Comput. Phys. 301:77-101 [3] J. F. Gerbeau and B. Perthame (2001) "Derivation of the viscous Saint-Venant system for laminar shallow water; numerical validation" Discrete Contin. Dyn. Syst. Ser. B, 1:89?102 [4] F

  11. Effects of eddy viscosity and thermal conduction and Coriolis force in the dynamics of gravity wave driven fluctuations in the OH nightglow

    NASA Technical Reports Server (NTRS)

    Hickey, M. P.

    1988-01-01

    The chemical-dynamical model of Walterscheid et al. (1987), which describes wave-driven fluctuations in OH nightglow, was modified to include the effects of both eddy thermal conduction and viscosity, as well as the Coriolis force (with the shallow atmosphere approximation). Using the new model, calculations were performed for the same nominal case as used by Walterscheid et al. but with only wave periods considered. For this case, the Coriolis force was found to be unimportant at any wave period. For wave periods greater than 2 or 3 hours, the inclusion of thermal conduction alone greatly modified the results (in terms of a complex ratio 'eta' which expresses the relationship between the intensity oscillation about the time-averaged intensity and the temperature oscillation about the time-averaged temperature); this effect was reduced with the further inclusion of the eddy viscosity.

  12. Dynamic links between shape of the eddy viscosity profile and the vertical structure of tidal current amplitude in bays and estuaries

    NASA Astrophysics Data System (ADS)

    Chen, Wei; de Swart, Huib E.

    2016-03-01

    Several field studies in bays and estuaries have revealed pronounced subsurface maxima in the vertical profiles of the current amplitude of the principal tidal harmonic, or of its vertical shear, over the water column. To gain fundamental understanding about these phenomena, a semi-analytical model is designed and analysed, with focus on the sensitivity of the vertical structure of the tidal current amplitude to formulations of the vertical shape of the eddy viscosity. The new analytical solutions for the tidal current amplitude are used to explore their dependence on the degree of surface mixing, the vertical shape of eddy viscosity in the upper part of the water column and the density stratification. Sources of surface mixing are wind and whitecapping. Results show three types of current amplitude profiles of tidal harmonics, characterised by monotonically decreasing shear towards the surface, "surface jumps" (vertical shear of tidal current amplitude has a subsurface maximum) and "subsurface jets" (maximum tidal current amplitude below the surface), respectively. The "surface jumps" and "subsurface jets" both occur for low turbulence near the surface, whilst additionally the surface jumps only occur if the eddy viscosity in the upper part of the water column decreases faster than linearly to the surface. Furthermore, "surface jumps" take place for low density stratification, while and "subsurface jets" occur for high density stratification. The physics causing the presence of surface jumps and subsurface jets is also discussed.

  13. Investigation of numerical viscosities and dissipation rates of second-order TVD-MUSCL schemes for implicit large-eddy simulation

    NASA Astrophysics Data System (ADS)

    Bidadi, Shreyas; Rani, Sarma L.

    2015-01-01

    Monotonically integrated large-eddy simulation (MILES) approach utilizes the dissipation inherent to shock-capturing schemes to emulate the role played by explicit subgrid-scale eddy diffusivity at the high-wavenumber end of the turbulent energy spectrum. In the current study, a novel formulation is presented for quantifying the numerical viscosity inherent to Roe-based second-order TVD-MUSCL schemes for the Euler equations. Using this formulation, the effects of numerical viscosity and dissipation rate on implicit large-eddy simulations of turbulent flows are investigated. At first, the three-dimensional (3-D) finite-volume extension of the original Roe's flux, including Roe's Jacobian matrix, is presented. The fluxes are then extended to second-order using van Leer's MUSCL extrapolation technique. Starting from the 3-D Roe-MUSCL flux, an expression is derived for the numerical viscosity as a function of flux limiter and characteristic speed for each conserved variable, distance between adjacent cell centers, and a scaling parameter. Motivated by Thornber et al. [16] study, the high numerical viscosity inherent to TVD-MUSCL schemes is mitigated using a z-factor that depends on local Mach number. The TVD limiters, along with the z-factor, were initially applied to the 1-D shock-tube and 2-D inviscid supersonic wedge flows. Spatial profiles of numerical viscosities are plotted, which provide insights into the role of these limiters in controlling the dissipative nature of Roe's flux while maintaining monotonicity and stability in regions of high gradients. Subsequently, a detailed investigation was performed of decaying homogeneous isotropic turbulence with varying degrees of compressibility. Spectra of numerical viscosity and dissipation rate are presented, which clearly demonstrate the effectiveness of the z-factor both in narrowing the wavenumber range in which dissipation occurs, and in shifting the location of dissipation peak closer to the cut-off wavenumber

  14. An algebraic variational multiscale-multigrid method for large-eddy simulation: generalized-α time integration, Fourier analysis and application to turbulent flow past a square-section cylinder

    NASA Astrophysics Data System (ADS)

    Gravemeier, Volker; Kronbichler, Martin; Gee, Michael W.; Wall, Wolfgang A.

    2011-02-01

    This article studies three aspects of the recently proposed algebraic variational multiscale-multigrid method for large-eddy simulation of turbulent flow. First, the method is integrated into a second-order-accurate generalized-α time-stepping scheme. Second, a Fourier analysis of a simplified model problem is performed to assess the impact of scale separation on the overall performance of the method. The analysis reveals that scale separation implemented by projective operators provides modeling effects very close to an ideal small-scale subgrid viscosity, that is, it preserves low frequencies, in contrast to non-projective scale separations. Third, the algebraic variational multiscale-multigrid method is applied to turbulent flow past a square-section cylinder. The computational results obtained with the method reveal, on the one hand, the good accuracy achievable for this challenging test case already at a rather coarse discretization and, on the other hand, the superior computing efficiency, e.g., compared to a traditional dynamic Smagorinsky modeling approach.

  15. Fluid-structure interaction modeling of A F/A-18 twin-tail buffet using Non-linear Eddy Viscosity Models

    NASA Astrophysics Data System (ADS)

    Elmekawy, Ahmed M. Nagib M.

    When turbulent flow generates unsteady differential pressure over an aircraft's structure, this may generate buffeting, a random oscillation of the structure. The buffet phenomenon is observed on a wide range of fighter aircraft, especially fighters with twin-tail. More research is needed to better understand the physics behind the vortical flow over a delta wing and the subsequent tail buffet. This dissertation reports the modeling and simulation of a steady-state one-way fluid-structure interaction for the tail buffet problem observed on a F/A-18 fighter. The time-averaged computational results are compared to available experimental data. Next, computations are extended to simulate an unsteady two-way fluid-structure interaction problem of the tail buffet of a F/A-18 fighter. For the modeling herein, a commercial software ANSYS version 14.0, is employed. For the fluid domain, the unsteady Reynolds-averaged Navier Stokes (URANS) equations with different turbulent models are utilized. The first turbulence model selected is the modified Spalart-Allmaras model (SARRC) with a strain-vorticity based production and curvature treatment. The second turbulence model selected is the Non-linear Eddy Viscosity Model (NLEVM) based on the Wilcox k--o model. This model uses the formulation of an explicit algebraic Reynolds stress model. The structural simulation is conducted by a finite element analysis model with shell elements. Both SARRC and NLEVM turbulence models are in ANSYS software. The experimental data used for validation were conducted on a simplified geometry: a 0.3 Mach number flow past a 76-deg delta wing pitched to 30-deg. Two vertical tails were placed downstream of the delta wing. The present work is the first ever study of the tail buffet problem of the F/A-18 fighter with two-way fluid-structure interaction using the two advanced turbulence models. The steady-state, time-averaged, one-way fluid-structure interaction case of the present investigation indicates

  16. A parametric study on the rise of a pair of bubbles using algebraic volume of fluid method: effect of diameter and viscosity ratio

    NASA Astrophysics Data System (ADS)

    Dalal, Amaresh; Kulkarni, Amol C.; Manik, Jai; Natarajan, Ganesh

    2016-11-01

    The effect of droplet diameter and viscosity ratio on the coalescence of two bubbles rising in a quiescent liquid has been studied numerically using algebraic volume of fluid (VOF) method. If the upper bubble diameter is 75% of the lower bubble, the time taken for their coalescence increases in comparison with the case of equal bubble diameter. For the case, when the diameter of the upper bubble is reduced, this delay may be attributed to comparatively weaker jet formed behind the leading bubble, ultimately resulting in lesser acceleration of the trailing bubble. While for the other case, when the diameter of the lower bubble is reduced, it is because of a totally different scenario of liquid entrapment observed during coalescence. The effect of viscosity of the surrounding fluid is also noticed separately for the situation when the diameters of the bubbles are equal. It has been observed that, the increase in viscosity of the surrounding fluid will increase the form drag over the bubbles, eventually leading to the delay in their coalescence. This study is funded by a Grant from BRNS, DAE, Government of India.

  17. Constrained Large Eddy Simulation of Separated Turbulent Flows

    NASA Astrophysics Data System (ADS)

    Xia, Zhenhua; Shi, Yipeng; Wang, Jianchun; Xiao, Zuoli; Yang, Yantao; Chen, Shiyi

    2011-11-01

    Constrained Large-eddy Simulation (CLES) has been recently proposed to simulate turbulent flows with massive separation. Different from traditional large eddy simulation (LES) and hybrid RANS/LES approaches, the CLES simulates the whole flow domain by large eddy simulation while enforcing a RANS Reynolds stress constraint on the subgrid-scale (SGS) stress models in the near-wall region. Algebraic eddy-viscosity models and one-equation Spalart-Allmaras (S-A) model have been used to constrain the Reynolds stress. The CLES approach is validated a posteriori through simulation of flow past a circular cylinder and periodic hill flow at high Reynolds numbers. The simulation results are compared with those from RANS, DES, DDES and other available hybrid RANS/LES methods. It is shown that the capability of the CLES method in predicting separated flows is comparable to that of DES. Detailed discussions are also presented about the effects of the RANS models as constraint in the near-wall layers. Our results demonstrate that the CLES method is a promising alternative towards engineering applications.

  18. Computation of turbulent rotating channel flow with an algebraic Reynolds stress model

    NASA Technical Reports Server (NTRS)

    Warfield, M. J.; Lakshminarayana, B.

    1986-01-01

    An Algebraic Reynolds Stress Model has been implemented to modify the Kolmogorov-Prandtl eddy viscosity relation to produce an anisotropic turbulence model. The eddy viscosity relation becomes a function of the local turbulent production to dissipation ratio and local turbulence/rotation parameters. The model is used to predict fully-developed rotating channel flow over a diverse range of rotation numbers. In addition, predictions are obtained for a developing channel flow with high rotation. The predictions are compared with the experimental data available. Good predictions are achieved for mean velocity and wall shear stress over most of the rotation speeds tested. There is some prediction breakdown at high rotation (rotation number greater than .10) where the effects of the rotation on turbulence become quite complex. At high rotation and low Reynolds number, the laminarization on the trailing side represents a complex effect of rotation which is difficult to predict with the described models.

  19. Fully-Explicit and Self-Consistent Algebraic Reynolds Stress Models

    NASA Technical Reports Server (NTRS)

    Girimaji, Sharath S.

    1995-01-01

    A fully-explicit, self-consistent algebraic expression for the Reynolds stress, which is the exact solution to the Reynolds stress transport equation in the 'weak equilibrium' limit for two-dimensional mean flows for all linear and some quasi-linear pressure-strain models, is derived. Current explicit algebraic Reynolds stress models derived by employing the 'weak equilibrium' assumption treat the production-to-dissipation (P/epsilon) ratio implicitly, resulting in an effective viscosity that can be singular away from the equilibrium limit. In the present paper, the set of simultaneous algebraic Reynolds stress equations are solved in the full non-linear form and the eddy viscosity is found to be non-singular. Preliminary tests indicate that the model performs adequately, even for three dimensional mean flow cases. Due to the explicit and non-singular nature of the effective viscosity, this model should mitigate many of the difficulties encountered in computing complex turbulent flows with the algebraic Reynolds stress models.

  20. Hybrid Reynolds-Averaged/Large Eddy Simulation of a Cavity Flameholder; Assessment of Modeling Sensitivities

    NASA Technical Reports Server (NTRS)

    Baurle, R. A.

    2015-01-01

    Steady-state and scale-resolving simulations have been performed for flow in and around a model scramjet combustor flameholder. The cases simulated corresponded to those used to examine this flowfield experimentally using particle image velocimetry. A variety of turbulence models were used for the steady-state Reynolds-averaged simulations which included both linear and non-linear eddy viscosity models. The scale-resolving simulations used a hybrid Reynolds-averaged / large eddy simulation strategy that is designed to be a large eddy simulation everywhere except in the inner portion (log layer and below) of the boundary layer. Hence, this formulation can be regarded as a wall-modeled large eddy simulation. This effort was undertaken to formally assess the performance of the hybrid Reynolds-averaged / large eddy simulation modeling approach in a flowfield of interest to the scramjet research community. The numerical errors were quantified for both the steady-state and scale-resolving simulations prior to making any claims of predictive accuracy relative to the measurements. The steady-state Reynolds-averaged results showed a high degree of variability when comparing the predictions obtained from each turbulence model, with the non-linear eddy viscosity model (an explicit algebraic stress model) providing the most accurate prediction of the measured values. The hybrid Reynolds-averaged/large eddy simulation results were carefully scrutinized to ensure that even the coarsest grid had an acceptable level of resolution for large eddy simulation, and that the time-averaged statistics were acceptably accurate. The autocorrelation and its Fourier transform were the primary tools used for this assessment. The statistics extracted from the hybrid simulation strategy proved to be more accurate than the Reynolds-averaged results obtained using the linear eddy viscosity models. However, there was no predictive improvement noted over the results obtained from the explicit

  1. Application of the algebraic RNG model for transition simulation. [renormalization group theory

    NASA Technical Reports Server (NTRS)

    Lund, Thomas S.

    1990-01-01

    The algebraic form of the RNG model of Yakhot and Orszag (1986) is investigated as a transition model for the Reynolds averaged boundary layer equations. It is found that the cubic equation for the eddy viscosity contains both a jump discontinuity and one spurious root. A yet unpublished transformation to a quartic equation is shown to remove the numerical difficulties associated with the discontinuity, but only at the expense of merging both the physical and spurious root of the cubic. Jumps between the branches of the resulting multiple-valued solution are found to lead to oscillations in flat plate transition calculations. Aside from the oscillations, the transition behavior is qualitatively correct.

  2. Modifications of the law of the wall and algebraic turbulence modelling for separated boundary layers

    NASA Technical Reports Server (NTRS)

    Baldwin, B. S.; Maccormack, R. W.

    1976-01-01

    Various modifications of the conventional algebraic eddy viscosity turbulence model are investigated for application to separated flows. Friction velocity is defined in a way that avoids singular behavior at separation and reattachment but reverts to the conventional definition for flows with small pressure gradients. This leads to a modified law of the wall for separated flows. The effect on the calculated flow field of changes in the model that affect the eddy viscosity at various distances from the wall are determined by (1) switching from Prandtl's form to an inner layer formula due to Clauser at various distances from the wall, (2) varying the constant in the Van Driest damping factor, (3) using Clauser's inner layer formula all the way to the wall, and (4) applying a relaxation procedure in the evaluation of the constant in Clauser's inner layer formula. Numerical solutions of the compressible Navier-Stokes equations are used to determine the effects of the modifications. Experimental results from shock-induced separated flows at Mach numbers 2.93 and 8.45 are used for comparison. For these cases improved predictions of wall pressure distribution and positions of separation and reattachment are obtained from the relaxation version of the Clauser inner layer eddy viscosity formula.

  3. Production and destruction of eddy kinetic energy in forced submesoscale eddy-resolving simulations

    NASA Astrophysics Data System (ADS)

    Mukherjee, Sonaljit; Ramachandran, Sanjiv; Tandon, Amit; Mahadevan, Amala

    2016-09-01

    We study the production and dissipation of the eddy kinetic energy (EKE) in a submesoscale eddy field forced with downfront winds using the Process Study Ocean Model (PSOM) with a horizontal grid resolution of 0.5 km. We simulate an idealized 100 m deep mixed-layer front initially in geostrophic balance with a jet in a domain that permits eddies within a range of O(1 km-100 km). The vertical eddy viscosities and the dissipation are parameterized using four different subgrid vertical mixing parameterizations: the k - ɛ , the KPP, and two different constant eddy viscosity and diffusivity profiles with a magnitude of O(10-2m2s-1) in the mixed layer. Our study shows that strong vertical eddy viscosities near the surface reduce the parameterized dissipation, whereas strong vertical eddy diffusivities reduce the lateral buoyancy gradients and consequently the rate of restratification by mixed-layer instabilities (MLI). Our simulations show that near the surface, the spatial variability of the dissipation along the periphery of the eddies depends on the relative alignment of the ageostrophic and geostrophic shear. Analysis of the resolved EKE budgets in the frontal region from the simulations show important similarities between the vertical structure of the EKE budget produced by the k - ɛ and KPP parameterizations, and earlier LES studies. Such an agreement is absent in the simulations using constant eddy-viscosity parameterizations.

  4. Teaching Algebra without Algebra

    ERIC Educational Resources Information Center

    Kalman, Richard S.

    2008-01-01

    Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…

  5. Mesoscale Eddy - Internal Wave Coupling:

    NASA Astrophysics Data System (ADS)

    Polzin, K. L.

    2012-12-01

    The issue of internal wave--mesoscale eddy interactions is revisited. Direct estimates of energy transfer from the Local Dynamics Experiment of the PolyMode field program (Polzin, 2010 JPO) return viscosity estimates of ν h \\cong 50 m2 s-1 and ν v + (f2)/(N^2) Kh \\cong 2.5×10-3 m2 s-1. These estimates indicate that mesoscale eddy-internal wave interactions may play an O(1) role in the mesoscale eddy energy budget as dissipation and the internal wave budget as a source. Radiation balance equation formulations for this coupling (Müller 1976, JFM) are examined. In these formulations permanent transfer of energy and internal wave pseudomomentum for mesoscale eddy potential vorticity is enabled by nonlinearity in the wavefield. Revision of radiation balance equation formulations to account for non-local effects returns predictions of ν h \\cong 50-100 m2 s-1 and ν v + (f2)/(N^2) Kh \\cong -1×10-3 to 4×10-3 m2 s-1. The prediction for the effective vertical viscosity is sensitive to how internal wave energy is distributed in the spectral domain with negative values appropriate to the Garrett and Munk spectrum and positive values appropriate to the background spectrum in the LDE area. Geographic scalings in terms of latitude, stratification and mesoscale eddy variability will be described. The process described here is best interpreted as an amplifier of a pre-existing or externally forced finite amplitude wavefield rather than the spontaneous imbalance of a linear field. Energy, pseudomomentum and vorticity can be transfered from the slow manifold (geostrophically balanced motions) to the fast manifold (internal gravity waves) via linear wave propagation in asymmetric background flows, but that transfer is reversible. The permanent transfer is accomplished by nonlinearity on the fast manifold.

  6. Validity of Taylor's Dissipation-Viscosity Independence Postulate in Variable-Viscosity Turbulent Fluid Mixtures

    NASA Astrophysics Data System (ADS)

    Lee, Kurnchul; Girimaji, Sharath S.; Kerimo, Johannes

    2008-08-01

    G. I. Taylor’s postulate [Proc. R. Soc. APRLAAZ0080-4630 151, 421 (1935)10.1098/rspa.1935.0158] that dissipation is independent of viscosity at high Reynolds numbers is the foundation of many single-fluid turbulence theories and closure models. The validity of this key postulate in an important class of flows, turbulent mixtures, is not yet clearly established. We devise a simple numerical experiment of decaying turbulence in a mixture of two fluids of vastly different viscosities to examine dissipation scaling. Initially, the two fluids are segregated, and dissipation is directly proportional to viscosity. As turbulence evolves and fluids mix, the velocity gradients rapidly adapt to the viscosity field, and within one-half eddy turnover time, dissipation-viscosity independence is established. Viscosity-weighted velocity-gradient skewness is shown to be constant, leading to the validity of Taylor’s postulate in turbulent mixtures.

  7. Predicting NonInertial Effects with Algebraic Stress Models which Account for Dissipation Rate Anisotropies

    NASA Technical Reports Server (NTRS)

    Jongen, T.; Machiels, L.; Gatski, T. B.

    1997-01-01

    Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coriolis-modified eddy-viscosity model, a realizable algebraic stress model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the turbulent model validation. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.

  8. Kiddie Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2009-01-01

    As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…

  9. Large Eddy Simulation of Transitional Boundary Layer

    NASA Astrophysics Data System (ADS)

    Sayadi, Taraneh; Moin, Parviz

    2009-11-01

    A sixth order compact finite difference code is employed to investigate compressible Large Eddy Simulation (LES) of subharmonic transition of a spatially developing zero pressure gradient boundary layer, at Ma = 0.2. The computational domain extends from Rex= 10^5, where laminar blowing and suction excites the most unstable fundamental and sub-harmonic modes, to fully turbulent stage at Rex= 10.1x10^5. Numerical sponges are used in the neighborhood of external boundaries to provide non-reflective conditions. Our interest lies in the performance of the dynamic subgrid scale (SGS) model [1] in the transition process. It is observed that in early stages of transition the eddy viscosity is much smaller than the physical viscosity. As a result the amplitudes of selected harmonics are in very good agreement with the experimental data [2]. The model's contribution gradually increases during the last stages of transition process and the dynamic eddy viscosity becomes fully active and dominant in the turbulent region. Consistent with this trend the skin friction coefficient versus Rex diverges from its laminar profile and converges to the turbulent profile after an overshoot. 1. Moin P. et. al. Phys Fluids A, 3(11), 2746-2757, 1991. 2. Kachanov Yu. S. et. al. JFM, 138, 209-247, 1983.

  10. Color Algebras

    NASA Technical Reports Server (NTRS)

    Mulligan, Jeffrey B.

    2017-01-01

    A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.

  11. Steinberg conformal algebras

    NASA Astrophysics Data System (ADS)

    Mikhalev, A. V.; Pinchuk, I. A.

    2005-06-01

    The structure of Steinberg conformal algebras is studied; these are analogues of Steinberg groups (algebras, superalgebras).A Steinberg conformal algebra is defined as an abstract algebra by a system of generators and relations between the generators. It is proved that a Steinberg conformal algebra is the universal central extension of the corresponding conformal Lie algebra; the kernel of this extension is calculated.

  12. Southern Ocean eddy phenomenology

    NASA Astrophysics Data System (ADS)

    Frenger, I.; Münnich, M.; Gruber, N.; Knutti, R.

    2015-11-01

    Mesoscale eddies are ubiquitous features in the Southern Ocean, yet their phenomenology is not well quantified. To tackle this task, we use satellite observations of sea level anomalies and sea surface temperature (SST) as well as in situ temperature and salinity measurements from profiling floats. Over the period 1997-2010, we identified over a million mesoscale eddy instances and were able to track about 105 of them over 1 month or more. The Antarctic Circumpolar Current (ACC), the boundary current systems, and the regions where they interact are hot spots of eddy presence, representing also the birth places and graveyards of most eddies. These hot spots contrast strongly to areas shallower than about 2000 m, where mesoscale eddies are essentially absent, likely due to topographical steering. Anticyclones tend to dominate the southern subtropical gyres, and cyclones the northern flank of the ACC. Major causes of regional polarity dominance are larger formation numbers and lifespans, with a contribution of differential propagation pathways of long-lived eddies. Areas of dominance of one polarity are generally congruent with the same polarity being longer-lived, bigger, of larger amplitude, and more intense. Eddies extend down to at least 2000 m. In the ACC, eddies show near surface temperature and salinity maxima, whereas eddies in the subtropical areas generally have deeper anomaly maxima, presumably inherited from their origin in the boundary currents. The temperature and salinity signatures of the average eddy suggest that their tracer anomalies are a result of both trapping in the eddy core and stirring.

  13. On the dynamic computation of the model constant in delayed detached eddy simulation

    NASA Astrophysics Data System (ADS)

    Yin, Z.; Reddy, K. R.; Durbin, P. A.

    2015-02-01

    The current work puts forth an implementation of a dynamic procedure to locally compute the value of the model constant CDES, as used in the eddy simulation branch of Delayed Detached Eddy Simulation (DDES). Former DDES formulations [P. R. Spalart et al., "A new version of detached-eddy simulation, resistant to ambiguous grid densities," Theor. Comput. Fluid Dyn. 20, 181 (2006); M. S. Gritskevich et al., "Development of DDES and IDDES formulations for the k- ω shear stress transport model," Flow, Turbul. Combust. 88, 431 (2012)] are not conducive to the implementation of a dynamic procedure due to uncertainty as to what form the eddy viscosity expression takes in the eddy simulation branch. However, a recent, alternate formulation [K. R. Reddy et al., "A DDES model with a Smagorinsky-type eddy viscosity formulation and log-layer mismatch correction," Int. J. Heat Fluid Flow 50, 103 (2014)] casts the eddy viscosity in a form that is similar to the Smagorinsky, LES (Large Eddy Simulation) sub-grid viscosity. The resemblance to the Smagorinsky model allows the implementation of a dynamic procedure similar to that of Lilly [D. K. Lilly, "A proposed modification of the Germano subgrid-scale closure method," Phys. Fluids A 4, 633 (1992)]. A limiting function is proposed which constrains the computed value of CDES, depending on the fineness of the grid and on the computed solution.

  14. Impact of eddy-wind interaction on eddy demographics and phytoplankton community structure in a model of the North Atlantic Ocean

    NASA Astrophysics Data System (ADS)

    Anderson, Laurence A.; McGillicuddy, Dennis J.; Maltrud, Mathew E.; Lima, Ivan D.; Doney, Scott C.

    2011-09-01

    Two eddy-resolving (0.1°) physical-biological simulations of the North Atlantic Ocean are compared, one with the surface momentum flux computed only from wind velocities and the other using the difference between air and ocean velocity vectors. This difference in forcing has a significant impact on the intensities and relative number of different types of mesoscale eddies in the Sargasso Sea. Eddy/wind interaction significantly reduces eddy intensities and increases the number of mode-water eddies and "thinnies" relative to regular cyclones and anticyclones; it also modifies upward isopycnal displacements at the base of the euphotic zone, increasing them in the centers of mode water eddies and at the edges of cyclones, and decreasing them in the centers of cyclones. These physical changes increase phytoplankton growth rates and biomass in mode-water eddies, bringing the biological simulation into better agreement with field data. These results indicate the importance of including the eddy/wind interaction in simulations of the physics and biology of eddies in the subtropical North Atlantic. However, eddy intensities in the simulation with eddy/wind interaction are lower than observed, which suggests a decrease in horizontal viscosity or an increase in horizontal grid resolution will be necessary to regain the observed level of eddy activity.

  15. Web Algebra.

    ERIC Educational Resources Information Center

    Capani, Antonio; De Dominicis, Gabriel

    This paper proposes a model for a general interface between people and Computer Algebra Systems (CAS). The main features in the CAS interface are data navigation and the possibility of accessing powerful remote machines. This model is based on the idea of session management, in which the main engine of the tool enables interactions with the…

  16. Algebraic trigonometry

    NASA Astrophysics Data System (ADS)

    Vaninsky, Alexander

    2011-04-01

    This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos - satisfying an axiom sin2 + cos2 = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.

  17. Optical viscosity sensor

    NASA Astrophysics Data System (ADS)

    Chang, Cheng-Ling; Peyroux, Juliette; Perez, Alex; Tsui, Chi-Leung; Wang, Wei-Chih

    2009-03-01

    Viscosity measurement by bend loss of fiber is presented. The sensing principle makes use of the damping characteristic of a vibrating optical fiber probe with fix-free end configuration. By measuring the displacement of the fiber probe, the viscosity can be determined by matching the probe's displacement with the displacement built in the database obtained by either experimental method or Finite element calculation. Experimental results are presented by measuring the sucrose and glycerol solutions of different concentrations with a viscosity varying from 1 to 15 cP. Stokes' flow assumption is utilized to attenuate the mass density effect and simplify the viscosity measurement.

  18. Large eddy simulation of transitional flow in an idealized stenotic blood vessel: evaluation of subgrid scale models.

    PubMed

    Pal, Abhro; Anupindi, Kameswararao; Delorme, Yann; Ghaisas, Niranjan; Shetty, Dinesh A; Frankel, Steven H

    2014-07-01

    In the present study, we performed large eddy simulation (LES) of axisymmetric, and 75% stenosed, eccentric arterial models with steady inflow conditions at a Reynolds number of 1000. The results obtained are compared with the direct numerical simulation (DNS) data (Varghese et al., 2007, "Direct Numerical Simulation of Stenotic Flows. Part 1. Steady Flow," J. Fluid Mech., 582, pp. 253-280). An inhouse code (WenoHemo) employing high-order numerical methods for spatial and temporal terms, along with a 2nd order accurate ghost point immersed boundary method (IBM) (Mark, and Vanwachem, 2008, "Derivation and Validation of a Novel Implicit Second-Order Accurate Immersed Boundary Method," J. Comput. Phys., 227(13), pp. 6660-6680) for enforcing boundary conditions on curved geometries is used for simulations. Three subgrid scale (SGS) models, namely, the classical Smagorinsky model (Smagorinsky, 1963, "General Circulation Experiments With the Primitive Equations," Mon. Weather Rev., 91(10), pp. 99-164), recently developed Vreman model (Vreman, 2004, "An Eddy-Viscosity Subgrid-Scale Model for Turbulent Shear Flow: Algebraic Theory and Applications," Phys. Fluids, 16(10), pp. 3670-3681), and the Sigma model (Nicoud et al., 2011, "Using Singular Values to Build a Subgrid-Scale Model for Large Eddy Simulations," Phys. Fluids, 23(8), 085106) are evaluated in the present study. Evaluation of SGS models suggests that the classical constant coefficient Smagorinsky model gives best agreement with the DNS data, whereas the Vreman and Sigma models predict an early transition to turbulence in the poststenotic region. Supplementary simulations are performed using Open source field operation and manipulation (OpenFOAM) ("OpenFOAM," http://www.openfoam.org/) solver and the results are inline with those obtained with WenoHemo.

  19. Derive Workshop Matrix Algebra and Linear Algebra.

    ERIC Educational Resources Information Center

    Townsley Kulich, Lisa; Victor, Barbara

    This document presents the course content for a workshop that integrates the use of the computer algebra system Derive with topics in matrix and linear algebra. The first section is a guide to using Derive that provides information on how to write algebraic expressions, make graphs, save files, edit, define functions, differentiate expressions,…

  20. Eddies along western boundaries

    NASA Astrophysics Data System (ADS)

    Arruda, Wilton Zumpichiatti

    The Ulleung eddy owes its existence to beta and nonlinearities . A nonlinear theory for the Ulleung Warm Eddy (UWE) in the Japan/East Sea is proposed. Using the nonlinear reduced gravity (shallow water) equations, it is shown analytically and numerically that the eddy is established in order to balance the northward momentum flux exerted by the separating western boundary current (WBC). In this scenario the presence of beta produces a southward (eddy) force balancing the northward momentum flux of the separating East Korea Warm Current. In contrast to the familiar idea attributing the formation of eddies to instabilities (i.e., the breakdown of a known steady solution), the UWE is an integral part of the steady stable solution. On an f-plane no eddy is produced. To balance the northward momentum force imparted by the nonlinear WBC the f-plane system moves offshore producing a southward Coriolis force. We also found that the observed UWE scale agrees with the analytical and numerical estimates. The Mindanao and Halmahera eddies are due to the bending of their parent currents, nonlinearities and beta. Starting with the simple case of a northward (southward) WBC flowing along a concave solid boundary with a sharp corner on an beta-plane, it is shown that an anticyclonic (cyclonic) eddy is established to balance the upstream momentum flux. (On an f-plane no eddy is established because a pressure force which balances the WBC momentum flux is generated.) With the aid of the above analysis we then examine the collision of two opposing WBCs on a beta-plane. It is shown that this problem can be conceptually reduced to the above problem of two WBCs turning in a solid corner on a beta-plane where the streamline separating the two colliding currents acts like a "zonal wall." We show that an eddy is established (to balance the momentum flux of the respective WBC) on each side of the dividing streamline. Based on the collision problem, an explanation for the Mindanao and

  1. Viscosity measuring using microcantilevers

    DOEpatents

    Oden, Patrick Ian

    2001-01-01

    A method for the measurement of the viscosity of a fluid uses a micromachined cantilever mounted on a moveable base. As the base is rastered while in contact with the fluid, the deflection of the cantilever is measured and the viscosity determined by comparison with standards.

  2. Viscosity and Solvation

    ERIC Educational Resources Information Center

    Robertson, C. T.

    1973-01-01

    Discusses theories underlying the phenomena of solution viscosities, involving the Jones and Dole equation, B-coefficient determination, and flickering cluster model. Indicates that viscosity measurements provide a basis for the study of the structural effects of ions in aqueous solutions and are applicable in teaching high school chemistry. (CC)

  3. Dynamics of gelling liquids: algebraic relaxation.

    PubMed

    Srivastava, Sunita; Kumar, C N; Tankeshwar, K

    2009-08-19

    The sol-gel system which is known, experimentally, to exhibit a power law decay of stress autocorrelation function has been studied theoretically. A second-order nonlinear differential equation obtained from Mori's integro-differential equation is derived which provides the algebraic decay of a time correlation function. Involved parameters in the expression obtained are related to exact properties of the corresponding correlation function. The algebraic model has been applied to Lennard-Jones and sol-gel systems. The model shows the behaviour of viscosity as has been observed in computer simulation and theoretical studies. The expression obtained for the viscosity predicts a logarithmic divergence at a critical value of the parameter in agreement with the prediction of other theories.

  4. Quantum cluster algebras and quantum nilpotent algebras

    PubMed Central

    Goodearl, Kenneth R.; Yakimov, Milen T.

    2014-01-01

    A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197

  5. Application of renormalization group theory to the large-eddy simulation of transitional boundary layers

    NASA Technical Reports Server (NTRS)

    Piomelli, Ugo; Zang, Thomas A.; Speziale, Charles G.; Lund, Thomas S.

    1990-01-01

    An eddy viscosity model based on the renormalization group theory of Yakhot and Orszag (1986) is applied to the large-eddy simulation of transition in a flat-plate boundary layer. The simulation predicts with satisfactory accuracy the mean velocity and Reynolds stress profiles, as well as the development of the important scales of motion. The evolution of the structures characteristic of the nonlinear stages of transition is also predicted reasonably well.

  6. Large-Eddy Simulation of Boundary Layer Transition on Swept Wings

    NASA Technical Reports Server (NTRS)

    Huai, Xiaoli; Joslin, Ronald D.; Piomelli, Ugo

    1993-01-01

    The large-eddy simulation of the spatial evolution of a stationary crossflow vortex packet in a three-dimensional boundary layer was performed. Although a coarse grid was used (compared to that required by a direct numerical simulation) the essential features of the disturbance evolution, such as the spanwise disturbance spreading and the vortex rollover, were captured accurately. The eddy viscosity became significant only in the late nonlinear stages of the simulation.

  7. On explicit algebraic stress models for complex turbulent flows

    NASA Technical Reports Server (NTRS)

    Gatski, T. B.; Speziale, C. G.

    1992-01-01

    Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

  8. Modeling and eddy simulation of rotating and curved turbulent flows

    NASA Astrophysics Data System (ADS)

    Arolla, Sunil Kumar

    In the first part of this work, two different approaches to incorporate the effects of rotation and curvature in scalar eddy viscosity models have been explored. One is the "Modified coefficients approach"---to parameterize the model coefficients such that the growth rate of turbulent kinetic energy is suppressed or enhanced. The other is the "Bifurcation approach"---to parameterize eddy-viscosity coefficient such that the equilibrium solution bifurcates from healthy to decaying solution branches. Simple, yet, predictive models in each of these two approaches are proposed and validated on some benchmark test cases characterized by profound effects of system rotation and/or streamline curvature. The results obtained with both the models are encouraging. Application of the models to some practically relevant flow configurations is also discussed. In the second part, a computational framework is developed with recycling and rescaling method of inflow generation to perform eddy simulation of turbomachinery flows. A systematic validation is carried out on a spatially developing boundary layer on flat plate, flow through a channel and an annulus. Then, large eddy simulation of turbine transition duct is performed to demonstrate the effectiveness of this methodology.

  9. Viscosity of liquid anorthite.

    NASA Technical Reports Server (NTRS)

    Cukierman, M.; Uhlmann, D. R.

    1973-01-01

    The viscosity of liquid anorthite has been determined over the temperature ranges between 1450 to 1620 C and 820 to 950 C. The high-temperature data agree well with previous experimental data and with predictions of the Bottinga and Weill model. The overall log (viscosity) versus 1/T relation exhibits pronounced and rather continuous curvature. The viscosity of anorthite is higher at any given temperature and more strongly temperature-dependent than that of the anorthite-rich lunar compositions 14259, 14310, and 15418. The room-temperature density of glassy anorthite (2.64 gm/cu cm) and the thermal expansion coefficients of glassy and liquid anorthite have also been determined. The volume expansion coefficient for the glass is about 0.000018 per deg C, and that for the liquid is about 0.000048 per deg C. These values are used to relate the high-temperature flow data to the predictions of free-volume theories.

  10. Profiles of Algebraic Competence

    ERIC Educational Resources Information Center

    Humberstone, J.; Reeve, R.A.

    2008-01-01

    The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…

  11. Writing to Learn Algebra.

    ERIC Educational Resources Information Center

    Miller, L. Diane; England, David A.

    1989-01-01

    Describes a study in a large metropolitan high school to ascertain what influence the use of regular writing in algebra classes would have on students' attitudes towards algebra and their skills in algebra. Reports the simpler and more direct the writing topics the better. (MVL)

  12. Algebraic theory of molecules

    NASA Technical Reports Server (NTRS)

    Iachello, Franco

    1995-01-01

    An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.

  13. Applied Algebra Curriculum Modules.

    ERIC Educational Resources Information Center

    Texas State Technical Coll., Marshall.

    This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…

  14. Connecting Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Darley, Joy W.; Leapard, Barbara B.

    2010-01-01

    Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…

  15. Ternary Virasoro - Witt algebra.

    SciTech Connect

    Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham

    2008-01-01

    A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.

  16. Interview with Eddie Reisch

    ERIC Educational Resources Information Center

    Owen, Hazel

    2013-01-01

    Eddie Reisch is currently working as a policy advisor for Te Reo Maori Operational Policy within the Student Achievement group with the Ministry of Education in New Zealand, where he has implemented and led a range of e-learning initiatives and developments, particularly the Virtual Learning Network (VLN). He is regarded as one of the leading…

  17. Don Eddy; "Jewelry."

    ERIC Educational Resources Information Center

    Schaefer, Claire

    1989-01-01

    Presents a lesson that introduces students in grades K-three to sources of design inspiration in contemporary urban settings. Using Don Eddy's painting of a jewelry store window display, asks students to describe and analyze the interplay of shape, pattern, and color. Suggests studio activities, including an activity in which students build a…

  18. Eddies off Tasmania

    NASA Technical Reports Server (NTRS)

    2002-01-01

    This true-color satellite image shows a large phytoplankton bloom, several hundred square kilometers in size, in the Indian Ocean off the west coast of Tasmania. In this scene, the rich concentration of microscopic marine plants gives the water a lighter, more turquoise appearance which helps to highlight the current patterns there. Notice the eddies, or vortices in the water, that can be seen in several places. It is possible that these eddies were formed by converging ocean currents flowing around Tasmania, or by fresh river runoff from the island, or both. Often, eddies in the sea serve as a means for stirring the water, thus providing nutrients that help support phytoplankton blooms, which in turn provide nutrition for other organisms. Effectively, these eddies help feed the sea (click to read an article on this topic). This image was acquired November 7, 2000, by the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) flying aboard the Orbview-2 satellite. Tasmania is located off Australia's southeastern coast. Image courtesy SeaWiFS Project, NASA/Goddard Space Flight Center, and ORBIMAGE

  19. Computer algebra and operators

    NASA Technical Reports Server (NTRS)

    Fateman, Richard; Grossman, Robert

    1989-01-01

    The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.

  20. Viscosity of colloidal suspensions

    SciTech Connect

    Cohen, E.G.D.; Schepper, I.M. de

    1995-12-31

    Simple expressions are given for the effective Newtonian viscosity as a function of concentration as well as for the effective visco-elastic response as a function of concentration and imposed frequency, of monodisperse neutral colloidal suspensions over the entire fluid range. The basic physical mechanisms underlying these formulae are discussed. The agreement with existing experiments is very good.

  1. Discrete Minimal Surface Algebras

    NASA Astrophysics Data System (ADS)

    Arnlind, Joakim; Hoppe, Jens

    2010-05-01

    We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.

  2. Emergent eddy saturation from an energy constrained eddy parameterisation

    NASA Astrophysics Data System (ADS)

    Mak, J.; Marshall, D. P.; Maddison, J. R.; Bachman, S. D.

    2017-04-01

    The large-scale features of the global ocean circulation and the sensitivity of these features with respect to forcing changes are critically dependent upon the influence of the mesoscale eddy field. One such feature, observed in numerical simulations whereby the mesoscale eddy field is at least partially resolved, is the phenomenon of eddy saturation, where the time-mean circumpolar transport of the Antarctic Circumpolar Current displays relative insensitivity to wind forcing changes. Coarse-resolution models employing the Gent-McWilliams parameterisation with a constant Gent-McWilliams eddy transfer coefficient seem unable to reproduce this phenomenon. In this article, an idealised model for a wind-forced, zonally symmetric flow in a channel is used to investigate the sensitivity of the circumpolar transport to changes in wind forcing under different eddy closures. It is shown that, when coupled to a simple parameterised eddy energy budget, the Gent-McWilliams eddy transfer coefficient of the form described in Marshall et al. (2012) [A framework for parameterizing eddy potential vorticity fluxes, J. Phys. Oceanogr., vol. 42, 539-557], which includes a linear eddy energy dependence, produces eddy saturation as an emergent property.

  3. Derivation of an eddy diffusivity coefficient depending on source distance for a shear dominated planetary boundary layer

    NASA Astrophysics Data System (ADS)

    Alves, I. P.; Degrazia, G. A.; Buske, D.; Vilhena, M. T.; Moraes, O. L. L.; Acevedo, O. C.

    2012-12-01

    In this study an integral and an algebraic formulation for the eddy diffusivities in a shear driven planetary boundary layer are derived for pollutant dispersion applications. The expressions depend on the turbulence properties and on the distance from the source. They are based on the turbulent kinetic energy spectra, Taylor’s statistical diffusion theory and measured turbulent characteristics during intense wind events. The good agreement between the algebraic and the integral formulation for the eddy diffusivities corroborate the hypothesis that using an algebraic formulation as a surrogate for the eddy diffusivities in the neutral planetary boundary layer is valid. As a consequence, the vertical eddy diffusivity provided by the algebraic formulation and its asymptotic limit for large time (diffusion time much larger than the Lagrangian integral time scale), were introduced into an analytical air pollution model and validated against data from the classic Prairie Grass project. A statistical analysis, employing specific indices shows that the results are in good agreement with the observations. Furthermore, this study suggests that the inclusion of the memory effect, which is important in regions near to a continuous point source, improves the description of the turbulent transport process of atmospheric contaminants. Therefore, the major finding of this paper is the necessity of including the downwind distance-dependent eddy diffusivity for low continuous point sources in air quality modeling studies.

  4. Nonperiodic eddy pulsations

    USGS Publications Warehouse

    Rubin, David M.; McDonald, Richard R.

    1995-01-01

    Recirculating flow in lateral separation eddies is typically weaker than main stem flow and provides an effective environment for trapping sediment. Observations of recirculating flow and sedimentary structures demonstrate that eddies pulsate in size and in flow velocity even when main stem flow is steady. Time series measurements of flow velocity and location of the reattachment point indicate that these pulsations are nonperiodic. Nonperiodic flow in the lee of a channel margin constriction is grossly different from the periodic flow in the lee of a cylinder that is isolated in a flow. Our experiments demonstrate that placing a flow-parallel plate adjacent to a cylinder is sufficient to cause the leeside flow to change from a periodic sequence of vortices to a nonperiodically pulsating lateral separation eddy, even if flow conditions are otherwise unchanged. Two processes cause the leeside flow to become nonperiodic when the plate is added. First, vortices that are shed from the cylinder deform and become irregular as they impact the plate or interfere with remnants of other vortices near the reattachment point. Second, these deformed vortices and other flow structures are recirculated in the lateral separation eddy, thereby influencing the future state (pressure and momentum distribution) of the recirculating flow. The vortex deformation process was confirmed experimentally by documenting spatial differences in leeside flow; vortex shedding that is evident near the separation point is undetectable near the reattachment point. Nonlinear forecasting techniques were used in an attempt to distinguish among several possible kinds of nonperiodic flows. The computational techniques were unable to demonstrate that any of the nonperiodic flows result from low-dimensional nonlinear processes.

  5. Critical Viscosity of Xenon

    NASA Technical Reports Server (NTRS)

    2001-01-01

    The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. Shear thirning will cause a normally viscous fluid -- such as pie filling or whipped cream -- to deform and flow more readily under high shear conditions. In shear thinning, a pocket of fluid will deform and move one edge forward, as depicted here.

  6. The role of bulk viscosity on the decay of compressible, homogeneous, isotropic turbulence

    NASA Astrophysics Data System (ADS)

    Johnsen, Eric; Pan, Shaowu

    2016-11-01

    The practice of neglecting bulk viscosity in studies of compressible turbulence is widespread. While exact for monatomic gases and unlikely to strongly affect the dynamics of fluids whose bulk-to-shear viscosity ratio is small and/or of weakly compressible turbulence, this assumption is not justifiable for compressible, turbulent flows of gases whose bulk viscosity is orders of magnitude larger than their shear viscosities (e.g., CO2). To understand the mechanisms by which bulk viscosity and the associated phenomena affect compressible turbulence, we conduct DNS of freely decaying compressible, homogeneous, isotropic turbulence for ratios of bulk-to-shear viscosity ranging from 0-1000. Our simulations demonstrate that bulk viscosity increases the decay rate of turbulent kinetic energy; while enstrophy exhibits little sensitivity to bulk viscosity, dilatation is reduced by an order of magnitude within the two eddy turnover time. Via a Helmholtz decomposition of the flow, we determined that bulk viscosity damps the dilatational velocity and reduces dilatational-solenoidal exchanges, as well as pressure-dilatation coupling. In short, bulk viscosity renders compressible turbulence incompressible by reducing energy transfer between translational and internal modes.

  7. New subgrid-scale models for large-eddy simulation of Rayleigh-Bénard convection

    NASA Astrophysics Data System (ADS)

    Dabbagh, F.; Trias, F. X.; Gorobets, A.; Oliva, A.

    2016-09-01

    At the crossroad between flow topology analysis and the theory of turbulence, a new eddy-viscosity model for Large-eddy simulation has been recently proposed by Trias et al.[PoF, 27, 065103 (2015)]. The S3PQR-model has the proper cubic near-wall behaviour and no intrinsic limitations for statistically inhomogeneous flows. In this work, the new model has been tested for an air turbulent Rayleigh-Benard convection in a rectangular cell of aspect ratio unity and n span-wise open-ended distance. To do so, direct numerical simulation has been carried out at two Rayleigh numbers Ra = 108 and 1010, to assess the model performance and investigate a priori the effect of the turbulent Prandtl number. Using an approximate formula based on the Taylor series expansion, the turbulent Prandtl number has been calculated and revealed a constant and Ra-independent value across the bulk region equals to 0.55. It is found that the turbulent components of eddy-viscosity and eddy-diffusivity are positively prevalent to maintain a turbulent wind essentially driven by the mean buoyant force at the sidewalls. On the other hand, the new eddy-viscosity model is preliminary tested for the case of Ra = 108 and showed overestimation of heat flux within the boundary layer but fairly good prediction of turbulent kinetics at this moderate turbulent flow.

  8. Prediction of Algebraic Instabilities

    NASA Astrophysics Data System (ADS)

    Zaretzky, Paula; King, Kristina; Hill, Nicole; Keithley, Kimberlee; Barlow, Nathaniel; Weinstein, Steven; Cromer, Michael

    2016-11-01

    A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A new methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to the governing differential equation (or dispersion relation) describing wave propagation in dispersive media. Several types of algebraic instabilities are explored in the context of both linear and nonlinear waves.

  9. Connecting Algebra and Chemistry.

    ERIC Educational Resources Information Center

    O'Connor, Sean

    2003-01-01

    Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)

  10. Photoacoustic measurement of liquid viscosity

    NASA Astrophysics Data System (ADS)

    Lou, Cunguang; Xing, Da

    2010-05-01

    In this letter, we report on the use of photoacoustic method to measure the viscosity of viscous liquids. The theoretical and experimental study was performed on the influence of viscosity effects on photoacoustic generation. We provide evidence that the frequency spectrum of photoacoustic signal is precisely related to the viscosity. Measurements are validated on different water-glycerol mixtures. Good agreement between theoretical and experimental results is obtained. This present method provides an insight into in situ viscosity measurements, which has potential for noninvasive detection of blood viscosity.

  11. Explicit filtering and exact reconstruction of the sub-filter stresses in large eddy simulation

    NASA Astrophysics Data System (ADS)

    Bull, Jonathan R.; Jameson, Antony

    2016-02-01

    Explicit filtering has the effect of reducing numerical or aliasing errors near the grid scale in large eddy simulation (LES). We use a differential filter, namely the inverse Helmholtz operator, which is readily applied to unstructured meshes. The filter is invertible, which allows the sub-filter scale (SFS) stresses to be exactly reconstructed in terms of the filtered solution. Unlike eddy viscosity models, the method of filtering and reconstruction avoids making any physical assumptions and is therefore valid in any flow regime. The sub-grid scale (SGS) stresses are not recoverable by reconstruction, but the second-order finite element method used here is an adequate source of numerical dissipation in lieu of an SGS model. Results for incompressible turbulent channel flow at Reτ = 180 are presented which show that explicit filtering and exact SFS reconstruction is a significant improvement over the standard LES approach of implicit filtering and eddy-viscosity SGS modelling.

  12. Eddy Flow during Magma Emplacement: The Basemelt Sill, Antarctica

    NASA Astrophysics Data System (ADS)

    Petford, N.; Mirhadizadeh, S.

    2014-12-01

    The McMurdo Dry Valleys magmatic system, Antarctica, forms part of the Ferrar dolerite Large Igneous Province. Comprising a vertical stack of interconnected sills, the complex provides a world-class example of pervasive lateral magma flow on a continental scale. The lowermost intrusion (Basement Sill) offers detailed sections through the now frozen particle macrostructure of a congested magma slurry1. Image-based numerical modelling where the intrusion geometry defines its own unique finite element mesh allows simulations of the flow regime to be made that incorporate realistic magma particle size and flow geometries obtained directly from field measurements. One testable outcome relates to the origin of rhythmic layering where analytical results imply the sheared suspension intersects the phase space for particle Reynolds and Peclet number flow characteristic of macroscopic structures formation2. Another relates to potentially novel crystal-liquid segregation due to the formation of eddies locally at undulating contacts at the floor and roof of the intrusion. The eddies are transient and mechanical in origin, unrelated to well-known fluid dynamical effects around obstacles where flow is turbulent. Numerical particle tracing reveals that these low Re number eddies can both trap (remove) and eject particles back into the magma at a later time according to their mass density. This trapping mechanism has potential to develop local variations in structure (layering) and magma chemistry that may otherwise not occur where the contact between magma and country rock is linear. Simulations indicate that eddy formation is best developed where magma viscosity is in the range 1-102 Pa s. Higher viscosities (> 103 Pa s) tend to dampen the effect implying eddy development is most likely a transient feature. However, it is nice to think that something as simple as a bumpy contact could impart physical and by implication chemical diversity in igneous rocks. 1Marsh, D.B. (2004), A

  13. Viscosity Destabilizes Sonoluminescing Bubbles

    NASA Astrophysics Data System (ADS)

    Toegel, Ruediger; Luther, Stefan; Lohse, Detlef

    2006-03-01

    In single-bubble sonoluminescence (SBSL) microbubbles are trapped in a standing sound wave, typically in water or water-glycerol mixtures. However, in viscous liquids such as glycol, methylformamide, or sulphuric acid it is not possible to trap the bubble in a stable position. This is very peculiar as larger viscosity normally stabilizes the dynamics. Suslick and co-workers call this new mysterious state of SBSL “moving-SBSL.” We identify the history force (a force nonlocal in time) as the origin of this destabilization and show that the instability is parametric. A force balance model quantitatively accounts for the observed quasiperiodic bubble trajectories.

  14. Viscosity destabilizes sonoluminescing bubbles.

    PubMed

    Toegel, Ruediger; Luther, Stefan; Lohse, Detlef

    2006-03-24

    In single-bubble sonoluminescence (SBSL) microbubbles are trapped in a standing sound wave, typically in water or water-glycerol mixtures. However, in viscous liquids such as glycol, methylformamide, or sulphuric acid it is not possible to trap the bubble in a stable position. This is very peculiar as larger viscosity normally stabilizes the dynamics. Suslick and co-workers call this new mysterious state of SBSL "moving-SBSL." We identify the history force (a force nonlocal in time) as the origin of this destabilization and show that the instability is parametric. A force balance model quantitatively accounts for the observed quasiperiodic bubble trajectories.

  15. Critical Viscosity of Xenon

    NASA Technical Reports Server (NTRS)

    2001-01-01

    The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. The sample cell at the heart of CVX-2 will sit inside a thermostat providing three layers of insulation. The cell itself comprises a copper body that conducts heat efficiently and smoothes out thermal variations that that would destroy the xenon's uniformity. Inside the cell, the oscillating screen viscometer element is supported between two pairs of electrodes that deflect the screen and then measure screen motion.

  16. Critical Viscosity of Xenon

    NASA Technical Reports Server (NTRS)

    2001-01-01

    The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2001 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. The thermostat for CVX sits inside the white cylinder on a support structure that is placed inside a pressure canister. A similar canister holds the electronics and control systems. The CVX-2 arrangement is identical. The principal investigator is Dr. Robert F. Berg (not shown) of the National Institutes of Standards and Technology, Gaithersburg, MD. This is a detail view of MSFC 0100143.

  17. Critical Viscosity of Xenon

    NASA Technical Reports Server (NTRS)

    2001-01-01

    The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. Because xenon near the critical point will collapse under its own weight, experiments on Earth (green line) are limited as they get closer (toward the left) to the critical point. CVX in the microgravity of space (red line) moved into unmeasured territory that scientists had not been able to reach.

  18. A Realizable Reynolds Stress Algebraic Equation Model

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.

    1993-01-01

    The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

  19. Bicovariant quantum algebras and quantum Lie algebras

    NASA Astrophysics Data System (ADS)

    Schupp, Peter; Watts, Paul; Zumino, Bruno

    1993-10-01

    A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(mathfrak{G}_q ) to U q g, given by elements of the pure braid group. These operators—the “reflection matrix” Y≡L + SL - being a special case—generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N).

  20. Multi-layer quasi-geostrophic ocean dynamics in Eddy-resolving regimes

    NASA Astrophysics Data System (ADS)

    Shevchenko, I. V.; Berloff, P. S.

    2015-10-01

    The multi-layer quasi-geostrophic model of the wind-driven ocean gyres is numerically investigated using a combination of long-time runs (200 years) needed for accurate statistics, spatial resolutions (grid interval of less than one kilometer) needed for accurate representation of mesoscale eddies, and large Reynolds number (Re > 104) needed for more realistic flow regimes. We gradually increased the Reynolds number by lowering the eddy viscosity and analysed the corresponding changes of the large-scale circulation, energetics and eddy fluxes, with the goal to understand how the nonlinear eddy dynamics affects the large-scale ocean circulation, as more and more degrees of freedom become dynamically available. Three- and six-layer configurations of the model are considered in order to understand effects of higher baroclinic modes. A parameter sensitivity study is also carried out to show that the explored flow regime is robust. As Re increases, most properties of the flow show no signs of approaching an asymptote, and the following tendencies are found. The time-mean flow properties tend to an asymptote in the three-layer model but not in the six-layer one, suggesting that higher baroclinic modes are dynamically more active at larger Re. The eddy kinetic and potential energies grow faster in the six-layer case. The intensity of the eddy forcing (eddy flux divergence) increases with Re. The inter-gyre eddy potential vorticity flux is predominantly northward and up-gradient for all Re studied. A comparison of the three- and six-layer model solutions revealed an inhibitory influence of high baroclinic modes on the penetration length of the eastward jet extension of the western boundary currents and on the strength of the adjacent recirculation zones. In large-Re regimes, the population of eddies is mostly sustained by the eddy generation at the eastern end of the eastward jet rather than in its central section. Finally, by studying the numerical convergence of the

  1. Catching Up on Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2008-01-01

    A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…

  2. Parastatistics Algebras and Combinatorics

    NASA Astrophysics Data System (ADS)

    Popov, T.

    2005-03-01

    We consider the algebras spanned by the creation parafermionic and parabosonic operators which give rise to generalized parastatistics Fock spaces. The basis of such a generalized Fock space can be labelled by Young tableaux which are combinatorial objects. By means of quantum deformations a nice combinatorial structure of the algebra of the plactic monoid that lies behind the parastatistics is revealed.

  3. Algebraic Reasoning through Patterns

    ERIC Educational Resources Information Center

    Rivera, F. D.; Becker, Joanne Rossi

    2009-01-01

    This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…

  4. Learning Activity Package, Algebra.

    ERIC Educational Resources Information Center

    Evans, Diane

    A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…

  5. Linear-Algebra Programs

    NASA Technical Reports Server (NTRS)

    Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

    1982-01-01

    The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

  6. Ready, Set, Algebra?

    ERIC Educational Resources Information Center

    Levy, Alissa Beth

    2012-01-01

    The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this dissertation,…

  7. Teaching Structure in Algebra

    ERIC Educational Resources Information Center

    Merlin, Ethan M.

    2013-01-01

    This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…

  8. A posteriori testing of algebraic flame surface density models for LES

    NASA Astrophysics Data System (ADS)

    Ma, T.; Stein, O. T.; Chakraborty, N.; Kempf, A. M.

    2013-06-01

    In the application of Large Eddy Simulation (LES) to premixed combustion, the unknown filtered chemical source term can be modelled by the generalised flame surface density (FSD) using algebraic models for the wrinkling factor Ξ. The present study compares the behaviour of the various models by first examining the effect of sub-grid turbulent velocity fluctuation on Ξ through a one-dimensional analysis and by the LES of the ORACLES burner (Nguyen, Bruel, and Reichstadt, Flow, Turbulence and Combustion Vol. 82 [2009], pp. 155-183) and the Volvo Rig (Sjunnesson, Nelsson, and Max, Laser Anemometry, Vol. 3 [1991], pp. 83-90; Sjunnesson, Henrikson, and Löfström, AIAA Journal, Vol. 28 [1992], pp. AIAA-92-3650). Several sensitivity studies on parameters such as the turbulent viscosity and the grid resolution are also carried out. A statistically 1-D analysis of turbulent flame propagation reveals that counter gradient transport of the progress variable needs to be accounted for to obtain a realistic flame thickness from the simulations using algebraic FSD based closure. The two burner setups are found to operate mainly within the wrinkling/corrugated flamelet regime based on the premixed combustion diagram for LES (Pitsch and Duchamp de Lageneste, Proceedings of the Combustion Institute, Vol. 29 [2002], pp. 2001-2008) and this suggests that the models are operating within their ideal range. The performance of the algebraic models are then assessed by comparing velocity statistics, followed by a detailed error analysis for the ORACLES burner. Four of the tested models were found to perform reasonably well against experiments, and one of these four further excels in being the most grid-independent. For the Volvo Rig, more focus is placed upon the comparison of temperature data and identifying changes in flame structure amongst the different models. It is found that the few models which largely over-predict velocities in the ORACLES case and volume averaged ? in a

  9. Eddy current enhancement for EMATs

    NASA Astrophysics Data System (ADS)

    Palmer, S. B.; Jian, X.; Dixon, S.

    2007-04-01

    When an electromagnetic acoustic transducer (EMAT) is used to generate ultrasound in an electrically conducting sample, eddy currents are generated in the sample's skin depth as the first stage in transduction. The resultant acoustic wave amplitude is proportional to the amplitude of this eddy current, and so anything that we can do to increase the eddy current will lead to the generation of larger amplitude ultrasonic waves. In eddy current testing, wire coils are often wound onto a ferrite core to increase the generated eddy current, with the effect that inductance of the coil increases greatly. When we are dealing with an EMAT, any increase in the coil inductance is usually unacceptable as it leads to a reduction in the amplitude of a given frequency of eddy current from a limited voltage source. This is particularly relevant where current arises from capacitor discharge, as is typically used in EMAT driver current circuitry. We present a method for electromagnetic acoustic transduction where ferrite is used to increase eddy current amplitude, without significantly increasing coil inductance or changing the frequency content of the eddy current or the generated acoustic wave.

  10. Study of eddy current probes

    NASA Technical Reports Server (NTRS)

    Workman, Gary L.; Wang, Morgan

    1992-01-01

    The recognition of materials properties still presents a number of problems for nondestructive testing in aerospace systems. This project attempts to utilize current capabilities in eddy current instrumentation, artificial intelligence, and robotics in order to provide insight into defining geometrical aspects of flaws in composite materials which are capable of being evaluated using eddy current inspection techniques.

  11. Eddy diffusivity in the ocean surface

    NASA Astrophysics Data System (ADS)

    Redondo, Jose M.; Castilla, Robert; Platonov, Alexei

    2010-05-01

    In order to measure eddy diffusivity in the ocean using a scaling that includes the thickness of the surf zone as well as the depth and the wave period[1,2]. Measurements in the Mediterranean are almost two orders of magnitude smaller than in the Pacific coast. On a larger scale, and further away from the coast the relevant eddy diffusivities are much larger, because large eddies often scale on the Rossby deformation radius, LR. Direct measurements of the diffusion and the horizontal velocity field were performed at several sites in the coastal areas of Spain. The diffusion coeficients were calculated by evaluation from video images of the area of milk and fluoresceine blobs released at different positions and with different wave heights, wind speeds and tidal induced currents[1-3]. There are instances with either low hipo-diffusivity or high hyper-diffusivity and local measurements in both cases indicate that spectra deviate strongly from an equilibrium spectrum. A generalized Richardson law [3,4] deduced from Kinematic Simulation (KS) numerical models may be applied also to coastal diffusion[5]. The eddy viscosity values show a complex behaviour that depends on wind friction, wave induced Reynolds number and flow topology. The results of more than 100 experiments show that there is a dependence of the maximum diffusivity on a Reynolds number derived from the wave height[1]. The increase of diffusivity with wave height only occurs for large enough wave Reynolds numbers. Other important factors are wind speed and tidal currents. The horizontal diffusivity shows also a marked anisotropy and spectral dependence [4,6]. [1] M. Diez, M. O. Bezerra, C. Mosso, R. Castilla and J. M. Redondo,Experimental measurements and diffusion in harbor and coastal zones. Il Nuovo Cimento Vol. 31 C, N. 5-6 Settembre-Dicembre (2008), 843. [2] Carrillo A., Sanchez M. A., Platonov A. and Redondo J. M., Phys. Chem. Earth B, 26. 4 (2001) 305. [3] Redondo J. M., Sanchez M. A. and Castilla R

  12. Viscosity of the earth's core.

    NASA Technical Reports Server (NTRS)

    Gans, R. F.

    1972-01-01

    Calculation of the viscosity of the core at the boundary of the inner and outer core. It is assumed that this boundary is a melting transition and the viscosity limits of the Andrade (1934,1952) hypothesis (3.7 to 18.5 cp) are adopted. The corresponding kinematic viscosities are such that the precessional system explored by Malkus (1968) would be unstable. Whether it would be sufficiently unstable to overcome a severely subadiabatic temperature gradient cannot be determined.

  13. Modeling mesoscale eddies

    NASA Astrophysics Data System (ADS)

    Canuto, V. M.; Dubovikov, M. S.

    Mesoscale eddies are not resolved in coarse resolution ocean models and must be modeled. They affect both mean momentum and scalars. At present, no generally accepted model exists for the former; in the latter case, mesoscales are modeled with a bolus velocity u∗ to represent a sink of mean potential energy. However, comparison of u∗(model) vs. u∗ (eddy resolving code, [J. Phys. Ocean. 29 (1999) 2442]) has shown that u∗(model) is incomplete and that additional terms, "unrelated to thickness source or sinks", are required. Thus far, no form of the additional terms has been suggested. To describe mesoscale eddies, we employ the Navier-Stokes and scalar equations and a turbulence model to treat the non-linear interactions. We then show that the problem reduces to an eigenvalue problem for the mesoscale Bernoulli potential. The solution, which we derive in analytic form, is used to construct the momentum and thickness fluxes. In the latter case, the bolus velocity u∗ is found to contain two types of terms: the first type entails the gradient of the mean potential vorticity and represents a positive contribution to the production of mesoscale potential energy; the second type of terms, which is new, entails the velocity of the mean flow and represents a negative contribution to the production of mesoscale potential energy, or equivalently, a backscatter process whereby a fraction of the mesoscale potential energy is returned to the original reservoir of mean potential energy. This type of terms satisfies the physical description of the additional terms given by [J. Phys. Ocean. 29 (1999) 2442]. The mesoscale flux that enters the momentum equations is also contributed by two types of terms of the same physical nature as those entering the thickness flux. The potential vorticity flux is also shown to contain two types of terms: the first is of the gradient-type while the other terms entail the velocity of the mean flow. An expression is derived for the mesoscale

  14. Viscosity measuring instrument

    NASA Technical Reports Server (NTRS)

    Feinstein, S. P. (Inventor)

    1980-01-01

    A method and apparatus are provided for enabling the measurement of the viscosity of substances, especially those containing volatiles at elevated temperatures, with greater accuracy and at less cost than before. The apparatus includes a cylinder with a narrow exit opening at one end and a piston which closely slides within the cylinder to apply force against a sample in the cylinder to force the sample through the exit opening. In order to more rapidly heat a sample the ends of the cylinder and piston are tapered and the sample is correspondingly tapered, to provide a large surface to volume ratio. A corresponding coal sample is formed by compressing particles of coal under high pressure in a mold of appropriate shape.

  15. Critical Viscosity of Xenon

    NASA Technical Reports Server (NTRS)

    2001-01-01

    The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of liquid xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. Resembling a tiny bit of window screen, the oscillator at the heart of CVX-2 will vibrate between two pairs of paddle-like electrodes. The slight bend in the shape of the mesh has no effect on the data. What counts are the mesh's displacement in the xenon fluid and the rate at which the displacement dampens. The unit shown here is encased in a small test cell and capped with a sapphire windown to contain the xenon at high pressure.

  16. Negative-viscosity lattice gases

    SciTech Connect

    Rothman, D.H. )

    1989-08-01

    A new irreversible collision rule is introduced for lattice-gas automata. The rule maximizes the flux of momentum in the direction of the local momentum gradient, yielding a negative shear viscosity. Numerically results in 2D show that the negative viscosity leads to the spontaneous ordering of the velocity field, with vorticity resolvable down to one lattice-link length. The new rule may be used in conjunction with previously proposed collision rules to yield a positive shear viscosity lower than the previous rules provide. In particular, Poiseuille flow tests demonstrate a decrease in viscosity by more than a factor of 2.

  17. Algebraic Nonlinear Collective Motion

    NASA Astrophysics Data System (ADS)

    Troupe, J.; Rosensteel, G.

    1998-11-01

    Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real numberΛ. TheΛ=0 solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positiveΛ, the droplets have a neck that becomes more pronounced asΛincreases; for negativeΛ, the droplets contain a spherical bubble of radius |Λ|1/3. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes (Λ>0) and bubble and two-fluid nuclei (Λ<0).

  18. Algebraic invariants for homotopy types

    NASA Astrophysics Data System (ADS)

    Blanc, David

    1999-11-01

    We define a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the [Pi]-algebra [pi][low asterisk]X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract [Pi]-algebra can be realized as the homotopy [Pi]-algebra of a space.

  19. A Richer Understanding of Algebra

    ERIC Educational Resources Information Center

    Foy, Michelle

    2008-01-01

    Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number,…

  20. Large eddy simulation of the flow in a transpired channel

    NASA Technical Reports Server (NTRS)

    Piomelli, Ugo; Moin, Parviz; Ferziger, Joel

    1989-01-01

    The flow in a transpired channel has been computed by large eddy simulation. The numerical results compare very well with experimental data. Blowing decreases the wall shear stress and enhances turbulent fluctuations, while suction has the opposite effect. The wall layer thickness normalized by the local wall shear velocity and kinematic viscosity increases on the blowing side of the channel and decreases on the suction side. Suction causes more rapid decay of the spectra, larger mean streak spacing and higher two-point correlations. On the blowing side, the wall layer structures lie at a steeper angle to the wall, whereas on the suction side this angle is shallower.

  1. A dynamic framework for subgrid-scale parametrization of mesoscale eddies in geophysical flows

    NASA Astrophysics Data System (ADS)

    San, Omer; Maulik, Romit

    2016-11-01

    This study puts forth a modular dynamic subgrid-scale modeling framework for large eddy simulation of quasigeostrophic turbulence based upon minimizing the errors between structural and functional subgrid-scale models. The approximate deconvolution procedure (AD) is used to estimate the free modeling parameters for the eddy viscosity coefficient parameterized in space and time using the Smagorinsky and Leith models. The novel idea here is to estimate the modeling parameters using the AD method rather than a test filter. The proposed model is applied to a wind-driven quasigeostrophic four-gyre ocean circulation problem, which is a standard prototype of more realistic ocean dynamics. Results show that the proposed model captures the quasi-stationary ocean dynamics and provides the time averaged four-gyre circulation patterns. Taking into account for local resolved flow characteristics, the model dynamically provides higher eddy viscosity values for lower resolutions. Furthermore, our first step in the numerical assessment for solving the quasigeostrophic turbulence problem addresses the intimate relationship between the eddy viscosity coefficients and the numerical resolution employed by the quasigeostrophic models.

  2. Pseudo-Riemannian Novikov algebras

    NASA Astrophysics Data System (ADS)

    Chen, Zhiqi; Zhu, Fuhai

    2008-08-01

    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.

  3. Effective Viscosity Coefficient of Nanosuspensions

    NASA Astrophysics Data System (ADS)

    Rudyak, V. Ya.; Belkin, A. A.; Egorov, V. V.

    2008-12-01

    Systematic calculations of the effective viscosity coefficient of nanosuspensions have been performed using the molecular dynamics method. It is established that the viscosity of a nanosuspension depends not only on the volume concentration of the nanoparticles but also on their mass and diameter. Differences from Einstein's relation are found even for nanosuspensions with a low particle concentration.

  4. Low viscosity oils. [oxidation resistance

    SciTech Connect

    Harris, S.W.; Schaap, L.A.; Udelhofen, J.H.

    1981-08-04

    An improved low viscosity (I.E.) 5 W to 7 1/2 W engine oil resistant to oxidation and consumption comprising a major portion of a lubricating oil stock, a sulfurized oil, a dispersant, an anti-corrosion agent, an anti-rust agent, a detergent, an antioxidant, and a viscosity index improver.

  5. Weyl n-Algebras

    NASA Astrophysics Data System (ADS)

    Markarian, Nikita

    2017-03-01

    We introduce Weyl n-algebras and show how their factorization complex may be used to define invariants of manifolds. In the appendix, we heuristically explain why these invariants must be perturbative Chern-Simons invariants.

  6. Developing Algebraic Thinking.

    ERIC Educational Resources Information Center

    Alejandre, Suzanne

    2002-01-01

    Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)

  7. Jordan Algebraic Quantum Categories

    NASA Astrophysics Data System (ADS)

    Graydon, Matthew; Barnum, Howard; Ududec, Cozmin; Wilce, Alexander

    2015-03-01

    State cones in orthodox quantum theory over finite dimensional complex Hilbert spaces enjoy two particularly essential features: homogeneity and self-duality. Orthodox quantum theory is not, however, unique in that regard. Indeed, all finite dimensional formally real Jordan algebras -- arenas for generalized quantum theories with close algebraic kinship to the orthodox theory -- admit homogeneous self-dual positive cones. We construct categories wherein these theories are unified. The structure of composite systems is cast from universal tensor products of the universal C*-algebras enveloping ambient spaces for the constituent state cones. We develop, in particular, a notion of composition that preserves the local distinction of constituent systems in quaternionic quantum theory. More generally, we explicitly derive the structure of hybrid quantum composites with subsystems of arbitrary Jordan algebraic type.

  8. Accounting Equals Applied Algebra.

    ERIC Educational Resources Information Center

    Roberts, Sondra

    1997-01-01

    Argues that students should be given mathematics credits for completing accounting classes. Demonstrates that, although the terminology is different, the mathematical concepts are the same as those used in an introductory algebra class. (JOW)

  9. Volatiles Which Increase Magma Viscosity

    NASA Astrophysics Data System (ADS)

    Webb, S.

    2015-12-01

    The standard model of an erupting volcano is one in which the viscosity of a decompressing magma increases as the volatiles leave the melt structure to form bubbles. It has now been observed that the addition of the "volatiles" P, Cl and F result in an increase in silicate melt viscosity. This observation would mean that the viscosity of selected degassing magmas would decrease rather than increase. Here we look at P, Cl and F as three volatiles which increase viscosity through different structural mechanisms. In all three cases the volatiles increase the viscosity of peralkaline composition melts, but appear to always decrease the viscosity of peraluminous melts. Phosphorus causes the melt to unmix into a Na-P rich phase and a Na-poor silicate phase. Thus as the network modifying Na (or Ca) are removed to the phosphorus-rich melt, the matrix melt viscosity increases. With increasing amounts of added phosphorus (at network modifying Na ~ P) the addition of further phosphorus causes a decrease in viscosity. The addition of chlorine to Fe-free aluminosilicate melts results in an increase in viscosity. NMR data on these glass indicates that the chlorine sits in salt-like structures surrounded by Na and/or Ca. Such structures would remove network-modifying atoms from the melt structure and thus result in an increase in viscosity. The NMR spectra of fluorine-bearing glasses shows that F takes up at least 5 different structural positions in peralkaline composition melts. Three of these positions should result in a decrease in viscosity due to the removal of bridging oxygens. Two of the structural positons of F, however, should result in an increase in viscosity as they require the removal of network-modifying atoms from the melt structure (with one of the structures being that observed for Cl). This would imply that increasing amounts of F might result in an increase in viscosity. This proposed increase in viscosity with increasing F has now been experimentally confirmed.

  10. Covariant deformed oscillator algebras

    NASA Technical Reports Server (NTRS)

    Quesne, Christiane

    1995-01-01

    The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.

  11. Aprepro - Algebraic Preprocessor

    SciTech Connect

    2005-08-01

    Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.

  12. Plasma viscosity: a forgotten variable.

    PubMed

    Késmárky, Gábor; Kenyeres, Péter; Rábai, Miklós; Tóth, Kálmán

    2008-01-01

    Evaluation of plasma viscosity has been underutilized in the clinical practice. Plasma viscosity is determined by water-content and macromolecular components. Plasma is a highly concentrated protein solution, therefore weak protein-protein interactions can play a role that is not characterized by electrophoresis. The effect of a protein on plasma viscosity depends on its molecular weight and structure. The less spheroid shape, the higher molecular weight, the higher aggregating capacity, and the higher temperature or pH sensitivity a protein has, the higher plasma viscosity results. Plasma is a Newtonian fluid, its viscosity does not depend on flow characteristics, therefore it is simple to measure, especially in capillary viscosimeters. Its normal value is 1.10-1.30 mPa s at 37 degrees C and independent of age and gender. The measurement has high stability and accuracy, thus little alterations may be pathologically important. Inflammations, tissue injuries resulting in plasma protein changes can increase its value with high sensitivity, though low specificity. It can increase in parallel with erythrocyte sedimentation rate (ESR), but it is not influenced by hematocrit (anemia, polycytemia), or time to analysis. Based on these favorable features, in 1942 plasma viscosity was recommended to substitute ESR. In hyperviscosity syndromes plasma viscosity is better in follow-up than ESR. In rheumatoid arthritis, its sensitivity and specificity are better than that of ESR or C-reactive protein. Plasma fibrinogen concentration and plasma viscosity are elevated in unstable angina pectoris and stroke and their higher values are associated with higher rate of major adverse clinical events. Elevation of plasma viscosity correlates to the progression of coronary and peripheral artery diseases. In conclusion, plasma viscosity should be measured routinely in medical practice.

  13. Anomalous - viscosity current drive

    DOEpatents

    Stix, Thomas H.; Ono, Masayuki

    1988-01-01

    An apparatus and method for maintaining a steady-state current in a toroidal magnetically confined plasma. An electric current is generated in an edge region at or near the outermost good magnetic surface of the toroidal plasma. The edge current is generated in a direction parallel to the flow of current in the main plasma and such that its current density is greater than the average density of the main plasma current. The current flow in the edge region is maintained in a direction parallel to the main current for a period of one or two of its characteristic decay times. Current from the edge region will penetrate radially into the plasma and augment the main plasma current through the mechanism of anomalous viscosity. In another aspect of the invention, current flow driven between a cathode and an anode is used to establish a start-up plasma current. The plasma-current channel is magnetically detached from the electrodes, leaving a plasma magnetically insulated from contact with any material obstructions including the cathode and anode.

  14. An eddy closure for potential vorticity

    SciTech Connect

    Ringler, Todd D

    2009-01-01

    The Gent-McWilliams (GM) parameterization is extended to include a direct influence in the momentum equation. The extension is carried out in two stages; an analysis of the inviscid system is followed by an analysis of the viscous system. In the inviscid analysis the momentum equation is modified such that potential vorticity is conserved along particle trajectories following a transport velocity that includes the Bolus velocity in a manner exactly analogous to the continuity and tracer equations. In addition (and in contrast to traditional GM closures), the new formulation of the inviscid momentum equation results in a conservative exchange between potential and kinetic forms of energy. The inviscid form of the eddy closure conserves total energy to within an error proportional to the time derivative of the Bolus velocity. The hypothesis that the viscous term in the momentum equation should give rise to potential vorticity being diffused along isopycnals in a manner analogous to other tracers is examined in detail. While the form of the momentum closure that follows from a strict adherence to this hypothesis is not immediately interpretable within the constructs of traditional momentum closures, three approximations to this hypothesis results in a form of dissipation that is consistent with traditional Laplacian diffusion. The first two approximations are that relative vorticity, not potential vorticity, is diffused along isopyncals and that the flow is in approximate geostrophic balance. An additional approximation to the Jacobian term is required when the dissipation coefficient varies in space. More importantly, the critique of this hypothesis results in the conclusion that the viscosity parameter in the momentum equation should be identical to the tradition GM closure parameter {Kappa}. Overall, we deem the viscous form of the eddy closure for potential vorticity as a viable closure for use in ocean circulation models.

  15. ZBLAN Viscosity Instrumentation

    NASA Technical Reports Server (NTRS)

    Kaukler, William

    2001-01-01

    The past year's contribution from Dr. Kaukler's experimental effort consists of these 5 parts: a) Construction and proof-of-concept testing of a novel shearing plate viscometer designed to produce small shear rates and operate at elevated temperatures; b) Preparing nonlinear polymeric materials to serve as standards of nonlinear Theological behavior; c) Measurements and evaluation of above materials for nonlinear rheometric behavior at room temperature using commercial spinning cone and plate viscometers available in the lab; d) Preparing specimens from various forms of pitch for quantitative comparative testing in a Dynamic Mechanical Analyzer, Thermal Mechanical Analyzer; and Archeological Analyzer; e) Arranging to have sets of pitch specimens tested using the various instruments listed above, from different manufacturers, to form a baseline of the viscosity variation with temperature using the different test modes offered by these instruments by compiling the data collected from the various test results. Our focus in this project is the shear thinning behavior of ZBLAN glass over a wide range of temperature. Experimentally, there are no standard techniques to perform such measurements on glasses, particularly at elevated temperatures. Literature reviews to date have shown that shear thinning in certain glasses appears to occur, but no data is available for ZBLAN glass. The best techniques to find shear thinning behavior require the application of very low rates of shear. In addition, because the onset of the thinning behavior occurs at an unknown elevated temperature, the instruments used in this study must provide controlled low rates of shear and do so for temperatures approaching 600 C. In this regard, a novel shearing parallel plate viscometer was designed and a prototype built and tested.

  16. Critical Viscosity of Xenon investigators

    NASA Technical Reports Server (NTRS)

    2001-01-01

    Dr. Dr. Robert F. Berg (right), principal investigator and Dr. Micheal R. Moldover (left), co-investigator, for the Critical Viscosity of Xenon (CVX/CVX-2) experiment. They are with the National Institutes of Standards and Technology, Gaithersburg, MD. The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. Although it does not easily combine with other chemicals, its viscosity at the critical point can be used as a model for a range of chemicals.

  17. Fluid Merging Viscosity Measurement (FMVM)

    NASA Technical Reports Server (NTRS)

    2004-01-01

    Astronaut Mike Fincke places droplets of honey onto the strings for the Fluid Merging Viscosity Measurement (FMVM) investigation onboard the International Space Station (ISS). The FMVM experiment measures the time it takes for two individual highly viscous fluid droplets to coalesce or merge into one droplet. Different fluids and droplet size combinations were tested in the series of experiments. By using the microgravity environment, researchers can measure the viscosity or 'thickness' of fluids without the influence of containers and gravity using this new technique. Understanding viscosity could help scientists understand industrially important materials such as paints, emulsions, polymer melts and even foams used to produce pharmaceutical, food, and cosmetic products.

  18. Viscosity Measurement for Tellurium Melt

    NASA Technical Reports Server (NTRS)

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

    2006-01-01

    The viscosity of high temperature Te melt was measured using a new technique in which a rotating magnetic field was applied to the melt sealed in a suspended ampoule, and the torque exerted by rotating melt flow on the ampoule wall was measured. Governing equations for the coupled melt flow and ampoule torsional oscillation were solved, and the viscosity was extracted from the experimental data by numerical fitting. The computational result showed good agreement with experimental data. The melt velocity transient initiated by the rotating magnetic field reached a stable condition quickly, allowing the viscosity and electrical conductivity of the melt to be determined in a short period.

  19. Scale-Similar Models for Large-Eddy Simulations

    NASA Technical Reports Server (NTRS)

    Sarghini, F.

    1999-01-01

    Scale-similar models employ multiple filtering operations to identify the smallest resolved scales, which have been shown to be the most active in the interaction with the unresolved subgrid scales. They do not assume that the principal axes of the strain-rate tensor are aligned with those of the subgrid-scale stress (SGS) tensor, and allow the explicit calculation of the SGS energy. They can provide backscatter in a numerically stable and physically realistic manner, and predict SGS stresses in regions that are well correlated with the locations where large Reynolds stress occurs. In this paper, eddy viscosity and mixed models, which include an eddy-viscosity part as well as a scale-similar contribution, are applied to the simulation of two flows, a high Reynolds number plane channel flow, and a three-dimensional, nonequilibrium flow. The results show that simulations without models or with the Smagorinsky model are unable to predict nonequilibrium effects. Dynamic models provide an improvement of the results: the adjustment of the coefficient results in more accurate prediction of the perturbation from equilibrium. The Lagrangian-ensemble approach [Meneveau et al., J. Fluid Mech. 319, 353 (1996)] is found to be very beneficial. Models that included a scale-similar term and a dissipative one, as well as the Lagrangian ensemble averaging, gave results in the best agreement with the direct simulation and experimental data.

  20. Algebraic mesh quality metrics

    SciTech Connect

    KNUPP,PATRICK

    2000-04-24

    Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally-invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix of an ideal reference element. Scale and orientation-invariant algebraic mesh quality metrics are defined. the singular value decomposition is used to study relationships between metrics. Equivalence of the element condition number and mean ratio metrics is proved. Condition number is shown to measure the distance of an element to the set of degenerate elements. Algebraic measures for skew, length ratio, shape, volume, and orientation are defined abstractly, with specific examples given. Combined metrics for shape and volume, shape-volume-orientation are algebraically defined and examples of such metrics are given. Algebraic mesh quality metrics are extended to non-simplical elements. A series of numerical tests verify the theoretical properties of the metrics defined.

  1. Applied large eddy simulation.

    PubMed

    Tucker, Paul G; Lardeau, Sylvain

    2009-07-28

    Large eddy simulation (LES) is now seen more and more as a viable alternative to current industrial practice, usually based on problem-specific Reynolds-averaged Navier-Stokes (RANS) methods. Access to detailed flow physics is attractive to industry, especially in an environment in which computer modelling is bound to play an ever increasing role. However, the improvement in accuracy and flow detail has substantial cost. This has so far prevented wider industrial use of LES. The purpose of the applied LES discussion meeting was to address questions regarding what is achievable and what is not, given the current technology and knowledge, for an industrial practitioner who is interested in using LES. The use of LES was explored in an application-centred context between diverse fields. The general flow-governing equation form was explored along with various LES models. The errors occurring in LES were analysed. Also, the hybridization of RANS and LES was considered. The importance of modelling relative to boundary conditions, problem definition and other more mundane aspects were examined. It was to an extent concluded that for LES to make most rapid industrial impact, pragmatic hybrid use of LES, implicit LES and RANS elements will probably be needed. Added to this further, highly industrial sector model parametrizations will be required with clear thought on the key target design parameter(s). The combination of good numerical modelling expertise, a sound understanding of turbulence, along with artistry, pragmatism and the use of recent developments in computer science should dramatically add impetus to the industrial uptake of LES. In the light of the numerous technical challenges that remain it appears that for some time to come LES will have echoes of the high levels of technical knowledge required for safe use of RANS but with much greater fidelity.

  2. Viscosity Depressants for Coal Liquefaction

    NASA Technical Reports Server (NTRS)

    Kalfayan, S. H.

    1983-01-01

    Proposed process modification incorporates viscosity depressants to prevent coal from solidifying during liquefaction. Depressants reduce amount of heat needed to liquefy coal. Possible depressants are metallic soaps, such as stearate, and amides, such as stearamide and dimer acid amides.

  3. On the roles of baroclinic modes in eddy-resolving midlatitude ocean dynamics

    NASA Astrophysics Data System (ADS)

    Shevchenko, Igor; Berloff, Pavel

    2017-03-01

    This work concerns how different baroclinic modes interact and influence solutions of the midlatitude ocean dynamics described by the eddy-resolving quasi-geostrophic model of wind-driven gyres. We developed multi-modal energetics analysis to illuminate dynamical roles of the vertical modes, carried out a systematic analysis of modal energetics and found that the eddy-resolving dynamics of the eastward jet extension of the western boundary currents, such as the Gulf Stream or Kuroshio, is dominated by the barotropic, and the first and second baroclinic modes, which become more energized with smaller eddy viscosity. In the absence of high baroclinic modes, the energy input from the wind is more efficiently focused onto the lower modes, therefore, the eddy backscatter maintaining the eastward jet and its adjacent recirculation zones is the strongest and overestimated with respect to cases including higher baroclinic modes. In the presence of high baroclinic modes, the eddy backscatter effect on the eastward jet is much weaker. Thus, the higher baroclinic modes play effectively the inhibiting role in the backscatter, which is opposite to what has been previously thought. The higher baroclinic modes are less energetic and have progressively decreasing effect on the flow dynamics; nevertheless, they still play important roles in inter-mode energy transfers (by injecting energy into the region of the most intensive eddy forcing, in the neighborhood of the eastward jet) that have to be taken into account for correct representation of the backscatter and, thus, for determining the eastward jet extension.

  4. Hydrodynamic Viscosity in Accretion Disks

    NASA Astrophysics Data System (ADS)

    Duschl, Wolfgang J.; Strittmatter, Peter A.; Biermann, Peter L.

    We propose a generalized accretion disk viscosity prescription based on hydrodynamically driven turbulence at the critical effective Reynolds number. This approach is consistent with recent re-analysis by Richard & Zahn (1999) of experimental results on turbulent Couette-Taylor flows. This new β-viscosity formulation applies to both selfgravitating and non-selfgravitating disks and is shown to yield the standard α-disk prescription in the case of shock dissipation limited, non-selfgravitating disks.

  5. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2016-01-01

    This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

  6. Adaptive Algebraic Multigrid Methods

    SciTech Connect

    Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J

    2004-04-09

    Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.

  7. Resonant algebras and gravity

    NASA Astrophysics Data System (ADS)

    Durka, R.

    2017-04-01

    The S-expansion framework is analyzed in the context of a freedom in closing the multiplication tables for the abelian semigroups. Including the possibility of the zero element in the resonant decomposition, and associating the Lorentz generator with the semigroup identity element, leads to a wide class of the expanded Lie algebras introducing interesting modifications to the gauge gravity theories. Among the results, we find all the Maxwell algebras of type {{B}m} , {{C}m} , and the recently introduced {{D}m} . The additional new examples complete the resulting generalization of the bosonic enlargements for an arbitrary number of the Lorentz-like and translational-like generators. Some further prospects concerning enlarging the algebras are discussed, along with providing all the necessary constituents for constructing the gravity actions based on the obtained results.

  8. On weak Lie 2-algebras

    NASA Astrophysics Data System (ADS)

    Roytenberg, Dmitry

    2007-11-01

    A Lie 2-algebra is a linear category equipped with a functorial bilinear operation satisfying skew-symmetry and Jacobi identity up to natural transformations which themselves obey coherence laws of their own. Functors and natural transformations between Lie 2-algebras can also be defined, yielding a 2-category. Passing to the normalized chain complex gives an equivalence of 2-categories between Lie 2-algebras and certain "up to homotopy" structures on the complex; for strictly skew-symmetric Lie 2-algebras these are L∞-algebras, by a result of Baez and Crans. Lie 2-algebras appear naturally as infinitesimal symmetries of solutions of the Maurer-Cartan equation in some differential graded Lie algebras and L∞-algebras. In particular, (quasi-) Poisson manifolds, (quasi-) Lie bialgebroids and Courant algebroids provide large classes of examples.

  9. Algebra for Gifted Third Graders.

    ERIC Educational Resources Information Center

    Borenson, Henry

    1987-01-01

    Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)

  10. A Holistic Approach to Algebra.

    ERIC Educational Resources Information Center

    Barbeau, Edward J.

    1991-01-01

    Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

  11. Computer Program For Linear Algebra

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.; Hanson, R. J.

    1987-01-01

    Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.

  12. An algebra of reversible computation.

    PubMed

    Wang, Yong

    2016-01-01

    We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.

  13. Large Eddy Simulations of Transverse Combustion Instability in a Multi-Element Injector

    DTIC Science & Technology

    2016-07-27

    simulate sub-scale experiments. The efforts have focused on validating the potential use of CFD to study instability followed by the application of the...limits their applicability in new or novel designs, or in building a fundamental under- standing of the instability. The conditions inside the combustor...discretization scheme. A sub-grid eddy- viscosity based model that utilizes the sub-grid kinetic energy (ksgs) as characteristic velocity scale and a local filter

  14. Discontinuous Galerkin methods for dispersive shallow water models in closed basins: Spurious eddies and their removal using curved boundary methods

    NASA Astrophysics Data System (ADS)

    Steinmoeller, D. T.; Stastna, M.; Lamb, K. G.

    2016-11-01

    Discontinuous Galerkin methods offer a promising methodology for treating nearly hyperbolic systems such as dispersion-modified shallow water equations in complicated basins. Use of straight-edged triangular elements can lead to the generation of spurious eddies when wave fronts propagate around sharp, re-entrant obstacles such as headlands. While these eddies may be removed by adding strong artificial dissipation (e.g., eddy viscosity), for nearly inviscid simulations that focus on wave phenomena this approach is not reasonable. We demonstrate that the moderate order Discontinuous Galerkin methodology may be extended to curved triangular elements provided that the integral formulations are computed with high-order quadrature and cubature rules. Simulations with the new technique do not exhibit spurious eddy generation in idealized complex domains or real-world basins as exemplified by Pinehurst Lake, Alberta, Canada.

  15. From Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott

    2007-01-01

    Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…

  16. Computers in Abstract Algebra

    ERIC Educational Resources Information Center

    Nwabueze, Kenneth K.

    2004-01-01

    The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…

  17. Algebraic Thinking through Origami.

    ERIC Educational Resources Information Center

    Higginson, William; Colgan, Lynda

    2001-01-01

    Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)

  18. Computer Algebra versus Manipulation

    ERIC Educational Resources Information Center

    Zand, Hossein; Crowe, David

    2004-01-01

    In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…

  19. Viscosities of aqueous blended amines

    SciTech Connect

    Hsu, C.H.; Li, M.H.

    1997-07-01

    Solutions of alkanolamines are an industrially important class of compounds used in the natural gas, oil refineries, petroleum chemical plants, and synthetic ammonia industries for the removal of acidic components like CO{sub 2} and H{sub 2}S from gas streams. The viscosities of aqueous mixtures of diethanolamine (DEA) + N-methyldiethanolamine (MDEA), DEA + 2-amino-2-methyl-1-propanol (AMP), and monoethanolamine (MEA) + 2-piperidineethanol (2-PE) were measured from 30 C to 80 C. A Redlich-Kister equation for the viscosity deviation was applied to represent the viscosity. On the basis of the available viscosity data for five ternary systems, MEA + MDEA + H{sub 2}O, MEA + AMP + H{sub 2}O, DEA + MDEA + H{sub 2}O, DEA + AMP + H{sub 2}O, and MEA + 2-PE + H{sub 2}O, a generalized set of binary parameters were determined. For the viscosity calculation of the systems tested, the overall average absolute percent deviation is about 1.0% for a total of 499 data points.

  20. Viscosity-dependent protein dynamics.

    PubMed

    Finkelstein, Ilya J; Massari, Aaron M; Fayer, M D

    2007-05-15

    Spectrally resolved stimulated vibrational echo spectroscopy is used to investigate the dependence of fast protein dynamics on bulk solution viscosity at room temperature in four heme proteins: hemoglobin, myoglobin, a myoglobin mutant with the distal histidine replaced by a valine (H64V), and a cytochrome c552 mutant with the distal methionine replaced by an alanine (M61A). Fructose is added to increase the viscosity of the aqueous protein solutions over many orders of magnitude. The fast dynamics of the four globular proteins were found to be sensitive to solution viscosity and asymptotically approached the dynamical behavior that was previously observed in room temperature sugar glasses. The viscosity-dependent protein dynamics are analyzed in the context of a viscoelastic relaxation model that treats the protein as a deformable breathing sphere. The viscoelastic model is in qualitative agreement with the experimental data but does not capture sufficient system detail to offer a quantitative description of the underlying fluctuation amplitudes and relaxation rates. A calibration method based on the near-infrared spectrum of water overtones was constructed to accurately determine the viscosity of small volumes of protein solutions.

  1. The Viscosity-Temperature-Dependence of Liquids,

    DTIC Science & Technology

    The viscosity-temperature- dependence of liquids of different types can be represented by the formula lg kinematic viscosity = A/T to the x power + B...if A has a constant value, only one viscosity measurement at one temperature is necessary for the characterization of the viscosity-temperature- dependence . Examples for each different case are given. (Author)

  2. Dynamic Model of Mesoscale Eddies

    NASA Astrophysics Data System (ADS)

    Dubovikov, Mikhail S.

    2003-04-01

    Oceanic mesoscale eddies which are analogs of well known synoptic eddies (cyclones and anticyclones), are studied on the basis of the turbulence model originated by Dubovikov (Dubovikov, M.S., "Dynamical model of turbulent eddies", Int. J. Mod. Phys.B7, 4631-4645 (1993).) and further developed by Canuto and Dubovikov (Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: I. General formalism", Phys. Fluids8, 571-586 (1996a) (CD96a); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: II. Sheardriven flows", Phys. Fluids8, 587-598 (1996b) (CD96b); Canuto, V.M., Dubovikov, M.S., Cheng, Y. and Dienstfrey, A., "A dynamical model for turbulence: III. Numerical results", Phys. Fluids8, 599-613 (1996c)(CD96c); Canuto, V.M., Dubovikov, M.S. and Dienstfrey, A., "A dynamical model for turbulence: IV. Buoyancy-driven flows", Phys. Fluids9, 2118-2131 (1997a) (CD97a); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: V. The effect of rotation", Phys. Fluids9, 2132-2140 (1997b) (CD97b); Canuto, V.M., Dubovikov, M.S. and Wielaard, D.J., "A dynamical model for turbulence: VI. Two dimensional turbulence", Phys. Fluids9, 2141-2147 (1997c) (CD97c); Canuto, V.M. and Dubovikov, M.S., "Physical regimes and dimensional structure of rotating turbulence", Phys. Rev. Lett. 78, 666-669 (1997d) (CD97d); Canuto, V.M., Dubovikov, M.S. and Dienstfrey, A., "Turbulent convection in a spectral model", Phys. Rev. Lett. 78, 662-665 (1997e) (CD97e); Canuto, V.M. and Dubovikov, M.S., "A new approach to turbulence", Int. J. Mod. Phys.12, 3121-3152 (1997f) (CD97f); Canuto, V.M. and Dubovikov, M.S., "Two scaling regimes for rotating Raleigh-Benard convection", Phys. Rev. Letters78, 281-284, (1998) (CD98); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: VII. The five invariants for shear driven flows", Phys. Fluids11, 659-664 (1999a) (CD99a); Canuto, V.M., Dubovikov, M.S. and Yu, G., "A dynamical model for turbulence: VIII. IR and UV

  3. Expert system for analyzing eddy current measurements

    DOEpatents

    Levy, Arthur J.; Oppenlander, Jane E.; Brudnoy, David M.; Englund, James M.; Loomis, Kent C.

    1994-01-01

    A method and apparatus (called DODGER) analyzes eddy current data for heat exchanger tubes or any other metallic object. DODGER uses an expert system to analyze eddy current data by reasoning with uncertainty and pattern recognition. The expert system permits DODGER to analyze eddy current data intelligently, and obviate operator uncertainty by analyzing the data in a uniform and consistent manner.

  4. Expert system for analyzing eddy current measurements

    SciTech Connect

    Levy, A.J.; Oppenlander, J.E.; Brudnoy, D.M.; Englund, J.M.; Loomis, K.C.

    1994-08-16

    A method and apparatus (called DODGER) analyzes eddy current data for heat exchanger tubes or any other metallic object. DODGER uses an expert system to analyze eddy current data by reasoning with uncertainty and pattern recognition. The expert system permits DODGER to analyze eddy current data intelligently, and obviate operator uncertainty by analyzing the data in a uniform and consistent manner. 21 figs.

  5. Eddy-Resolving Global Ocean Prediction

    DTIC Science & Technology

    2009-07-01

    key observing system for mapping ocean eddies and current meanders, but sea surface temperature, temperature and salinity profiles, and atmospheric...for mapping ocean eddies and current meanders, but sea surface temperature, temperature and salinity profiles, and atmospheric forcing arc also...fronts, eddies, Rossby waves, and the associated temperature, salinity, currents, and sea surface height (SSH). Only since the turn of the century

  6. Algebraic connectivity and graph robustness.

    SciTech Connect

    Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.

    2009-07-01

    Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.

  7. On Dunkl angular momenta algebra

    NASA Astrophysics Data System (ADS)

    Feigin, Misha; Hakobyan, Tigran

    2015-11-01

    We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.

  8. Eddy current thickness measurement apparatus

    DOEpatents

    Rosen, Gary J.; Sinclair, Frank; Soskov, Alexander; Buff, James S.

    2015-06-16

    A sheet of a material is disposed in a melt of the material. The sheet is formed using a cooling plate in one instance. An exciting coil and sensing coil are positioned downstream of the cooling plate. The exciting coil and sensing coil use eddy currents to determine a thickness of the solid sheet on top of the melt.

  9. Hypoxic viscosity and diabetic retinopathy.

    PubMed Central

    Rimmer, T; Fleming, J; Kohner, E M

    1990-01-01

    Diabetic and sickle retinopathy have features in common--for example, venous dilatation, microaneurysms, and capillary closure preceding neovascularisation. Bearing in mind that haemoglobin in poorly controlled diabetes is abnormal and that extremely low oxygen tensions (known to cause sickling) exist in the healthy cat retina, we wished to explore the possibility that diabetic blood, like that of sickle cell disease, may become more viscous when deoxygenated. To do this we measured whole blood viscosity, under oxygenated and deoxygenated conditions, of 23 normal persons, 23 diabetic patients without retinopathy, and 34 diabetic patients with retinopathy. The shear rate used was 230 s-1, which is similar to that thought to prevail in the major retinal veins. The viscosity of blood from normal persons, corrected for packed cell volume, did not change significantly on deoxygenation: mean 4.54 (SD 0.38) cps, versus, 4.57 (0.39) paired t test, p = 0.66. Similarly the blood from diabetics without retinopathy showed no change: 4.42 (0.45) versus 4.42 (0.30), p = 0.98; whereas the blood from patients with retinopathy changed from 4.82 (0.48) to 4.95 (0.63), p = 0.027. The hypoxic viscosity ratio (deoxygenated divided by oxygenated viscosity) correlated with total serum cholesterol (r = 0.44, p = 0.018) but not with HbA1, serum glucose, triglycerides, or age. A disproportionate increase in venous viscosity relative to arterial viscosity would lead to increased intraluminal and transmural pressure and therefore exacerbate leakage across capillary walls. PMID:2378855

  10. Quantifying mesoscale eddies in the Lofoten Basin

    NASA Astrophysics Data System (ADS)

    Raj, R. P.; Johannessen, J. A.; Eldevik, T.; Nilsen, J. E. Ø.; Halo, I.

    2016-07-01

    The Lofoten Basin is the most eddy rich region in the Norwegian Sea. In this paper, the characteristics of these eddies are investigated from a comprehensive database of nearly two decades of satellite altimeter data (1995-2013) together with Argo profiling floats and surface drifter data. An automated method identified 1695/1666 individual anticyclonic/cyclonic eddies in the Lofoten Basin from more than 10,000 altimeter-based eddy observations. The eddies are found to be predominantly generated and residing locally. The spatial distributions of lifetime, occurrence, generation sites, size, intensity, and drift of the eddies are studied in detail. The anticyclonic eddies in the Lofoten Basin are the most long-lived eddies (>60 days), especially in the western part of the basin. We reveal two hotspots of eddy occurrence on either side of the Lofoten Basin. Furthermore, we infer a cyclonic drift of eddies in the western Lofoten Basin. Barotropic energy conversion rates reveals energy transfer from the slope current to the eddies during winter. An automated colocation of surface drifters trapped inside the altimeter-based eddies are used to corroborate the orbital speed of the anticyclonic and cyclonic eddies. Moreover, the vertical structure of the altimeter-based eddies is examined using colocated Argo profiling float profiles. Combination of altimetry, Argo floats, and surface drifter data is therefore considered to be a promising observation-based approach for further studies of the role of eddies in transport of heat and biomass from the slope current to the Lofoten Basin.

  11. Large eddy simulations of laminar separation bubble

    NASA Astrophysics Data System (ADS)

    Cadieux, Francois

    The flow over blades and airfoils at moderate angles of attack and Reynolds numbers ranging from ten thousand to a few hundred thousands undergoes separation due to the adverse pressure gradient generated by surface curvature. In many cases, the separated shear layer then transitions to turbulence and reattaches, closing off a recirculation region -- the laminar separation bubble. To avoid body-fitted mesh generation problems and numerical issues, an equivalent problem for flow over a flat plate is formulated by imposing boundary conditions that lead to a pressure distribution and Reynolds number that are similar to those on airfoils. Spalart & Strelet (2000) tested a number of Reynolds-averaged Navier-Stokes (RANS) turbulence models for a laminar separation bubble flow over a flat plate. Although results with the Spalart-Allmaras turbulence model were encouraging, none of the turbulence models tested reliably recovered time-averaged direct numerical simulation (DNS) results. The purpose of this work is to assess whether large eddy simulation (LES) can more accurately and reliably recover DNS results using drastically reduced resolution -- on the order of 1% of DNS resolution which is commonly achievable for LES of turbulent channel flows. LES of a laminar separation bubble flow over a flat plate are performed using a compressible sixth-order finite-difference code and two incompressible pseudo-spectral Navier-Stokes solvers at resolutions corresponding to approximately 3% and 1% of the chosen DNS benchmark by Spalart & Strelet (2000). The finite-difference solver is found to be dissipative due to the use of a stability-enhancing filter. Its numerical dissipation is quantified and found to be comparable to the average eddy viscosity of the dynamic Smagorinsky model, making it difficult to separate the effects of filtering versus those of explicit subgrid-scale modeling. The negligible numerical dissipation of the pseudo-spectral solvers allows an unambiguous

  12. A new climatological oceanic eddy census

    NASA Astrophysics Data System (ADS)

    Mason, Evan; Pascual, Ananda; Pujol, Isabel; Faugère, Yannice; Delepoulle, Antoine; Briol, Frederic

    2015-04-01

    We present a new climatological oceanic eddy census dataset based on gridded sea level anomalies from satellite altimeter observations that is due for release by Archiving, Validation and Interpretation of Satellite Oceanographic data (AVISO). The identification and automated tracking of oceanic eddies is carried out using the py-eddy-tracker of Mason et al. (2014). Daily outputs of eddy properties (including position, radius, amplitude and nonlinearity) covering the period 1993-2013 over the global domain are presented and discussed. Validation and comparison is made with the published global eddy track database of Chelton et al. (2011).

  13. Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras

    SciTech Connect

    Marquette, Ian

    2013-07-15

    We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.

  14. Transient eddies in the MACDA Mars reanalysis

    NASA Astrophysics Data System (ADS)

    Mooring, Todd A.; Wilson, R. John

    2015-10-01

    We present a survey of the transient eddy activity in the Mars Analysis Correction Data Assimilation (MACDA) reanalysis. The spatial structure and propagation characteristics of the eddies are emphasized. Band-pass-filtered variance and covariance fields are found to be zonally modulated, indicating a longitude dependence of the typical amplitudes of Martian transient eddies. Considerable repeatability of the eddy field spatial structures is found across Mars years, including a roughly wave number 3 pattern of low-level eddy meridional temperature transport (v'T'¯) in the northern hemisphere that is evident before and after winter solstice and a possible tendency for northern hemisphere eddy kinetic energy maxima to be located above low-lying areas. Southern hemisphere eddy fields tend to feature two local maxima, one roughly south of Tharsis and the other associated with Hellas. Eddies are weakened near winter solstice in both hemispheres and were generally weakened in the northern hemisphere during the 2001 (Mars year 25) global dust storm, albeit with little change in spatial patterns. Because the transient eddies propagate in space, we also used a teleconnection map-based technique to estimate their phase velocities. Eddy propagation at the surface is found to follow topography, a phenomenon less evident at higher altitude. Possible physical mechanisms underlying the documented eddy phenomena are discussed.

  15. Observed eddy dissipation in the Agulhas Current

    NASA Astrophysics Data System (ADS)

    Braby, Laura; Backeberg, Björn C.; Ansorge, Isabelle; Roberts, Michael J.; Krug, Marjolaine; Reason, Chris J. C.

    2016-08-01

    Analyzing eddy characteristics from a global data set of automatically tracked eddies for the Agulhas Current in combination with surface drifters as well as geostrophic currents from satellite altimeters, it is shown that eddies from the Mozambique Channel and south of Madagascar dissipate as they approach the Agulhas Current. By tracking the offshore position of the current core and its velocity at 30°S in relation to eddies, it is demonstrated that eddy dissipation occurs through a transfer of momentum, where anticyclones consistently induce positive velocity anomalies, and cyclones reduce the velocities and cause offshore meanders. Composite analyses of the anticyclonic (cyclonic) eddy-current interaction events demonstrate that the positive (negative) velocity anomalies propagate downstream in the Agulhas Current at 44 km/d (23 km/d). Many models are unable to represent these eddy dissipation processes, affecting our understanding of the Agulhas Current.

  16. Assessment of large-eddy simulation in capturing preferential concentration of heavy particles in isotropic turbulent flows

    NASA Astrophysics Data System (ADS)

    Jin, Guodong; Zhang, Jian; He, Guo-Wei; Wang, Lian-Ping

    2010-12-01

    Particle-laden turbulent flow is a typical non-equilibrium process characterized by particle relaxation time τp and the characteristic timescale of the flows τf, in which the turbulent mixing of heavy particles is related to different scales of fluid motions. The preferential concentration (PC) of heavy particles could be strongly affected by fluid motion at dissipation-range scales, which presents a major challenge to the large-eddy simulation (LES) approach. The errors in simulated PC by LES are due to both filtering and the subgrid scale (SGS) eddy viscosity model. The former leads to the removal of the SGS motion and the latter usually results in a more spatiotemporally correlated vorticity field. The dependence of these two factors on the flow Reynolds number is assessed using a priori and a posteriori tests, respectively. The results suggest that filtering is the dominant factor for the under-prediction of the PC for Stokes numbers less than 1, while the SGS eddy viscosity model is the dominant factor for the over-prediction of the PC for Stokes numbers between 1 and 10. The effects of the SGS eddy viscosity model on the PC decrease as the Reynolds number and Stokes number increase. LES can well predict the PC for particle Stokes numbers larger than 10. An SGS model for particles with small and intermediate Stokes numbers is needed to account for the effects of the removed SGS turbulent motion on the PC.

  17. Fluid viscosity under confined conditions

    NASA Astrophysics Data System (ADS)

    Rudyak, V. Ya.; Belkin, A. A.

    2014-12-01

    Closed equations of fluid transfer in confined conditions are constructed in this study using ab initio methods of nonequilibrium statistical mechanics. It is shown that the fluid viscosity is not determined by the fluid properties alone, but becomes a property of the "fluid-nanochannel walls" system as a whole. Relations for the tensor of stresses and the interphase force, which specifies the exchange by momentum of fluid molecules with the channel-wall molecules, are derived. It is shown that the coefficient of viscosity is now determined by the sum of three contributions. The first contribution coincides with the expression for the coefficient of the viscosity of fluid in the bulk being specified by the interaction of fluid molecules with each other. The second contribution has the same structure as the first one but is determined by the interaction of fluid molecules with the channel-wall molecules. Finally, the third contribution has no analog in the usual statistical mechanics of transport processes of a simple fluid. It is associated with the correlation of intermolecular forces of the fluid and the channel walls. Thus, it is established that the coefficient of viscosity of fluid in sufficiently small channels will substantially differ from its bulk value.

  18. Anomalous-viscosity current drive

    DOEpatents

    Stix, T.H.; Ono, M.

    1986-04-25

    The present invention relates to a method and apparatus for maintaining a steady-state current for magnetically confining the plasma in a toroidal magnetic confinement device using anomalous viscosity current drive. A second aspect of this invention relates to an apparatus and method for the start-up of a magnetically confined toroidal plasma.

  19. Algebraic Multigrid Benchmark

    SciTech Connect

    2013-05-06

    AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.

  20. Algebra of Majorana doubling.

    PubMed

    Lee, Jaehoon; Wilczek, Frank

    2013-11-27

    Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.

  1. The Algebra Artist

    ERIC Educational Resources Information Center

    Beigie, Darin

    2014-01-01

    Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…

  2. Priority in Process Algebras

    NASA Technical Reports Server (NTRS)

    Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.

    1999-01-01

    This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.

  3. Clifford Algebras and Their Decomposition into Conjugate Fermionic Heisenberg Algebras

    NASA Astrophysics Data System (ADS)

    Catto, Sultan; Gürcan, Yasemin; Khalfan, Amish; Kurt, Levent; Kato La, V.

    2016-10-01

    We discuss a construction scheme for Clifford numbers of arbitrary dimension. The scheme is based upon performing direct products of the Pauli spin and identity matrices. Conjugate fermionic algebras can then be formed by considering linear combinations of the Clifford numbers and the Hermitian conjugates of such combinations. Fermionic algebras are important in investigating systems that follow Fermi-Dirac statistics. We will further comment on the applications of Clifford algebras to Fueter analyticity, twistors, color algebras, M-theory and Leech lattice as well as unification of ancient and modern geometries through them.

  4. Duncan F. Gregory, William Walton and the development of British algebra: 'algebraical geometry', 'geometrical algebra', abstraction.

    PubMed

    Verburgt, Lukas M

    2016-01-01

    This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.

  5. Quantum computation using geometric algebra

    NASA Astrophysics Data System (ADS)

    Matzke, Douglas James

    This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.

  6. How Structure Sense for Algebraic Expressions or Equations Is Related to Structure Sense for Abstract Algebra

    ERIC Educational Resources Information Center

    Novotna, Jarmila; Hoch, Maureen

    2008-01-01

    Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…

  7. Applications of algebraic grid generation

    NASA Technical Reports Server (NTRS)

    Eiseman, Peter R.; Smith, Robert E.

    1990-01-01

    Techniques and applications of algebraic grid generation are described. The techniques are univariate interpolations and transfinite assemblies of univariate interpolations. Because algebraic grid generation is computationally efficient, the use of interactive graphics in conjunction with the techniques is advocated. A flexible approach, which works extremely well in an interactive environment, called the control point form of algebraic grid generation is described. The applications discussed are three-dimensional grids constructed about airplane and submarine configurations.

  8. Mesoscale Eddy - Internal Wave Coupling and Closure of the Thermocline Circulation

    NASA Astrophysics Data System (ADS)

    Polzin, K. L.

    2006-12-01

    The standard dynamical paradigm for oceanic dynamics is to consider the stratified interior as an ideal fluid and place all dissipative processes in either the bottom boundary layer or associate them with eddy/mixed layer interactions. This conceptual framework is consistent with an absence of mean interior potential vorticity gradients. On the other hand, background potential vorticity gradients are clearly documented in hydrographic data, e.g. [1]. Moreover, current meter data [2] also document the presence of downgradient eddy fluxes of potential vorticity. Thus we arrive at an essential conundrum: what is the frictional or diabatic process that permits the material modification of potential vorticity within the stratified oceanic interior associated with the downgradient fluxes? It is clear that diabatic processes are far too weak. A case will be made here that a coupling between mesoscale eddies and the internal wavefield acts as a frictional process. The case to be presented will focus on the interpretation of observations. These include current meter array data obtained as part of the POLYMODE Local Dynamics Experiment (LDE). [3] found correlations between internal wave momentum fluxes (stresses) and eddy rate of strain estimates that they interpreted in terms of a horizontal viscosity ν_h=200-400 m2 s-1. A revised estimate of this horizontal viscosity (ν_h=50 m2 s-1) and a vertical viscosity (ν_v=3×10-3 m2 s-1) estimate will be presented. Viscosity coefficients of this magnitude indicate that transfers of energy, momentum and potential vorticity between internal waves and mesoscale eddies are a significant part of the eddy energy^{[4]} and eddy enstrophy (potential vorticity squared) budgets. Finally, an attempt will be made to relate such coupling coefficients to recent satellite altimetry based estimates of mesoscale eddy kinetic energy cascades^{[5]} (see also Scott et al., this session), which, according to a preliminary numerical study (Arbic et al

  9. Loop Current Eddy formation and baroclinic instability

    NASA Astrophysics Data System (ADS)

    Donohue, K. A.; Watts, D. R.; Hamilton, P.; Leben, R.; Kennelly, M.

    2016-12-01

    The formation of three Loop Current Eddies, Ekman, Franklin, and Hadal, during the period April 2009 through November 2011 was observed by an array of moored current meters and bottom mounted pressure equipped inverted echo sounders. The array design, areal extent nominally 89° W to 85° W, 25° N to 27° N with 30-50 km mesoscale resolution, permits quantitative mapping of the regional circulation at all depths. During Loop Current Eddy detachment and formation events, a marked increase in deep eddy kinetic energy occurs coincident with the growth of a large-scale meander along the northern and eastern parts of the Loop Current. Deep eddies develop in a pattern where the deep fields were offset and leading upper meanders consistent with developing baroclinic instability. The interaction between the upper and deep fields is quantified by evaluating the mean eddy potential energy budget. Largest down-gradient heat fluxes are found along the eastern side of the Loop Current. Where strong, the horizontal down-gradient eddy heat flux (baroclinic conversion rate) nearly balances the vertical down-gradient eddy heat flux indicating that eddies extract available potential energy from the mean field and convert eddy potential energy to eddy kinetic energy.

  10. The eddy, wave, and interface structure of turbulent shear layers below/above stably stratified regions

    NASA Astrophysics Data System (ADS)

    Hunt, Julian C. R.; Moustaoui, Mohamed; Mahalov, Alex

    2015-09-01

    High resolution three-dimensional simulations are presented of the interactions between turbulent shear flows moving with mean relative velocity ΔU below a stably stratified region with buoyancy frequency (N+). An artificial forcing in the simulation, with a similar effect as a small negative eddy viscosity, leads to a steady state flow which models thin interfaces. Characteristic eddies of the turbulence have length scale L. If the bulk Richardson number Rib=(LN+/ΔU)2 lies between lower and upper critical values denoted as Ri∗(<1/5) and R~i(˜ 1), a "detached" layer is formed in the stable region with thickness L+ greater than L, in which rotational fluctuations and inhomogeneous turbulence are induced above an interface with large gradients of density/temperature. Comparisons are made with shear turbulent interfaces with no stratification. When Rib>R~i, vertical propagating waves are generated, with shear stresses carrying significant momentum flux and progressively less as Rib increases. Simulations for a jet and a turbulent mixing layer show similar results. A perturbation analysis, using inhomogeneous Rapid Distortion Theory, models the transition zone between shear eddies below the interface and the fluctuations in the stratified region, consistent with the simulations. It demonstrates how the wave-momentum-flux has a maximum when Rib˜2 and then decreases as Rib increases. This coupling mechanism between eddies and waves, which is neglected in eddy viscosity models for shear layers, can drive flows in the stratosphere and the deeper ocean, with significant consequences for short- and long-term flow phenomena. The "detached layer" is a mechanism that contributes to the formation of stratus clouds and polluted layers above the atmospheric boundary layer.

  11. Algebra and Algebraic Thinking in School Math: 70th YB

    ERIC Educational Resources Information Center

    National Council of Teachers of Mathematics, 2008

    2008-01-01

    Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…

  12. Abstract Algebra to Secondary School Algebra: Building Bridges

    ERIC Educational Resources Information Center

    Christy, Donna; Sparks, Rebecca

    2015-01-01

    The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

  13. Formation of the Haida-1998 oceanic eddy

    NASA Astrophysics Data System (ADS)

    Crawford, W. R.; Cherniawsky, J. Y.; Foreman, M. G. G.; Gower, J. F. R.

    2002-07-01

    Two large, mesoscale, anticyclonic eddies formed along the west coast of the Queen Charlotte Islands of western Canada in early 1998. Altimetry measurements from TOPEX/Poseidon and ERS-2 satellites suggest that these eddies first appeared near Cape St. James at the southern tip of the islands. The eddies merged in June to form ``Haida-1998,'' the highest eddy ever observed in the region. Currents near Cape St. James in winter follow complicated patterns attributed to tidal rectification and pressure-driven outflow from Hecate Strait. The adjustment of these flows to the bathymetric features likely contributes to the formation of Haida Eddies. Eddies that first appear farther north along the west coast of the Queen Charlotte Islands are set up by other processes, such as baroclinic instability.

  14. Large eddy simulation of incompressible turbulent channel flow

    NASA Technical Reports Server (NTRS)

    Moin, P.; Reynolds, W. C.; Ferziger, J. H.

    1978-01-01

    The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.

  15. Progress in the Variational Multiscale Formulation of Large Eddy Simulation

    NASA Astrophysics Data System (ADS)

    Wang, Zhen; Oberai, Assad

    2007-11-01

    In the variational multiscale (VMS) formulation of large eddy simulation subgrid models are introduced in the variational (or weak) formulation of the Navier Stokes equations and a-priori scale separation is accomplished using projection operators to create coarse and fine scales. This separation also leads to two sets of evolution equations: one for the coarse scales and another for the fine scales. The coarse scale equations are solved numerically while the fine scale equations are solved analytically to obtain an expression for the fine scales in terms of the coarse scales and hence achieve closure. Till date, the VMS formulation has lead to accurate results in the simulation of canonical turbulent flow problems. It has been implemented using spectral, finite element and finite volume methods. In this talk, for the incompressible Navier Stokes equations, we willpresent some new ideas for modeling the fine scales within the context of the VMS formulation and discuss their impact on the coarse scale solution. We will present a simple residual-based approximation for the fine scales that accurately models the cross-stress term and demonstrate that when this term is append with an eddy viscosity model for the Reynolds stress, a new mixed-model is obtained. The application of these ideas will be illustrated through some simple numerical examples.

  16. A family of dynamic models for large-eddy simulation

    NASA Technical Reports Server (NTRS)

    Carati, D.; Jansen, K.; Lund, T.

    1995-01-01

    Since its first application, the dynamic procedure has been recognized as an effective means to compute rather than prescribe the unknown coefficients that appear in a subgrid-scale model for Large-Eddy Simulation (LES). The dynamic procedure is usually used to determine the nondimensional coefficient in the Smagorinsky (1963) model. In reality the procedure is quite general and it is not limited to the Smagorinsky model by any theoretical or practical constraints. The purpose of this note is to consider a generalized family of dynamic eddy viscosity models that do not necessarily rely on the local equilibrium assumption built into the Smagorinsky model. By invoking an inertial range assumption, it will be shown that the coefficients in the new models need not be nondimensional. This additional degree of freedom allows the use of models that are scaled on traditionally unknown quantities such as the dissipation rate. In certain cases, the dynamic models with dimensional coefficients are simpler to implement, and allow for a 30% reduction in the number of required filtering operations.

  17. Large eddy simulation of mechanical mixing in anaerobic digesters.

    PubMed

    Wu, Binxin

    2012-03-01

    A comprehensive study of anaerobic digestion requires an advanced turbulence model technique to accurately predict mixing flow patterns because the digestion process that involves mass transfer between anaerobes and their substrates is primarily dependent on detailed information about the fine structure of turbulence in the digesters. This study presents a large eddy simulation (LES) of mechanical agitation of non-Newtonian fluids in anaerobic digesters, in which the sliding mesh method is used to characterize the impeller rotation. The three subgrid scale (SGS) models investigated are: (i) Smagorinsky-Lilly model, (ii) wall-adapting local eddy-viscosity model, and (iii) kinetic energy transport (KET) model. The simulation results show that the three SGS models produce very similar flow fields. A comparison of the simulated and measured axial velocities indicates that the LES profile shapes are in general agreement with the experimental data but they differ markedly in velocity magnitudes. A check of impeller power and flow numbers demonstrates that all the SGS models give excellent predictions, with the KET model performing the best. Moreover, the performance of six Reynolds-averaged Navier-Stokes turbulence models are assessed and compared with the LES results.

  18. Density and viscosity of lipids under pressure

    Technology Transfer Automated Retrieval System (TEKTRAN)

    There is a lack of data for the viscosity of lipids under pressure. The current report is a part of the effort to fill this gap. The viscosity, density, and elastohydrodynamic film thicknesses of vegetable oil (HOSuO) were investigated. Pressure–viscosity coefficients (PVC) of HOSuO at different tem...

  19. Statecharts Via Process Algebra

    NASA Technical Reports Server (NTRS)

    Luttgen, Gerald; vonderBeeck, Michael; Cleaveland, Rance

    1999-01-01

    Statecharts is a visual language for specifying the behavior of reactive systems. The Language extends finite-state machines with concepts of hierarchy, concurrency, and priority. Despite its popularity as a design notation for embedded system, precisely defining its semantics has proved extremely challenging. In this paper, a simple process algebra, called Statecharts Process Language (SPL), is presented, which is expressive enough for encoding Statecharts in a structure-preserving and semantic preserving manner. It is establish that the behavioral relation bisimulation, when applied to SPL, preserves Statecharts semantics

  20. Observations of Three Dimensional Surfzone Eddies

    NASA Astrophysics Data System (ADS)

    Arnold, J. L.; Henderson, S. M.; Solovitz, S.

    2012-12-01

    We present measurements of the vertical structure of surfzone eddies (frequencies 0.0005-0.01 Hz). From 16 Oct to 07 Nov 2011, an array of 12 Acoustic Doppler Profilers (ADPs) measured velocity profiles in 0-6 m water depth on a natural beach near Duck, North Carolina. We will analyze and describe vertical variations in eddy velocity. Vertical variability of eddy magnitude will be presented, as well as coherence and phase between near-surface and near-bed velocities. We aim to shed light on the causes and consequences of vertical eddy variability, which has recently been recognized in observations, but is not yet well understood.

  1. Patterns to Develop Algebraic Reasoning

    ERIC Educational Resources Information Center

    Stump, Sheryl L.

    2011-01-01

    What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

  2. Viterbi/algebraic hybrid decoder

    NASA Technical Reports Server (NTRS)

    Boyd, R. W.; Ingels, F. M.; Mo, C.

    1980-01-01

    Decoder computer program is hybrid between optimal Viterbi and optimal algebraic decoders. Tests have shown that hybrid decoder outperforms any strictly Viterbi or strictly algebraic decoder and effectively handles compound channels. Algorithm developed uses syndrome-detecting logic to direct two decoders to assume decoding load alternately, depending on real-time channel characteristics.

  3. Online Algebraic Tools for Teaching

    ERIC Educational Resources Information Center

    Kurz, Terri L.

    2011-01-01

    Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics. (Contains 1 table and 4 figures.)

  4. Astro Algebra [CD-ROM].

    ERIC Educational Resources Information Center

    1997

    Astro Algebra is one of six titles in the Mighty Math Series from Edmark, a comprehensive line of math software for students from kindergarten through ninth grade. Many of the activities in Astro Algebra contain a unique technology that uses the computer to help students make the connection between concrete and abstract mathematics. This software…

  5. Elementary maps on nest algebras

    NASA Astrophysics Data System (ADS)

    Li, Pengtong

    2006-08-01

    Let , be algebras and let , be maps. An elementary map of is an ordered pair (M,M*) such that for all , . In this paper, the general form of surjective elementary maps on standard subalgebras of nest algebras is described. In particular, such maps are automatically additive.

  6. Linear algebra and image processing

    NASA Astrophysics Data System (ADS)

    Allali, Mohamed

    2010-09-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty.

  7. Linear Algebra and Image Processing

    ERIC Educational Resources Information Center

    Allali, Mohamed

    2010-01-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)

  8. Learning Algebra from Worked Examples

    ERIC Educational Resources Information Center

    Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.

    2014-01-01

    For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

  9. The Algebra of the Arches

    ERIC Educational Resources Information Center

    Buerman, Margaret

    2007-01-01

    Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…

  10. The Algebra of Complex Numbers.

    ERIC Educational Resources Information Center

    LePage, Wilbur R.

    This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

  11. On Eddy Viscosity, Energy Cascades, and the Horizontal Resolution of Gridded Satellite Altimeter Products

    DTIC Science & Technology

    2013-02-01

    Manuscript received 21 December 2011, in final form 23 August 2012) ABSTRACT Motivated by the recent interest in ocean energetics, the widespread use...Inhomogeneous two-dimensional turbu- lence in the atmosphere. Advances in Turbulence, G. Comte - Bellot and J. Mathieu, Eds., Springer-Verlag, 269-278

  12. Thermodynamics. [algebraic structure

    NASA Technical Reports Server (NTRS)

    Zeleznik, F. J.

    1976-01-01

    The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of entropy and identifies it as a purely mathematical concept. It also permits the construction of an entropy function from heat measurements alone when appropriate conditions are satisfied. Topology is required only for a discussion of the continuity of thermodynamic properties, and then the weak topology is the relevant topology. The integrability of the differential form of the first law can be examined independently of Caratheodory's theorem and his inaccessibility axiom. Criteria are established by which one can determine when an integrating factor can be made intensive and the pseudopotential extensive and also an entropy. Finally, a realization of the first law is constructed which is suitable for all systems whether they are solids or fluids, whether they do or do not exhibit chemical reactions, and whether electromagnetic fields are or are not present.

  13. Symplectic Clifford Algebraic Field Theory.

    NASA Astrophysics Data System (ADS)

    Dixon, Geoffrey Moore

    We develop a mathematical framework on which is built a theory of fermion, scalar, and gauge vector fields. This field theory is shown to be equivalent to the original Weinberg-Salam model of weak and electromagnetic interactions, but since the new framework is more rigid than that on which the original Weinberg-Salam model was built, a concomitant reduction in the number of assumptions lying outside of the framework has resulted. In particular, parity violation is actually hiding within our framework, and with little difficulty we are able to manifest it. The mathematical framework upon which we build our field theory is arrived at along two separate paths. The first is by the marriage of a Clifford algebra and a Lie superalgebra, the result being called a super Clifford algebra. The second is by providing a new characterization for a Clifford algebra employing its generators and a symmetric array of metric coefficients. Subsequently we generalize this characterization to the case of an antisymmetric array of metric coefficients, and we call the algebra which results a symplectic Clifford algebra. It is upon one of these that we build our field theory, and it is shown that this symplectic Clifford algebra is a particular subalgebra of a super Clifford algebra. The final ingredient is the operation of bracketing which involves treating the elements of our algebra as endomorphisms of a particular inner product space, and employing this space and its inner product to provide us with maps from our algebra to the reals. It is this operation which enables us to manifest the parity violation hiding in our algebra.

  14. Film cooling from inclined cylindrical holes using large eddy simulations

    NASA Astrophysics Data System (ADS)

    Peet, Yulia V.

    2006-12-01

    The goal of the present study is to investigate numerically the physics of the flow, which occurs during the film cooling from inclined cylindrical holes, Film cooling is a technique used in gas turbine industry to reduce heat fluxes to the turbine blade surface. Large Eddy Simulation (LES) is performed modeling a realistic film cooling configuration, which consists of a large stagnation-type reservoir, feeding an array of discrete cooling holes (film holes) flowing into a flat plate turbulent boundary layer. Special computational methodology is developed for this problem, involving coupled simulations using multiple computational codes. A fully compressible LES code is used in the area above the flat plate, while a low Mach number LES code is employed in the plenum and film holes. The motivation for using different codes comes from the essential difference in the nature of the flow in these different regions. Flowfield is analyzed inside the plenum, film hole and a crossflow region. Flow inside the plenum is stagnating, except for the region close to the exit, where it accelerates rapidly to turn into the hole. The sharp radius of turning at the trailing edge of the plenum pipe connection causes the flow to separate from the downstream wall of the film hole. After coolant injection occurs, a complex flowfield is formed consisting of coherent vortical structures responsible for bringing hot crossflow fluid in contact with the walls of either the film hole or the blade, thus reducing cooling protection. Mean velocity and turbulent statistics are compared to experimental measurements, yielding good agreement for the mean flowfield and satisfactory agreement for the turbulence quantities. LES results are used to assess the applicability of basic assumptions of conventional eddy viscosity turbulence models used with Reynolds-averaged (RANS) approach, namely the isotropy of an eddy viscosity and thermal diffusivity. It is shown here that these assumptions do not hold

  15. Superparamagnetic nanoparticle-based viscosity test

    NASA Astrophysics Data System (ADS)

    Wu, Kai; Liu, Jinming; Wang, Yi; Ye, Clark; Feng, Yinglong; Wang, Jian-Ping

    2015-08-01

    Hyperviscosity syndrome is triggered by high blood viscosity in the human body. This syndrome can result in retinopathy, vertigo, coma, and other unanticipated complications. Serum viscosity is one of the important factors affecting whole blood viscosity, which is regarded as an indicator of general health. In this letter, we propose and demonstrate a Brownian relaxation-based mixing frequency method to test human serum viscosity. This method uses excitatory and detection coils and Brownian relaxation-dominated superparamagnetic nanoparticles, which are sensitive to variables of the liquid environment such as viscosity and temperature. We collect the harmonic signals produced by magnetic nanoparticles and estimate the viscosity of unknown solutions by comparison to the calibration curves. An in vitro human serum viscosity test is performed in less than 1.5 min.

  16. Method of adaptive artificial viscosity

    NASA Astrophysics Data System (ADS)

    Popov, I. V.; Fryazinov, I. V.

    2011-09-01

    A new finite-difference method for the numerical solution of gas dynamics equations is proposed. This method is a uniform monotonous finite-difference scheme of second-order approximation on time and space outside of domains of shock and compression waves. This method is based on inputting adaptive artificial viscosity (AAV) into gas dynamics equations. In this paper, this method is analyzed for 2D geometry. The testing computations of the movement of contact discontinuities and shock waves and the breakup of discontinuities are demonstrated.

  17. Effective Viscosity of Microswimmer Suspensions

    NASA Astrophysics Data System (ADS)

    Rafaï, Salima; Jibuti, Levan; Peyla, Philippe

    2010-03-01

    The measurement of a quantitative and macroscopic parameter to estimate the global motility of a large population of swimming biological cells is a challenge. Experiments on the rheology of active suspensions have been performed. Effective viscosity of sheared suspensions of live unicellular motile microalgae (Chlamydomonas Reinhardtii) is far greater than for suspensions containing the same volume fraction of dead cells. In addition, suspensions show shear thinning behavior. We relate these macroscopic measurements to the orientation of individual swimming cells under flow and discuss our results in the light of several existing models.

  18. Effective viscosity of microswimmer suspensions.

    PubMed

    Rafaï, Salima; Jibuti, Levan; Peyla, Philippe

    2010-03-05

    The measurement of a quantitative and macroscopic parameter to estimate the global motility of a large population of swimming biological cells is a challenge. Experiments on the rheology of active suspensions have been performed. Effective viscosity of sheared suspensions of live unicellular motile microalgae (Chlamydomonas Reinhardtii) is far greater than for suspensions containing the same volume fraction of dead cells. In addition, suspensions show shear thinning behavior. We relate these macroscopic measurements to the orientation of individual swimming cells under flow and discuss our results in the light of several existing models.

  19. Critical Viscosity of Xenon team

    NASA Technical Reports Server (NTRS)

    2001-01-01

    The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. The thermostat for CVX sits inside the white cylinder on a support structure (at left) that is placed inside a pressure canister. A similar canister (right) holds the electronics and control systems. The CVX-2 arrangement is identical. The principal investigator is Dr. Robert F. Berg (left) of the National Institutes of Standards and Technology, Gaithersburg, MD.

  20. Critical Viscosity of Xenon team

    NASA Technical Reports Server (NTRS)

    2001-01-01

    The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. The thermostat for CVX sits inside the white cylinder on a support structure (at left) that is placed inside a pressure canister. A similar canister (right) holds the electronics and control systems. The CVX-2 arrangement is identical. The principal investigator is Dr. Robert F. Berg (not shown) of the National Institutes of Standards and Technology, Gaithersburg, MD.

  1. Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

    ERIC Educational Resources Information Center

    Gonzalez-Vega, Laureano

    1999-01-01

    Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

  2. Mesoscale Ocean Large Eddy Simulations

    NASA Astrophysics Data System (ADS)

    Pearson, Brodie; Fox-Kemper, Baylor; Bachman, Scott; Bryan, Frank

    2015-11-01

    The highest resolution global climate models (GCMs) can now resolve the largest scales of mesoscale dynamics in the ocean. This has the potential to increase the fidelity of GCMs. However, the effects of the smallest, unresolved, scales of mesoscale dynamics must still be parametrized. One such family of parametrizations are mesoscale ocean large eddy simulations (MOLES), but the effects of including MOLES in a GCM are not well understood. In this presentation, several MOLES schemes are implemented in a mesoscale-resolving GCM (CESM), and the resulting flow is compared with that produced by more traditional sub-grid parametrizations. Large eddy simulation (LES) is used to simulate flows where the largest scales of turbulent motion are resolved, but the smallest scales are not resolved. LES has traditionally been used to study 3D turbulence, but recently it has also been applied to idealized 2D and quasi-geostrophic (QG) turbulence. The MOLES presented here are based on 2D and QG LES schemes.

  3. Exploring Eddy-Covariance Measurements Using a Spatial Approach: The Eddy Matrix

    NASA Astrophysics Data System (ADS)

    Engelmann, Christian; Bernhofer, Christian

    2016-10-01

    Taylor's frozen turbulence hypothesis states that "standard" eddy-covariance measurements of fluxes at a fixed location can replace a spatial ensemble of instantaneous values at multiple locations. For testing this hypothesis, a unique turbulence measurement set-up was used for two measurement campaigns over desert (Namibia) and grassland (Germany) in 2012. This "Eddy Matrix" combined nine ultrasonic anemometer-thermometers and 17 thermocouples in a 10 m × 10 m regular grid with 2.5-m grid distance. The instantaneous buoyancy flux derived from the spatial eddy covariance of the Eddy Matrix was highly variable in time (from -0.3 to 1 m K s^{-1}). However, the 10-min average reflected 83 % of the reference eddy-covariance flux with a good correlation. By introducing a combined eddy-covariance method (the spatial eddy covariance plus the additional flux of the temporal eddy covariance of the spatial mean values), the mean flux increases by 9 % relative to the eddy-covariance reference. Considering the typical underestimation of fluxes by the standard eddy-covariance method, this is seen as an improvement. Within the limits of the Eddy Matrix, Taylor's hypothesis is supported by the results.

  4. Modelling the generation of Haida Eddies

    NASA Astrophysics Data System (ADS)

    Di Lorenzo, E.; Foreman, M. G. G.; Crawford, W. R.

    2005-04-01

    A numerical model forced with average annual cycles of climatological winds, surface heat flux, and temperature and salinity along the open boundaries is used to demonstrate that Haida Eddies are typically generated each winter off Cape St. James, at the southern tip of the Queen Charlotte Islands of western Canada. Annual cycles of sea-surface elevation measured at coastal tide gauges and TOPEX/POSEIDON crossover locations are reproduced with reasonable accuracy. Model sensitivity studies show that Haida Eddies are baroclinic in nature and are generated by the merging of several smaller eddies that have been formed to the west of Cape St. James. The generation mechanism does not require the existence of instability processes and is associated with the mean advection of warmer and fresher water masses around the cape from Hecate Strait and from the southeast. These advected water masses generate plumes of buoyant flow, which intensify and sustain small patches of anticyclonic circulation immediately to the northwest of the cape. When the flow is stronger, several of these smaller eddies can merge to generate a larger eddy, the Haida Eddy. Similar to observations, a typical generation-shedding cycle for larger Haida Eddies in the model is 3-4 months. Consistent with previous in situ water property measurements, these experiments show that the eddies are generally comprised of mixed-layer water from Hecate Strait, Queen Charlotte Sound, and the continental shelves off northern Vancouver Island. Their vertical extent during the mature stage is roughly 1000 m.

  5. Observed deep energetic eddies by seamount wake.

    PubMed

    Chen, Gengxin; Wang, Dongxiao; Dong, Changming; Zu, Tingting; Xue, Huijie; Shu, Yeqiang; Chu, Xiaoqing; Qi, Yiquan; Chen, Hui

    2015-11-30

    Despite numerous surface eddies are observed in the ocean, deep eddies (a type of eddies which have no footprints at the sea surface) are much less reported in the literature due to the scarcity of their observation. In this letter, from recently collected current and temperature data by mooring arrays, a deep energetic and baroclinic eddy is detected in the northwestern South China Sea (SCS) with its intensity, size, polarity and structure being characterized. It remarkably deepens isotherm at deep layers by the amplitude of ~120 m and induces a maximal velocity amplitude about 0.18 m/s, which is far larger than the median velocity (0.02 m/s). The deep eddy is generated in a wake when a steering flow in the upper layer passes a seamount, induced by a surface cyclonic eddy. More observations suggest that the deep eddy should not be an episode in the area. Deep eddies significantly increase the velocity intensity and enhance the mixing in the deep ocean, also have potential implication for deep-sea sediments transport.

  6. Mesoscale Eddies in the Solomon Sea

    NASA Astrophysics Data System (ADS)

    Hristova, H. G.; Kessler, W. S.; McWilliams, J. C.; Molemaker, M. J.

    2011-12-01

    Water mass transformation in the strong equatorward flows through the Solomon Sea influences the properties of the Equatorial Undercurrent and subsequent cold tongue upwelling. High eddy activity in the interior Solomon Sea seen in altimetric sea surface height (SSH) and in several models may provide a mechanism for these transformations. We investigate these effects using a mesoscale (4-km resolution) sigma-coordinate (ROMS) model of the Solomon Sea nested in a basin solution, forced by a repeating seasonal cycle, and evaluated against observational data. The model generates a vigorous upper layer eddy field; some of these are apparently shed as the New Guinea Coastal Undercurrent threads through the complex topography of the region, others are independent of the strong western boundary current. We diagnose the scales and vertical structure of the eddies in different parts of the Solomon Sea to illuminate their generation processes and propagation characteristics, and compare these to observed eddy statistics. Hypotheses tested are that the Solomon Sea mesoscale eddies are generated locally by baroclinic instability, that the eddies are shed as the South Equatorial Current passes around and through the Solomon Island chain, that eddies are generated by the New Guinea Coastal Undercurrent, or that eddies occurring outside of the Solomon Sea propagate into the Solomon Sea. These different mechanisms have different implications for the resulting mixing and property fluxes. They also provide different interpretations for SSH signals observed from satellites (e.g., that will be observed by the upcoming SWOT satellite).

  7. Diapycnal mixing by meso-scale eddies

    NASA Astrophysics Data System (ADS)

    Eden, Carsten; Greatbatch, Richard J.

    The mean available potential energy released by baroclinic instability into the meso-scale eddy field has to be dissipated in some way and Tandon and Garrett [Tandon, A., Garrett, C., 1996. On a recent parameterization of mesoscale eddies. J. Phys. Oceanogr. 26 (3), 406-416] suggested that this dissipation could ultimately involve irreversible mixing of buoyancy by molecular processes at the small-scale end of the turbulence cascade. We revisit this idea and argue that the presence of dissipation within the thermocline automatically requires that a component of the eddy flux associated with meso-scale eddies must be associated with irreversible mixing of buoyancy within the thermocline. We offer a parameterisation of the implied diapycnal diffusivity based on (i) the dissipation rate for eddy kinetic energy given by the meso-scale eddy closure of Eden and Greatbatch [Eden, C., Greatbatch, R.J., 2008. Towards a meso-scale eddy closure. Ocean Modell. 20, 223-239.] and (ii) a fixed mixing efficiency. The implied eddy-induced diapycnal diffusivity ( κ) is implemented in a coarse resolution model of the North Atlantic. In contrast to the vertical diffusivity given by a standard vertical mixing scheme, large lateral inhomogeneities can be found for κ in the interior of the ocean. In general, κ is large, i.e. up to o(10) cm 2/s, near the western boundaries and almost vanishing in the interior of the ocean.

  8. Temporal evolution of Townsend's attached eddies

    NASA Astrophysics Data System (ADS)

    Lozano-Duran, Adrian; Jimenez, Javier

    2013-11-01

    The temporal evolution of the eddies responsible for the momentum transfer in a turbulent channel are studied using time-resolved DNS data at Reτ = 4000 . The eddies are identified as connected regions of intense tangential Reynolds stress, and tracked in time. Once their evolutions are properly organized, they provide the necessary information to characterize eddies from birth to death. Eddies are born at all distances from the wall, although with higher probability near it, where the shear is strongest. Most of them stay small and do not last for long times. However, there is a family of eddies that become large enough to get attached to the wall while they reach into the logarithmic layer. They can be considered the best candidates for Townsend's attached eddies found until now. They are geometrically self-similar, with sizes and lifetimes proportional to their distance from the wall. Eddies associated with ejections move away from the wall with dy / dt =uτ , and their base attaches very fast at the beginning of their lives. Conversely, sweeps move towards the wall at -uτ , and attach later. In both cases, they remain attached for 2 / 3 of their lives. In the streamwise direction, eddies are advected and sheared by the local mean velocity. Funded by ERC, CICYT and Spanish Ministry of Science.

  9. Observed deep energetic eddies by seamount wake

    NASA Astrophysics Data System (ADS)

    Chen, Gengxin; Wang, Dongxiao; Dong, Changming; Zu, Tingting; Xue, Huijie; Shu, Yeqiang; Chu, Xiaoqing; Qi, Yiquan; Chen, Hui

    2015-11-01

    Despite numerous surface eddies are observed in the ocean, deep eddies (a type of eddies which have no footprints at the sea surface) are much less reported in the literature due to the scarcity of their observation. In this letter, from recently collected current and temperature data by mooring arrays, a deep energetic and baroclinic eddy is detected in the northwestern South China Sea (SCS) with its intensity, size, polarity and structure being characterized. It remarkably deepens isotherm at deep layers by the amplitude of ~120 m and induces a maximal velocity amplitude about 0.18 m/s, which is far larger than the median velocity (0.02 m/s). The deep eddy is generated in a wake when a steering flow in the upper layer passes a seamount, induced by a surface cyclonic eddy. More observations suggest that the deep eddy should not be an episode in the area. Deep eddies significantly increase the velocity intensity and enhance the mixing in the deep ocean, also have potential implication for deep-sea sediments transport.

  10. Observed deep energetic eddies by seamount wake

    PubMed Central

    Chen, Gengxin; Wang, Dongxiao; Dong, Changming; Zu, Tingting; Xue, Huijie; Shu, Yeqiang; Chu, Xiaoqing; Qi, Yiquan; Chen, Hui

    2015-01-01

    Despite numerous surface eddies are observed in the ocean, deep eddies (a type of eddies which have no footprints at the sea surface) are much less reported in the literature due to the scarcity of their observation. In this letter, from recently collected current and temperature data by mooring arrays, a deep energetic and baroclinic eddy is detected in the northwestern South China Sea (SCS) with its intensity, size, polarity and structure being characterized. It remarkably deepens isotherm at deep layers by the amplitude of ~120 m and induces a maximal velocity amplitude about 0.18 m/s, which is far larger than the median velocity (0.02 m/s). The deep eddy is generated in a wake when a steering flow in the upper layer passes a seamount, induced by a surface cyclonic eddy. More observations suggest that the deep eddy should not be an episode in the area. Deep eddies significantly increase the velocity intensity and enhance the mixing in the deep ocean, also have potential implication for deep-sea sediments transport. PMID:26617343

  11. Quantum algebra of N superspace

    SciTech Connect

    Hatcher, Nicolas; Restuccia, A.; Stephany, J.

    2007-08-15

    We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the {kappa}-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.

  12. Algebraic distance on graphs.

    SciTech Connect

    Chen, J.; Safro, I.

    2011-01-01

    Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.

  13. Drop spreading with random viscosity

    PubMed Central

    2016-01-01

    We examine theoretically the spreading of a viscous liquid drop over a thin film of uniform thickness, assuming the liquid’s viscosity is regulated by the concentration of a solute that is carried passively by the spreading flow. The solute is assumed to be initially heterogeneous, having a spatial distribution with prescribed statistical features. To examine how this variability influences the drop’s motion, we investigate spreading in a planar geometry using lubrication theory, combining numerical simulations with asymptotic analysis. We assume diffusion is sufficient to suppress solute concentration gradients across but not along the film. The solute field beneath the bulk of the drop is stretched by the spreading flow, such that the initial solute concentration immediately behind the drop’s effective contact lines has a long-lived influence on the spreading rate. Over long periods, solute swept up from the precursor film accumulates in a short region behind the contact line, allowing patches of elevated viscosity within the precursor film to hinder spreading. A low-order model provides explicit predictions of the variances in spreading rate and drop location, which are validated against simulations. PMID:27843398

  14. Drop spreading with random viscosity

    NASA Astrophysics Data System (ADS)

    Xu, Feng; Jensen, Oliver E.

    2016-10-01

    We examine theoretically the spreading of a viscous liquid drop over a thin film of uniform thickness, assuming the liquid's viscosity is regulated by the concentration of a solute that is carried passively by the spreading flow. The solute is assumed to be initially heterogeneous, having a spatial distribution with prescribed statistical features. To examine how this variability influences the drop's motion, we investigate spreading in a planar geometry using lubrication theory, combining numerical simulations with asymptotic analysis. We assume diffusion is sufficient to suppress solute concentration gradients across but not along the film. The solute field beneath the bulk of the drop is stretched by the spreading flow, such that the initial solute concentration immediately behind the drop's effective contact lines has a long-lived influence on the spreading rate. Over long periods, solute swept up from the precursor film accumulates in a short region behind the contact line, allowing patches of elevated viscosity within the precursor film to hinder spreading. A low-order model provides explicit predictions of the variances in spreading rate and drop location, which are validated against simulations.

  15. Drop Spreading with Random Viscosity

    NASA Astrophysics Data System (ADS)

    Xu, Feng; Jensen, Oliver

    2016-11-01

    Airway mucus acts as a barrier to protect the lung. However as a biological material, its physical properties are known imperfectly and can be spatially heterogeneous. In this study we assess the impact of these uncertainties on the rate of spreading of a drop (representing an inhaled aerosol) over a mucus film. We model the film as Newtonian, having a viscosity that depends linearly on the concentration of a passive solute (a crude proxy for mucin proteins). Given an initial random solute (and hence viscosity) distribution, described as a Gaussian random field with a given correlation structure, we seek to quantify the uncertainties in outcomes as the drop spreads. Using lubrication theory, we describe the spreading of the drop in terms of a system of coupled nonlinear PDEs governing the evolution of film height and the vertically-averaged solute concentration. We perform Monte Carlo simulations to predict the variability in the drop centre location and width (1D) or area (2D). We show how simulation results are well described (at much lower computational cost) by a low-order model using a weak disorder expansion. Our results show for example how variability in the drop location is a non-monotonic function of the solute correlation length increases. Engineering and Physical Sciences Research Council.

  16. Wind changes above warm Agulhas Current eddies

    NASA Astrophysics Data System (ADS)

    Rouault, M.; Verley, P.; Backeberg, B.

    2016-04-01

    Sea surface temperature (SST) estimated from the Advanced Microwave Scanning Radiometer E onboard the Aqua satellite and altimetry-derived sea level anomalies are used south of the Agulhas Current to identify warm-core mesoscale eddies presenting a distinct SST perturbation greater than to 1 °C to the surrounding ocean. The analysis of twice daily instantaneous charts of equivalent stability-neutral wind speed estimates from the SeaWinds scatterometer onboard the QuikScat satellite collocated with SST for six identified eddies shows stronger wind speed above the warm eddies than the surrounding water in all wind directions, if averaged over the lifespan of the eddies, as was found in previous studies. However, only half of the cases showed higher wind speeds above the eddies at the instantaneous scale; 20 % of cases had incomplete data due to partial global coverage by the scatterometer for one path. For cases where the wind is stronger above warm eddies, there is no relationship between the increase in surface wind speed and the SST perturbation, but we do find a linear relationship between the decrease in wind speed from the centre to the border of the eddy downstream and the SST perturbation. SST perturbations range from 1 to 6 °C for a mean eddy SST of 15.9 °C and mean SST perturbation of 2.65 °C. The diameter of the eddies range from 100 to 250 km. Mean background wind speed is about 12 m s-1 (mostly southwesterly to northwesterly) and ranging mainly from 4 to 16 m s-1. The mean wind increase is about 15 %, which corresponds to 1.8 m s-1. A wind speed increase of 4 to 7 m s-1 above warm eddies is not uncommon. Cases where the wind did not increase above the eddies or did not decrease downstream had higher wind speeds and occurred during a cold front associated with intense cyclonic low-pressure systems, suggesting certain synoptic conditions need to be met to allow for the development of wind speed anomalies over warm-core ocean eddies. In many cases

  17. Investigating Teacher Noticing of Student Algebraic Thinking

    ERIC Educational Resources Information Center

    Walkoe, Janet Dawn Kim

    2013-01-01

    Learning algebra is critical for students in the U.S. today. Algebra concepts provide the foundation for much advanced mathematical content. In addition, algebra serves as a gatekeeper to opportunities such as admission to college. Yet many students in the U.S. struggle in algebra classes. Researchers claim that one reason for these difficulties…

  18. Intense submesoscale upwelling in anticyclonic eddies

    NASA Astrophysics Data System (ADS)

    Brannigan, L.

    2016-04-01

    Observations from around the global ocean show that enhanced biological activity can be found in anticyclonic eddies. This may mean that upwelling of nutrient-rich water occurs within the eddy, but such upwelling is not captured by models that resolve mesoscale processes. High-resolution simulations presented here show intense submesoscale upwelling from the thermocline to the mixed layer in anticyclonic eddies. The properties of the upwelling are consistent with a process known as symmetric instability. A simple limiting nutrient experiment shows that this upwelling can drive much higher biological activity in anticyclonic eddies when there is a high nutrient concentration in the thermocline. An estimate for the magnitude of upwelling associated with symmetric instability in anticyclonic eddies in the Sargasso Sea shows that it may be of comparable magnitude to other processes, though further work is required to understand the full implications for basin-scale nutrient budgets.

  19. Unified Ultrasonic/Eddy-Current Data Acquisition

    NASA Technical Reports Server (NTRS)

    Chern, E. James; Butler, David W.

    1993-01-01

    Imaging station for detecting cracks and flaws in solid materials developed combining both ultrasonic C-scan and eddy-current imaging. Incorporation of both techniques into one system eliminates duplication of computers and of mechanical scanners; unifies acquisition, processing, and storage of data; reduces setup time for repetitious ultrasonic and eddy-current scans; and increases efficiency of system. Same mechanical scanner used to maneuver either ultrasonic or eddy-current probe over specimen and acquire point-by-point data. For ultrasonic scanning, probe linked to ultrasonic pulser/receiver circuit card, while, for eddy-current imaging, probe linked to impedance-analyzer circuit card. Both ultrasonic and eddy-current imaging subsystems share same desktop-computer controller, containing dedicated plug-in circuit boards for each.

  20. Large Eddy Simulation of a Turbulent Jet

    NASA Technical Reports Server (NTRS)

    Webb, A. T.; Mansour, Nagi N.

    2001-01-01

    Here we present the results of a Large Eddy Simulation of a non-buoyant jet issuing from a circular orifice in a wall, and developing in neutral surroundings. The effects of the subgrid scales on the large eddies have been modeled with the dynamic large eddy simulation model applied to the fully 3D domain in spherical coordinates. The simulation captures the unsteady motions of the large-scales within the jet as well as the laminar motions in the entrainment region surrounding the jet. The computed time-averaged statistics (mean velocity, concentration, and turbulence parameters) compare well with laboratory data without invoking an empirical entrainment coefficient as employed by line integral models. The use of the large eddy simulation technique allows examination of unsteady and inhomogeneous features such as the evolution of eddies and the details of the entrainment process.

  1. Eddy Generation by a Steady Poleward Outflow

    NASA Astrophysics Data System (ADS)

    Durland, T. S.; Pedlosky, J.; Spall, M. A.

    2008-12-01

    The energetic eddy field coincident with the South Equatorial Current (SEC) in the eastern Indian Ocean has been variously attributed to baroclinic instability of the SEC, barotropic instability of the SEC and shedding of eddies by the branch of the Indonesian Throughflow (ITF) entering the basin through Timor Passage. We present an additional mechanism by demonstrating that in an idealized numerical model, a steady poleward outflow (meant to simulate the Lombok Strait branch of the ITF) can generate an eddy field with spatial and temporal patterns that bear a remarkable resemblance to observations of sea surface height varibility in the region. A simple conceptual model will be presented which links the nonlinear, eddy-generating dynamics to linear dynamics, thus making possible the prediction of eddy amplitudes and periodicity for a wide range of outflow latitudes and volume fluxes.

  2. Central extensions of Lax operator algebras

    NASA Astrophysics Data System (ADS)

    Schlichenmaier, M.; Sheinman, O. K.

    2008-08-01

    Lax operator algebras were introduced by Krichever and Sheinman as a further development of Krichever's theory of Lax operators on algebraic curves. These are almost-graded Lie algebras of current type. In this paper local cocycles and associated almost-graded central extensions of Lax operator algebras are classified. It is shown that in the case when the corresponding finite-dimensional Lie algebra is simple the two-cohomology space is one-dimensional. An important role is played by the action of the Lie algebra of meromorphic vector fields on the Lax operator algebra via suitable covariant derivatives.

  3. Large eddy simulation of Rayleigh-Taylor instability using the arbitrary Lagrangian-Eulerian method

    NASA Astrophysics Data System (ADS)

    Darlington, Rebecca Mattson

    This research addresses the application of a large eddy simulation (LES) to Arbitrary Lagrangian Eulerian (ALE) simulations of Rayleigh-Taylor instability. First, ALE simulations of simplified Rayleigh-Taylor instability are studied. The advantages of ALE over Eulerian simulations are shown. Next, the behavior of the LES is examined in a more complicated ALE simulation of Rayleigh-Taylor instability. The effects of eddy viscosity and stochastic backscatter are examined. The LES is also coupled with ALE to increase grid resolution in areas where it is needed. Finally, the methods studied above are applied to two sets of experimental simulations. In these simulations, ALE allows the mesh to follow expanding experimental targets, while LES can be used to mimic the effect of unresolved instability modes.

  4. Large eddy simulation of Rayleigh-Taylor instability using the arbitrary Lagrangian-Eulerian method

    SciTech Connect

    Darlington, Rebecca Mattson

    1999-12-01

    This research addresses the application of a large eddy simulation (LES) to Arbitrary Lagrangian Eulerian (ALE) simulations of Rayleigh-Taylor instability. First, ALE simulations of simplified Rayleigh-Taylor instability are studied. The advantages of ALE over Eulerian simulations are shown. Next, the behavior of the LES is examined in a more complicated ALE simulation of Rayleigh-Taylor instability. The effects of eddy viscosity and stochastic backscatter are examined. The LES is also coupled with ALE to increase grid resolution in areas where it is needed. Finally, the methods studied above are applied to two sets of experimental simulations. In these simulations, ALE allows the mesh to follow expanding experimental targets, while LES can be used to mimic the effect of unresolved instability modes.

  5. A dynamic hybrid subgrid-scale modeling framework for large eddy simulations

    NASA Astrophysics Data System (ADS)

    Maulik, Romit; San, Omer

    2016-11-01

    We put forth a dynamic modeling framework for sub-grid parameterization of large eddy simulation of turbulent flows based upon the use of the approximate deconvolution (AD) procedure to compute the eddy viscosity constant self-adaptively from the resolved flow quantities. In our proposed framework, the test filtering process of the standard dynamic model is replaced by the AD procedure and a posteriori error analysis is performed. The robustness of the model has been tested considering the Burgers, Kraichnan, Kolmogorov turbulence problems. Our numerical assessments for solving these canonical decaying turbulence problems show that the proposed approach could be used as a viable tool to address the turbulence closure problem due to its flexibility.

  6. Viscosity dictates metabolic activity of Vibrio ruber

    PubMed Central

    Borić, Maja; Danevčič, Tjaša; Stopar, David

    2012-01-01

    Little is known about metabolic activity of bacteria, when viscosity of their environment changes. In this work, bacterial metabolic activity in media with viscosity ranging from 0.8 to 29.4 mPas was studied. Viscosities up to 2.4 mPas did not affect metabolic activity of Vibrio ruber. On the other hand, at 29.4 mPas respiration rate and total dehydrogenase activity increased 8 and 4-fold, respectively. The activity of glucose-6-phosphate dehydrogenase (GPD) increased up to 13-fold at higher viscosities. However, intensified metabolic activity did not result in faster growth rate. Increased viscosity delayed the onset as well as the duration of biosynthesis of prodigiosin. As an adaptation to viscous environment V. ruber increased metabolic flux through the pentose phosphate pathway and reduced synthesis of a secondary metabolite. In addition, V. ruber was able to modify the viscosity of its environment. PMID:22826705

  7. Asymptotic aspect of derivations in Banach algebras.

    PubMed

    Roh, Jaiok; Chang, Ick-Soon

    2017-01-01

    We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.

  8. Computing Matrix Representations of Filiform Lie Algebras

    NASA Astrophysics Data System (ADS)

    Ceballos, Manuel; Núñez, Juan; Tenorio, Ángel F.

    In this paper, we compute minimal faithful unitriangular matrix representations of filiform Lie algebras. To do it, we use the nilpotent Lie algebra, g_n, formed of n ×n strictly upper-triangular matrices. More concretely, we search the lowest natural number n such that the Lie algebra g_n contains a given filiform Lie algebra, also computing a representative of this algebra. All the computations in this paper have been done using MAPLE 9.5.

  9. Cartooning in Algebra and Calculus

    ERIC Educational Resources Information Center

    Moseley, L. Jeneva

    2014-01-01

    This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

  10. GCD, LCM, and Boolean Algebra?

    ERIC Educational Resources Information Center

    Cohen, Martin P.; Juraschek, William A.

    1976-01-01

    This article investigates the algebraic structure formed when the process of finding the greatest common divisor and the least common multiple are considered as binary operations on selected subsets of positive integers. (DT)

  11. Ada Linear-Algebra Program

    NASA Technical Reports Server (NTRS)

    Klumpp, A. R.; Lawson, C. L.

    1988-01-01

    Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.

  12. Bulk viscosity of multiparticle collision dynamics fluids.

    PubMed

    Theers, Mario; Winkler, Roland G

    2015-03-01

    We determine the viscosity parameters of the multiparticle collision dynamics (MPC) approach, a particle-based mesoscale hydrodynamic simulation method for fluids. We perform analytical calculations and verify our results by simulations. The stochastic rotation dynamics and the Andersen thermostat variant of MPC are considered, both with and without angular momentum conservation. As an important result, we find a nonzero bulk viscosity for every MPC version. The explicit calculation shows that the bulk viscosity is determined solely by the collisional interactions of MPC.

  13. Bacterial accumulation in viscosity gradients

    NASA Astrophysics Data System (ADS)

    Waisbord, Nicolas; Guasto, Jeffrey

    2016-11-01

    Cell motility is greatly modified by fluid rheology. In particular, the physical environments in which cells function, are often characterized by gradients of viscous biopolymers, such as mucus and extracellular matrix, which impact processes ranging from reproduction to digestion to biofilm formation. To understand how spatial heterogeneity of fluid rheology affects the motility and transport of swimming cells, we use hydrogel microfluidic devices to generate viscosity gradients in a simple, polymeric, Newtonian fluid. Using video microscopy, we characterize the random walk motility patterns of model bacteria (Bacillus subtilis), showing that both wild-type ('run-and-tumble') cells and smooth-swimming mutants accumulate in the viscous region of the fluid. Through statistical analysis of individual cell trajectories and body kinematics in both homogeneous and heterogeneous viscous environments, we discriminate passive, physical effects from active sensing processes to explain the observed cell accumulation at the ensemble level.

  14. Coherent States for Hopf Algebras

    NASA Astrophysics Data System (ADS)

    Škoda, Zoran

    2007-07-01

    Families of Perelomov coherent states are defined axiomatically in the context of unitary representations of Hopf algebras. A global geometric picture involving locally trivial noncommutative fibre bundles is involved in the construction. If, in addition, the Hopf algebra has a left Haar integral, then a formula for noncommutative resolution of identity in terms of the family of coherent states holds. Examples come from quantum groups.

  15. Multiplier operator algebras and applications

    PubMed Central

    Blecher, David P.; Zarikian, Vrej

    2004-01-01

    The one-sided multipliers of an operator space X are a key to “latent operator algebraic structure” in X. We begin with a survey of these multipliers, together with several of the applications that they have had to operator algebras. We then describe several new results on one-sided multipliers, and new applications, mostly to one-sided M-ideals. PMID:14711990

  16. Hopf algebras and topological recursion

    NASA Astrophysics Data System (ADS)

    Esteves, João N.

    2015-11-01

    We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).

  17. Conformable eddy current array delivery

    NASA Astrophysics Data System (ADS)

    Summan, Rahul; Pierce, Gareth; Macleod, Charles; Mineo, Carmelo; Riise, Jonathan; Morozov, Maxim; Dobie, Gordon; Bolton, Gary; Raude, Angélique; Dalpé, Colombe; Braumann, Johannes

    2016-02-01

    The external surface of stainless steel containers used for the interim storage of nuclear material may be subject to Atmospherically Induced Stress Corrosion Cracking (AISCC). The inspection of such containers poses a significant challenge due to the large quantities involved; therefore, automating the inspection process is of considerable interest. This paper reports upon a proof-of-concept project concerning the automated NDT of a set of test containers containing artificially generated AISCCs. An Eddy current array probe with a conformable padded surface from Eddyfi was used as the NDT sensor and end effector on a KUKA KR5 arc HW robot. A kinematically valid cylindrical raster scan path was designed using the KUKA|PRC path planning software. Custom software was then written to interface measurement acquisition from the Eddyfi hardware with the motion control of the robot. Preliminary results and analysis are presented from scanning two canisters.

  18. Rotating concave eddy current probe

    DOEpatents

    Roach, Dennis P.; Walkington, Phil; Rackow, Kirk A.; Hohman, Ed

    2008-04-01

    A rotating concave eddy current probe for detecting fatigue cracks hidden from view underneath the head of a raised head fastener, such as a buttonhead-type rivet, used to join together structural skins, such as aluminum aircraft skins. The probe has a recessed concave dimple in its bottom surface that closely conforms to the shape of the raised head. The concave dimple holds the probe in good alignment on top of the rivet while the probe is rotated around the rivet's centerline. One or more magnetic coils are rigidly embedded within the probe's cylindrical body, which is made of a non-conducting material. This design overcomes the inspection impediment associated with widely varying conductivity in fastened joints.

  19. A western boundary current eddy characterisation study

    NASA Astrophysics Data System (ADS)

    Ribbe, Joachim; Brieva, Daniel

    2016-12-01

    The analysis of an eddy census for the East Australian Current (EAC) region yielded a total of 497 individual short-lived (7-28 days) cyclonic and anticyclonic eddies for the period 1993 to 2015. This was an average of about 23 eddies per year. 41% of the tracked individual cyclonic and anticyclonic eddies were detected off southeast Queensland between about 25 °S and 29 °S. This is the region where the flow of the EAC intensifies forming a swift western boundary current that impinges near Fraser Island on the continental shelf. This zone was also identified as having a maximum in detected short-lived cyclonic eddies. A total of 94 (43%) individual cyclonic eddies or about 4-5 per year were tracked in this region. The census found that these potentially displaced entrained water by about 115 km with an average displacement speed of about 4 km per day. Cyclonic eddies were likely to contribute to establishing an on-shelf longshore northerly flow forming the western branch of the Fraser Island Gyre and possibly presented an important cross-shelf transport process in the life cycle of temperate fish species of the EAC domain. In-situ observations near western boundary currents previously documented the entrainment, off-shelf transport and export of near shore water, nutrients, sediments, fish larvae and the renewal of inner shelf water due to short-lived eddies. This study found that these cyclonic eddies potentially play an important off-shelf transport process off the central east Australian coast.

  20. The experimental viscosity and calculated relative viscosity of liquid In Sn allcoys

    NASA Astrophysics Data System (ADS)

    Wu, A. Q.; Guo, L. J.; Liu, C. S.; Jia, E. G.; Zhu, Z. G.

    2007-04-01

    The experimental measured viscosity of liquid pure Sn, In 20Sn 80 and In 80Sn 20 alloys was studied, and to make a comparison, the calculated relative viscosity based on the pair distribution functions, g( r), has also been studied. There is one peak in each experimental viscosity and calculated relative-viscosity curve of liquid pure Sn about 1000 °C. One valley appears in each experimental viscosity and calculated viscosity curve of liquid In 20Sn 80 alloy about 700 °C. There is no abnormal behavior on In 80Sn 20 alloy. The behavior of experimental viscosity and calculated relative viscosity is coincident with each other. Those results conformed that the temperature-induced structure anomalies reported before did take place.

  1. Eddy current technique for predicting burst pressure

    DOEpatents

    Petri, Mark C.; Kupperman, David S.; Morman, James A.; Reifman, Jaques; Wei, Thomas Y. C.

    2003-01-01

    A signal processing technique which correlates eddy current inspection data from a tube having a critical tubing defect with a range of predicted burst pressures for the tube is provided. The method can directly correlate the raw eddy current inspection data representing the critical tubing defect with the range of burst pressures using a regression technique, preferably an artificial neural network. Alternatively, the technique deconvolves the raw eddy current inspection data into a set of undistorted signals, each of which represents a separate defect of the tube. The undistorted defect signal which represents the critical tubing defect is related to a range of burst pressures utilizing a regression technique.

  2. Eddy current inspection of graphite fiber components

    NASA Technical Reports Server (NTRS)

    Workman, G. L.; Bryson, C. C.

    1990-01-01

    The recognition of defects in materials properties still presents a number of problems for nondestructive testing in aerospace systems. This project attempts to utilize current capabilities in eddy current instrumentation, artificial intelligence, and robotics in order to provide insight into defining geometrical aspects of flaws in composite materials which are capable of being evaluated using eddy current inspection techniques. The unique capabilities of E-probes and horseshoe probes for inspecting probes for inspecting graphite fiber materials were evaluated and appear to hold great promise once the technology development matures. The initial results are described of modeling eddy current interactions with certain flaws in graphite fiber samples.

  3. Eddy Current Testing, RQA/M1-5330.17.

    ERIC Educational Resources Information Center

    National Aeronautics and Space Administration, Huntsville, AL. George C. Marshall Space Flight Center.

    As one in the series of classroom training handbooks, prepared by the U.S. space program, instructional material is presented in this volume concerning familiarization and orientation on eddy current testing. The subject is presented under the following headings: Introduction, Eddy Current Principles, Eddy Current Equipment, Eddy Current Methods,…

  4. Artificial Fluid Properties for Large-Eddy Simulation of Compressible Turbulent Mixing

    SciTech Connect

    Cook, A W

    2007-01-08

    An alternative methodology is described for Large-Eddy Simulation of flows involving shocks, turbulence and mixing. In lieu of filtering the governing equations, it is postulated that the large-scale behavior of an ''LES'' fluid, i.e., a fluid with artificial properties, will be similar to that of a real fluid, provided the artificial properties obey certain constraints. The artificial properties consist of modifications to the shear viscosity, bulk viscosity, thermal conductivity and species diffusivity of a fluid. The modified transport coefficients are designed to damp out high wavenumber modes, close to the resolution limit, without corrupting lower modes. Requisite behavior of the artificial properties is discussed and results are shown for a variety of test problems, each designed to exercise different aspects of the models. When combined with a 10th-order compact scheme, the overall method exhibits excellent resolution characteristics for turbulent mixing, while capturing shocks and material interfaces in crisp fashion.

  5. Novikov algebras with associative bilinear forms

    NASA Astrophysics Data System (ADS)

    Zhu, Fuhai; Chen, Zhiqi

    2007-11-01

    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. The goal of this paper is to study Novikov algebras with non-degenerate associative symmetric bilinear forms, which we call quadratic Novikov algebras. Based on the classification of solvable quadratic Lie algebras of dimension not greater than 4 and Novikov algebras in dimension 3, we show that quadratic Novikov algebras up to dimension 4 are commutative. Furthermore, we obtain the classification of transitive quadratic Novikov algebras in dimension 4. But we find that not every quadratic Novikov algebra is commutative and give a non-commutative quadratic Novikov algebra in dimension 6.

  6. Quantum Q systems: from cluster algebras to quantum current algebras

    NASA Astrophysics Data System (ADS)

    Di Francesco, Philippe; Kedem, Rinat

    2017-02-01

    This paper gives a new algebraic interpretation for the algebra generated by the quantum cluster variables of the A_r quantum Q-system (Di Francesco and Kedem in Int Math Res Not IMRN 10:2593-2642, 2014). We show that the algebra can be described as a quotient of the localization of the quantum algebra U_{√{q}}({n}[u,u^{-1}])subset U_{√{q}}(widehat{{sl}}_2), in the Drinfeld presentation. The generating current is made up of a subset of the cluster variables which satisfy the Q-system, which we call fundamental. The other cluster variables are given by a quantum determinant-type formula, and are polynomials in the fundamental generators. The conserved quantities of the discrete evolution (Di Francesco and Kedem in Adv Math 228(1):97-152, 2011) described by quantum Q-system generate the Cartan currents at level 0, in a non-standard polarization. The rest of the quantum affine algebra is also described in terms of cluster variables.

  7. THE VISCOSITY OF HELIUM-CESIUM MIXTURES,

    DTIC Science & Technology

    The viscosities of helium-cesium mixtures having mole fractions of cesium from zero to unity were evaluated using a Lennard - Jones 6-12 interaction potential for all encounters in the Enskog Chapman expressions for the viscosity of a binary mixture. (Author)

  8. Surface dilatational viscosity of Langmuir monolayers

    NASA Astrophysics Data System (ADS)

    Lopez, Juan; Vogel, Michael; Hirsa, Amir

    2003-11-01

    With increased interest in microfluidic systems, interfacial phenomena is receiving more attention. As the length scales of fluid problems decrease, the surface to volume ratio increases and the coupling between interfacial flow and bulk flow becomes increasingly dominated by effects due to intrinsic surface viscosities (shear and dilatational), in comparison to elastic effects (due to surface tension gradients). The surface shear viscosity is well-characterized, as cm-scale laboratory experiments are able to isolate its effects from other interfacial processes (e.g., in the deep-channel viscometer). The same is not true for the dilatational viscosity, because it acts in the direction of surface tension gradients. Their relative strength scale with the capillary number, and for cm-scale laboratory flows, surface tension effects tend to dominate. In microfluidic scale flows, the scaling favors viscosity. We have devised an experimental apparatus which is capable of isolating and enhancing the effects of dilatational viscosity at the cm scales by driving the interface harmonically in time, while keeping the interface flat. In this talk, we shall present both the theory for how this works as well as experimental measurements of surface velocity from which we deduce the dilatational viscosity of several monolayers on the air-water interface over a substantial range of surface concentrations. Anomalous behavior over some range of concentration, which superficially indicates negative viscosity, maybe explained in terms of compositional effects due to large spatial and temporal variations in concentration and corresponding viscosity.

  9. Reducing blood viscosity with magnetic fields

    NASA Astrophysics Data System (ADS)

    Tao, R.; Huang, K.

    2011-07-01

    Blood viscosity is a major factor in heart disease. When blood viscosity increases, it damages blood vessels and increases the risk of heart attacks. Currently, the only method of treatment is to take drugs such as aspirin, which has, however, several unwanted side effects. Here we report our finding that blood viscosity can be reduced with magnetic fields of 1 T or above in the blood flow direction. One magnetic field pulse of 1.3 T lasting ˜1 min can reduce the blood viscosity by 20%-30%. After the exposure, in the absence of magnetic field, the blood viscosity slowly moves up, but takes a couple of hours to return to the original value. The process is repeatable. Reapplying the magnetic field reduces the blood viscosity again. By selecting the magnetic field strength and duration, we can keep the blood viscosity within the normal range. In addition, such viscosity reduction does not affect the red blood cells’ normal function. This technology has much potential for physical therapy.

  10. Viscosity test standards for engine oils

    SciTech Connect

    Not Available

    1990-01-01

    This report presents a compilation of 10 ASTM standards that cover both low and high temperature viscosity tests for automotive engine oils, with respect to low temperature flow properties and performance requirements under high temperature, high shear rate conditions. Society of Automotive Engineer's Engine Oil Viscosity Classification SAE J300 is included to provide low temperature high shear rate method.

  11. Large-eddy Advection in Evapotranspiration Estimates from an Array of Eddy Covariance Towers

    NASA Astrophysics Data System (ADS)

    Lin, X.; Evett, S. R.; Gowda, P. H.; Colaizzi, P. D.; Aiken, R.

    2014-12-01

    Evapotranspiration was continuously measured by an array of eddy covariance systems and large weighting lysimeter in a sorghum in Bushland, Texas in 2014. The advective divergence from both horizontal and vertical directions were measured through profile measurements above canopy. All storage terms were integrated from the depth of soil heat flux plate to the height of eddy covariance measurement. Therefore, a comparison between the eddy covariance system and large weighing lysimeter was conducted on hourly and daily basis. The results for the discrepancy between eddy covariance towers and the lysimeter will be discussed in terms of advection and storage contributions in time domain and frequency domain.

  12. Process Specification for Eddy Current Inspection

    NASA Technical Reports Server (NTRS)

    Koshti, Ajay

    2011-01-01

    This process specification establishes the minimum requirements for eddy current inspection of flat surfaces, fastener holes, threaded fasteners and seamless and welded tubular products made from nonmagnetic alloys such as aluminum and stainless steel.

  13. Plasma viscosity elevations with simulated weightlessness

    NASA Technical Reports Server (NTRS)

    Martin, D. G.; Convertino, V. A.; Goldwater, D.; Ferguson, E. W.; Schoomaker, E. B.

    1986-01-01

    A hypothesis correlating an increase in blood viscosity during bed rest to a decrease in aerobic capacity during simulated weightlessness is tested. Eight human subjects were studied on the sixth day of bed rest during two consecutive 10-d bed rest periods separated by a 14-d recovery interval designed to simulate the flight-layover schedule of Shuttle astronauts. Plasma viscosity and volume were measured, together with maximal aerobic capacity (VO2max). An increase in hematocrit, plasma protein, and fibrinogen concentrations was found, contributing to an elevation in plasma viscosity. VO2max decreased significantly in the first, but not the second bed rest cycle, and though many individuals exhibited a decrease in plasma volume and aerobic capacity coupled with elevated plasma viscosity, correlations between these variables were lacking. It is concluded that the decrease in VO2max observed following simulated weightlessness cannot be attributed to alterations in muscle blood flow resulting from increased blood viscosity.

  14. Anomalous magnetic viscosity in relativistic accretion disks

    NASA Astrophysics Data System (ADS)

    Lin, Fujun; Liu, Sanqiu; Li, Xiaoqing

    2013-07-01

    It has been proved that the self-generated magnetic fields by transverse plasmons in the relativistic regime are modulationally unstable, leading to a self-similar collapse of the magnetic flux tubes and resulting in local magnetic structures; highly spatially intermittent flux is responsible for generating the anomalous viscosity. We derive the anomalous magnetic viscosity coefficient, in accretion disks around compact objects, such as black holes, pulsars and quasars, where the plasmas are relativistic, in order to help clarify the nature of viscosity in the theory of accretion disks. The results indicate that, the magnetic viscosity is modified by the relativistic effects of plasmas, and its' strength would be 1015 stronger than the molecular viscosity, which may be helpful in explaining the observations.

  15. Winds, Eddies and Flow through Straits

    DTIC Science & Technology

    2010-01-01

    driven origin of the Philippine dipole eddies. By contrast, in other volcanic island regions of the world (including the Hawaiian, Cabo Verde, and... volcanic island regions of the world. By contrast in the Hawaiian, Cabo Verde and Canary Islands, the driving mechanism in the eddy dynamics is...J. Aristegui, and F. Herrera (2000), Lee region of Gran Canaria , J. Geophys. Res., 105(C7), 17173-17193. Chang, C.-P., Z. Wang, and H. Hendon

  16. Automated eddy current analysis of materials

    NASA Technical Reports Server (NTRS)

    Workman, Gary L.

    1991-01-01

    The use of eddy current techniques for characterizing flaws in graphite-based filament-wound cylindrical structures is described. A major emphasis was also placed upon incorporating artificial intelligence techniques into the signal analysis portion of the inspection process. Developing an eddy current scanning system using a commercial robot for inspecting graphite structures (and others) was a goal in the overall concept and is essential for the final implementation for the expert systems interpretation. Manual scans, as performed in the preliminary work here, do not provide sufficiently reproducible eddy current signatures to be easily built into a real time expert system. The expert systems approach to eddy current signal analysis requires that a suitable knowledge base exist in which correct decisions as to the nature of a flaw can be performed. A robotic workcell using eddy current transducers for the inspection of carbon filament materials with improved sensitivity was developed. Improved coupling efficiencies achieved with the E-probes and horseshoe probes are exceptional for graphite fibers. The eddy current supervisory system and expert system was partially developed on a MacIvory system. Continued utilization of finite element models for predetermining eddy current signals was shown to be useful in this work, both for understanding how electromagnetic fields interact with graphite fibers, and also for use in determining how to develop the knowledge base. Sufficient data was taken to indicate that the E-probe and the horseshoe probe can be useful eddy current transducers for inspecting graphite fiber components. The lacking component at this time is a large enough probe to have sensitivity in both the far and near field of a thick graphite epoxy component.

  17. Eruptive viscosity and volcano morphology

    NASA Technical Reports Server (NTRS)

    Posin, Seth B.; Greeley, Ronald

    1988-01-01

    Terrestrial central volcanoes formed predominantly from lava flows were classified as shields, stratovolcanoes, and domes. Shield volcanoes tend to be large in areal extent, have convex slopes, and are characterized by their resemblance to inverted hellenic war shields. Stratovolcanoes have concave slopes, whereas domes are smaller and have gentle convex slopes near the vent that increase near the perimeter. In addition to these differences in morphology, several other variations were observed. The most important is composition: shield volcanoes tend to be basaltic, stratovolcanoes tend to be andesitic, and domes tend to be dacitic. However, important exceptions include Fuji, Pico, Mayon, Izalco, and Fuego which have stratovolcano morphologies but are composed of basaltic lavas. Similarly, Ribkwo is a Kenyan shield volcano composed of trachyte and Suswa and Kilombe are shields composed of phonolite. These exceptions indicate that eruptive conditions, rather than composition, may be the primary factors that determine volcano morphology. The objective of this study is to determine the relationships, if any, between eruptive conditions (viscosity, erupted volume, and effusion rate) and effusive volcano morphology. Moreover, it is the goal of this study to incorporate these relationships into a model to predict the eruptive conditions of extraterrestrial (Martian) volcanoes based on their morphology.

  18. Mesoscale eddies transport deep-sea sediments.

    PubMed

    Zhang, Yanwei; Liu, Zhifei; Zhao, Yulong; Wang, Wenguang; Li, Jianru; Xu, Jingping

    2014-08-04

    Mesoscale eddies, which contribute to long-distance water mass transport and biogeochemical budget in the upper ocean, have recently been taken into assessment of the deep-sea hydrodynamic variability. However, how such eddies influence sediment movement in the deepwater environment has not been explored. Here for the first time we observed deep-sea sediment transport processes driven by mesoscale eddies in the northern South China Sea via a full-water column mooring system located at 2100 m water depth. Two southwestward propagating, deep-reaching anticyclonic eddies passed by the study site during January to March 2012 and November 2012 to January 2013, respectively. Our multiple moored instruments recorded simultaneous or lagging enhancement of suspended sediment concentration with full-water column velocity and temperature anomalies. We interpret these suspended sediments to have been trapped and transported from the southwest of Taiwan by the mesoscale eddies. The net near-bottom southwestward sediment transport by the two events is estimated up to one million tons. Our study highlights the significance of surface-generated mesoscale eddies on the deepwater sedimentary dynamic process.

  19. Eddies off the Queen Charlotte Islands

    NASA Technical Reports Server (NTRS)

    2002-01-01

    The bright red, green, and turquoise patches to the west of British Columbia's Queen Charlotte Islands and Alaska's Alexander Archipelago highlight the presence of biological activity in the ocean. These colors indicate high concentrations of chlorophyll, the primary pigment found in phytoplankton. Notice that there are a number of eddies visible in the Pacific Ocean in this pseudo-color scene. The eddies are formed by strong outflow currents from rivers along North America's west coast that are rich in nutrients from the springtime snowmelt running off the mountains. This nutrient-rich water helps stimulate the phytoplankton blooms within the eddies. (For more details, read Tracking Eddies that Feed the Sea.) To the west of the eddies in the water, another type of eddy-this one in the atmosphere-forms the clouds into the counterclockwise spiral characteristic of a low pressure system in the Northern Hemisphere. (Click on the image above to see it at full resolution; or click to see the scene in true-color.) The snow-covered mountains of British Columbia are visible in the upper righthand corner of the image. This scene was constructed using SeaWiFS data collected on June 13, 2002. SeaWiFS image courtesy the SeaWiFS Project, NASA/Goddard Space Flight Center, and ORBIMAGE

  20. Improved engine wall models for Large Eddy Simulation (LES)

    NASA Astrophysics Data System (ADS)

    Plengsaard, Chalearmpol

    Improved wall models for Large Eddy Simulation (LES) are presented in this research. The classical Werner-Wengle (WW) wall shear stress model is used along with near-wall sub-grid scale viscosity. A sub-grid scale turbulent kinetic energy is employed in a model for the eddy viscosity. To gain better heat flux results, a modified classical variable-density wall heat transfer model is also used. Because no experimental wall shear stress results are available in engines, the fully turbulent developed flow in a square duct is chosen to validate the new wall models. The model constants in the new wall models are set to 0.01 and 0.8, respectively and are kept constant throughout the investigation. The resulting time- and spatially-averaged velocity and temperature wall functions from the new wall models match well with the law-of-the-wall experimental data at Re = 50,000. In order to study the effect of hot air impinging walls, jet impingement on a flat plate is also tested with the new wall models. The jet Reynolds number is equal to 21,000 and a fixed jet-to-plate spacing of H/D = 2.0. As predicted by the new wall models, the time-averaged skin friction coefficient agrees well with experimental data, while the computed Nusselt number agrees fairly well when r/D > 2.0. Additionally, the model is validated using experimental data from a Caterpillar engine operated with conventional diesel combustion. Sixteen different operating engine conditions are simulated. The majority of the predicted heat flux results from each thermocouple location follow similar trends when compared with experimental data. The magnitude of peak heat fluxes as predicted by the new wall models is in the range of typical measured values in diesel combustion, while most heat flux results from previous LES wall models are over-predicted. The new wall models generate more accurate predictions and agree better with experimental data.

  1. Three-dimensional properties of mesoscale eddies in the South China Sea based on eddy-resolving model output

    NASA Astrophysics Data System (ADS)

    Lin, Xiayan; Dong, Changming; Chen, Dake; Liu, Yu; Yang, Jingsong; Zou, Bin; Guan, Yuping

    2015-05-01

    Last decade has witnessed extensive studies on mesoscale oceanic eddies in the Southern China Sea (SCS), however most of these studies are focused on the surface eddies, and three-dimensional features of eddies are not well known except some individual eddies. We apply a three-dimensional eddy detection scheme to a 9-year (2000-2008) eddy-resolving numerical solution to acquire three-dimensional eddy data set in the SCS. The model solution is validated with observational data in terms of both seasonal and intra-seasonal scales. The statistical characteristics of eddies at the sea surface, such as eddy number, lifetime and radius, from the model are comparable with those derived from the satellite altimetry data. The vertical profiles of the physical features of eddies are exposed from the statistical analysis of the three-dimensional eddy data set. For examples, more cyclonic eddies (CEs) are generated than anticyclonic eddies (AEs) in the depth above about 350 m and an opposite trend is presented below 350 m. The lifetimes of CEs and AEs are statistically equal and no significant variation at different vertical levels. Eddies in the central SCS have the largest size than in other areas and their sizes decrease with the increase in water depth. The relative vorticity amplitude of eddies decreases with the increase in the depth. There are three different types of eddies: bowl-shaped with the largest size at the surface, lens-shaped with the largest size in the middle and cone-shaped with the largest size at the bottom. Most of eddies are bowl-shaped eddies. The three types of eddies have different effects on the temperature and salinity profiles. Eddy genesis mechanisms are discussed and categorized into three types in the SCS: surface wind curl input, current interaction with the bottom topography and Kuroshio intrusion.

  2. Large Eddy Simulations in Astrophysics

    NASA Astrophysics Data System (ADS)

    Schmidt, Wolfram

    2015-12-01

    In this review, the methodology of large eddy simulations (LES) is introduced and applications in astrophysics are discussed. As theoretical framework, the scale decomposition of the dynamical equations for neutral fluids by means of spatial filtering is explained. For cosmological applications, the filtered equations in comoving coordinates are also presented. To obtain a closed set of equations that can be evolved in LES, several subgrid-scale models for the interactions between numerically resolved and unresolved scales are discussed, in particular the subgrid-scale turbulence energy equation model. It is then shown how model coefficients can be calculated, either by dynamic procedures or, a priori, from high-resolution data. For astrophysical applications, adaptive mesh refinement is often indispensable. It is shown that the subgrid-scale turbulence energy model allows for a particularly elegant and physically well-motivated way of preserving momentum and energy conservation in adaptive mesh refinement (AMR) simulations. Moreover, the notion of shear-improved models for in-homogeneous and non-stationary turbulence is introduced. Finally, applications of LES to turbulent combustion in thermonuclear supernovae, star formation and feedback in galaxies, and cosmological structure formation are reviewed.

  3. Assessment of dynamic closure for premixed combustion large eddy simulation

    NASA Astrophysics Data System (ADS)

    Langella, Ivan; Swaminathan, Nedunchezhian; Gao, Yuan; Chakraborty, Nilanjan

    2015-09-01

    Turbulent piloted Bunsen flames of stoichiometric methane-air mixtures are computed using the large eddy simulation (LES) paradigm involving an algebraic closure for the filtered reaction rate. This closure involves the filtered scalar dissipation rate of a reaction progress variable. The model for this dissipation rate involves a parameter βc representing the flame front curvature effects induced by turbulence, chemical reactions, molecular dissipation, and their interactions at the sub-grid level, suggesting that this parameter may vary with filter width or be a scale-dependent. Thus, it would be ideal to evaluate this parameter dynamically by LES. A procedure for this evaluation is discussed and assessed using direct numerical simulation (DNS) data and LES calculations. The probability density functions of βc obtained from the DNS and LES calculations are very similar when the turbulent Reynolds number is sufficiently large and when the filter width normalised by the laminar flame thermal thickness is larger than unity. Results obtained using a constant (static) value for this parameter are also used for comparative evaluation. Detailed discussion presented in this paper suggests that the dynamic procedure works well and physical insights and reasonings are provided to explain the observed behaviour.

  4. Moving frames and prolongation algebras

    NASA Technical Reports Server (NTRS)

    Estabrook, F. B.

    1982-01-01

    Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.

  5. Algebraic Lattices in QFT Renormalization

    NASA Astrophysics Data System (ADS)

    Borinsky, Michael

    2016-07-01

    The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.

  6. Viscosity measurement techniques in Dissipative Particle Dynamics

    NASA Astrophysics Data System (ADS)

    Boromand, Arman; Jamali, Safa; Maia, Joao M.

    2015-11-01

    In this study two main groups of viscosity measurement techniques are used to measure the viscosity of a simple fluid using Dissipative Particle Dynamics, DPD. In the first method, a microscopic definition of the pressure tensor is used in equilibrium and out of equilibrium to measure the zero-shear viscosity and shear viscosity, respectively. In the second method, a periodic Poiseuille flow and start-up transient shear flow is used and the shear viscosity is obtained from the velocity profiles by a numerical fitting procedure. Using the standard Lees-Edward boundary condition for DPD will result in incorrect velocity profiles at high values of the dissipative parameter. Although this issue was partially addressed in Chatterjee (2007), in this work we present further modifications (Lagrangian approach) to the original LE boundary condition (Eulerian approach) that will fix the deviation from the desired shear rate at high values of the dissipative parameter and decrease the noise to signal ratios in stress measurement while increases the accessible low shear rate window. Also, the thermostat effect of the dissipative and random forces is coupled to the dynamic response of the system and affects the transport properties like the viscosity and diffusion coefficient. We investigated thoroughly the dependency of viscosity measured by both Eulerian and Lagrangian methodologies, as well as numerical fitting procedures and found that all the methods are in quantitative agreement.

  7. Colored Quantum Algebra and Its Bethe State

    NASA Astrophysics Data System (ADS)

    Wang, Jin-Zheng; Jia, Xiao-Yu; Wang, Shi-Kun

    2014-12-01

    We investigate the colored Yang—Baxter equation. Based on a trigonometric solution of colored Yang—Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation.

  8. Using Number Theory to Reinforce Elementary Algebra.

    ERIC Educational Resources Information Center

    Covillion, Jane D.

    1995-01-01

    Demonstrates that using the elementary number theory in algebra classes helps students to use acquired algebraic skills as well as helping them to more clearly understand concepts that are presented. Discusses factoring, divisibility rules, and number patterns. (AIM)

  9. Requirements for large-eddy simulation of surface wind gusts in a mountain valley

    NASA Astrophysics Data System (ADS)

    Revell, Michael J.; Purnell, Don; Lauren, Michael K.

    1996-09-01

    During the passage of a front, data from a light-weight cup anemometer and wind vane, sited in a steep-walled glacial valley of the Mt Cook region of the Southern Alps of New Zealand, were analysed to derive a power spectrum of the wind velocity for periods between 0.5 and 16 min. The energy spectrum roughly followed a -5/3 power law over the range of periods from 0.5 4 min — as might be expected in the case of an inertial subrange of eddies. However, any inertial subrange clearly does not extend to periods longer than this. We suggest that the observed eddies were generated in a turbulent wake associated with flow separation at the ridge crests, and large eddies are shed at periods of 4 8 min or more. A compressible fluid-dynamic model, with a Smagorinsky turbulence closure scheme and a “law of the wall” at the surface, was used to calculate flow over a cross section through this area in neutrally stratified conditions. A range of parameters was explored to assess some of the requirements for simulating surface wind gusts in mountainous terrain in New Zealand. In order to approximate the observed wind spectrum at Tasman aerodrome, Mount Cook, we found the model must be three-dimensional, with a horizontal resolution better than 250 m and with a Reynolds-stress eddy viscosity of less than 5 m2 s-1. In two-dimensional simulations, the eddies were too big in size and in amplitude and at the surface this was associated with reversed flow extending too far downstream. In contrast the three-dimensional simulations gave a realistic gusting effect associated with large scale “cat's paws” (a bigger variety of those commonly seen over water downstream of moderate hills), with reversed flow only at the steep part of the lee slope. The simulations were uniformly improved by better resolution, at all tested resolutions down to 250 m mesh size. The spectra of large eddies simulated in steep terrain were not very sensitive to the details of the eddy stress formulation

  10. Algebraic orbifold conformal field theories

    PubMed Central

    Xu, Feng

    2000-01-01

    The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time. PMID:11106383

  11. Scalable Parallel Algebraic Multigrid Solvers

    SciTech Connect

    Bank, R; Lu, S; Tong, C; Vassilevski, P

    2005-03-23

    The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.

  12. Anticyclonic eddies are more productive than cyclonic eddies in subtropical gyres because of winter mixing

    PubMed Central

    Hardman-Mountford, Nick J.; Greenwood, Jim; Richardson, Anthony J.; Feng, Ming; Matear, Richard J.

    2016-01-01

    Mesoscale eddies are ubiquitous features of ocean circulation that modulate the supply of nutrients to the upper sunlit ocean, influencing the rates of carbon fixation and export. The popular eddy-pumping paradigm implies that nutrient fluxes are enhanced in cyclonic eddies because of upwelling inside the eddy, leading to higher phytoplankton production. We show that this view does not hold for a substantial portion of eddies within oceanic subtropical gyres, the largest ecosystems in the ocean. Using space-based measurements and a global biogeochemical model, we demonstrate that during winter when subtropical eddies are most productive, there is increased chlorophyll in anticyclones compared with cyclones in all subtropical gyres (by 3.6 to 16.7% for the five basins). The model suggests that this is a consequence of the modulation of winter mixing by eddies. These results establish a new paradigm for anticyclonic eddies in subtropical gyres and could have important implications for the biological carbon pump and the global carbon cycle. PMID:27386549

  13. Anticyclonic eddies are more productive than cyclonic eddies in subtropical gyres because of winter mixing.

    PubMed

    Dufois, François; Hardman-Mountford, Nick J; Greenwood, Jim; Richardson, Anthony J; Feng, Ming; Matear, Richard J

    2016-05-01

    Mesoscale eddies are ubiquitous features of ocean circulation that modulate the supply of nutrients to the upper sunlit ocean, influencing the rates of carbon fixation and export. The popular eddy-pumping paradigm implies that nutrient fluxes are enhanced in cyclonic eddies because of upwelling inside the eddy, leading to higher phytoplankton production. We show that this view does not hold for a substantial portion of eddies within oceanic subtropical gyres, the largest ecosystems in the ocean. Using space-based measurements and a global biogeochemical model, we demonstrate that during winter when subtropical eddies are most productive, there is increased chlorophyll in anticyclones compared with cyclones in all subtropical gyres (by 3.6 to 16.7% for the five basins). The model suggests that this is a consequence of the modulation of winter mixing by eddies. These results establish a new paradigm for anticyclonic eddies in subtropical gyres and could have important implications for the biological carbon pump and the global carbon cycle.

  14. Symmetry algebras of linear differential equations

    NASA Astrophysics Data System (ADS)

    Shapovalov, A. V.; Shirokov, I. V.

    1992-07-01

    The local symmetries of linear differential equations are investigated by means of proven theorems on the structure of the algebra of local symmetries of translationally and dilatationally invariant differential equations. For a nonparabolic second-order equation, the absence of nontrivial nonlinear local symmetries is proved. This means that the local symmetries reduce to the Lie algebra of linear differential symmetry operators. For the Laplace—Beltrami equation, all local symmetries reduce to the enveloping algebra of the algebra of the conformal group.

  15. Spatial-Operator Algebra For Robotic Manipulators

    NASA Technical Reports Server (NTRS)

    Rodriguez, Guillermo; Kreutz, Kenneth K.; Milman, Mark H.

    1991-01-01

    Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.

  16. Twining characters and orbit Lie algebras

    SciTech Connect

    Fuchs, Jurgen; Ray, Urmie; Schellekens, Bert; Schweigert, Christoph

    1996-12-05

    We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary characters of some other generalized Kac-Moody algebra, the so-called orbit Lie algebra. Some applications to problems in conformal field theory, algebraic geometry and the theory of sporadic simple groups are sketched.

  17. Viscoseal performance with rarefied-gas sealant

    NASA Technical Reports Server (NTRS)

    Milligan, M. W.

    1973-01-01

    A fundamental study of viscoseals having a rarefied gas as the sealant was conducted. Both experimental and analytical investigations are reported. Three different analytical models were formulated and are described in detail. An experimental investigation was conducted on multiple grooved two-inch diameter viscoseals over a wide range of gas densities and shaft speeds up to 30,000 rpm. Comparisons are presented between actual viscoseal performance and the theoretical predictions for both sealing coefficient and net leakage parameters as functions of the degree of gas rarefication. Recommendations are presented for the use of the analytical models.

  18. Shear viscosity in the postquasistatic approximation

    SciTech Connect

    Peralta, C.; Rosales, L.; Rodriguez-Mueller, B.; Barreto, W.

    2010-05-15

    We apply the postquasistatic approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of anisotropic nonadiabatic radiating and dissipative distributions in general relativity. Dissipation is described by viscosity and free-streaming radiation, assuming an equation of state to model anisotropy induced by the shear viscosity. We match the interior solution, in noncomoving coordinates, with the Vaidya exterior solution. Two simple models are presented, based on the Schwarzschild and Tolman VI solutions, in the nonadiabatic and adiabatic limit. In both cases, the eventual collapse or expansion of the distribution is mainly controlled by the anisotropy induced by the viscosity.

  19. Viscosity of high-temperature iodine

    NASA Technical Reports Server (NTRS)

    Kang, Steve H.; Kunc, Joseph A.

    1991-01-01

    The viscosity coefficient of iodine in the temperature range 500 - 3000 K is calculated. Because of the low dissociation energy of the I2 molecules, the dissociation degree of the gas increases quickly with temperature, and I + I2 and I + I collisions must be taken into account in calculation of viscosity at temperatures greater than 1000 deg. Several possible channels for atom-atom interaction are considered, and the resulting collision integrals are averaged over all the important channels. It is also shown that the rigid-sphere model is inaccurate in predictions of the viscosity.

  20. Viscosity studies of water based magnetite nanofluids

    NASA Astrophysics Data System (ADS)

    Anu, K.; Hemalatha, J.

    2016-05-01

    Magnetite nanofluids of various concentrations have been synthesized through co-precipitation method. The structural and topographical studies made with the X-Ray Diffractometer and Atomic Force Microscope are presented in this paper. The density and viscosity studies for the ferrofluids of various concentrations have been made at room temperature. The experimental viscosities are compared with theoretical values obtained from Einstein, Batchelor and Wang models. An attempt to modify the Rosensweig model is made and the modified Rosensweig equation is reported. In addition, new empirical correlation is also proposed for predicting viscosity of ferrofluid at various concentrations.

  1. Work done by atmospheric winds on mesoscale ocean eddies

    NASA Astrophysics Data System (ADS)

    Xu, Chi; Zhai, Xiaoming; Shang, Xiao-Dong

    2016-12-01

    Mesoscale eddies are ubiquitous in the ocean and dominate the ocean's kinetic energy. However, physical processes influencing ocean eddy energy remain poorly understood. Mesoscale ocean eddy-wind interaction potentially provides an energy flux into or out of the eddy field, but its effect on ocean eddies has not yet been determined. Here we examine work done by atmospheric winds on more than 1,200,000 mesoscale eddies identified from satellite altimetry data and show that atmospheric winds significantly damp mesoscale ocean eddies, particularly in the energetic western boundary current regions and the Southern Ocean. Furthermore, the large-scale wind stress curl is found to on average systematically inject kinetic energy into anticyclonic (cyclonic) eddies in the subtropical (subpolar) gyres while mechanically damps anticyclonic (cyclonic) eddies in the subpolar (subtropical) gyres.

  2. A daily global mesoscale ocean eddy dataset from satellite altimetry.

    PubMed

    Faghmous, James H; Frenger, Ivy; Yao, Yuanshun; Warmka, Robert; Lindell, Aron; Kumar, Vipin

    2015-01-01

    Mesoscale ocean eddies are ubiquitous coherent rotating structures of water with radial scales on the order of 100 kilometers. Eddies play a key role in the transport and mixing of momentum and tracers across the World Ocean. We present a global daily mesoscale ocean eddy dataset that contains ~45 million mesoscale features and 3.3 million eddy trajectories that persist at least two days as identified in the AVISO dataset over a period of 1993-2014. This dataset, along with the open-source eddy identification software, extract eddies with any parameters (minimum size, lifetime, etc.), to study global eddy properties and dynamics, and to empirically estimate the impact eddies have on mass or heat transport. Furthermore, our open-source software may be used to identify mesoscale features in model simulations and compare them to observed features. Finally, this dataset can be used to study the interaction between mesoscale ocean eddies and other components of the Earth System.

  3. Algebraic and Combinatorial Properties of Common RNA Pseudoknot Classes with Applications

    PubMed Central

    Weinberg, Frank

    2012-01-01

    Abstract Predicting RNA structures with pseudoknots in general is an NP-complete problem. Accordingly, several authors have suggested subclasses that provide polynomial time prediction algorithms by allowing (respectively, disallowing) certain structural motives. In this article, we introduce a unifying algebraic view on most of these classes. That way it becomes possible to find linear time recognition algorithms that decide whether or not a given structure is member of a class (we offer these algorithms as a web service to the scientific community). Furthermore, by presenting a general translation scheme of our algebraic descriptions into multiple context-free grammars, and proving a new correspondence of multiple context-free grammars and generating functions, it becomes possible to derive the precise asymptotic size of all the classes, solving some open problems such as enumerating the Rivas & Eddy class of pseudoknots. PMID:23057823

  4. Applications of Algebraic Logic and Universal Algebra to Computer Science

    DTIC Science & Technology

    1989-06-21

    conference, with roughly equal representation from Mathematics and Computer Science . The conference consisted of eight invited lectures (60 minutes...each) and 26 contributed talks (20-40 minutes each). There was also a round-table discussion on the role of algebra and logic in computer science . Keywords

  5. An improved dynamic non-equilibrium wall-model for large eddy simulation

    NASA Astrophysics Data System (ADS)

    Park, George Ilhwan; Moin, Parviz

    2013-11-01

    A non-equilibrium wall-model based on unsteady 3D Reynolds-averaged Navier-Stokes (RANS) equations has been implemented in an unstructured mesh environment. The method is similar to that of the wall-model described by Wang and Moin [Phys. Fluids 14, 2043-2051, (2002)], but is supplemented by a new dynamic eddy viscosity/conductivity model that corrects the effect of the resolved Reynolds stress (resolved turbulent heat flux) on the skin friction (wall heat flux). This correction is crucial for accurate prediction of the skin friction and wall heat flux. Unlike earlier models, this eddy viscosity/conductivity model does not have a stress-matching procedure or a tunable free parameter, and it shows consistent performance over a wide range of Reynolds numbers. The wall-model is validated against canonical (attached) transitional and fully turbulent flows at moderate to very high Reynolds number: a turbulent channel flow at Reτ = 2000, an H-type transitional boundary layer up to Reθ = 3300, and a high Reynolds number boundary layer at Reθ = 31000. An application to the flow over NACA4412 airfoil is ongoing and hopefully will be presented. This work was supported by the Winston and Fu-Mei Stanford Graduate Fellowship, NASA Aeronautics Scholarship Program, and NASA under the Subsonic Fixed-Wing Program and the Boeing Company.

  6. A numerical simulation of the Catalina Eddy

    SciTech Connect

    Ueyoshi, Kyozo; Roads, J.O.; Alpert, J.

    1991-12-31

    A shallow cyclonic eddy termed the Catalina Eddy has occasionally been observed during summer in the bight of southern California. The Catalina Eddy occurs within {approximately}100 km from the coastal mountains with a depth typically extending up to the marine inversion level of several hundred meters above sea level and a diameter on the order of 100--200 km. The Catalina Eddy is produced by the interaction between the synoptic-scale northerly flow and the formidable topography along the southern California coast. A favorable synoptic situation that enhances the increased low-level climatological northerly flow along the central California coastline is the presence of the prominent east-west pressure gradient between the subtropical East Pacific high and the inland thermal low over California. Increased northerlies impinging on the San Rafael mountains north of Santa Barbara result in enhanced mesoscale lee troughing in the bight and establishment of a narrow ridge alongshore, leading to establishment of cyclonic vorticity in the bight. This paper describes numerical simulations and predictions of a Catalina Eddy event with a high-resolution multi-level limited area model. The model is initialized and forced at the lateral boundaries by the National Meteorological Center`s (NMC) 2.5{degree} {times} 2.5{degree} global objective analysis and also by NMC`s medium range forecast model (MRF) 1--10 day forecasts. In the authors previous effort to simulate mesoscale disturbances such as the Catalina Eddy the integrations were performed up to 1 model-day utilizing the NMC analysis as fixed lateral boundary conditions. In this paper they describe the results of continuous 5- to 7-day simulations of the Catalina Eddy event of 26--30 June 1988 by utilizing time-dependent lateral boundary conditions obtained from NMC`s global objective analysis as well as NMC`s MRF forecasts.

  7. A Balancing Act: Making Sense of Algebra

    ERIC Educational Resources Information Center

    Gavin, M. Katherine; Sheffield, Linda Jensen

    2015-01-01

    For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

  8. Algebra? A Gate! A Barrier! A Mystery!

    ERIC Educational Resources Information Center

    Mathematics Educatio Dialogues, 2000

    2000-01-01

    This issue of Mathematics Education Dialogues focuses on the nature and the role of algebra in the K-14 curriculum. Articles on this theme include: (1) "Algebra For All? Why?" (Nel Noddings); (2) "Algebra For All: It's a Matter of Equity, Expectations, and Effectiveness" (Dorothy S. Strong and Nell B. Cobb); (3) "Don't Delay: Build and Talk about…

  9. Unifying the Algebra for All Movement

    ERIC Educational Resources Information Center

    Eddy, Colleen M.; Quebec Fuentes, Sarah; Ward, Elizabeth K.; Parker, Yolanda A.; Cooper, Sandi; Jasper, William A.; Mallam, Winifred A.; Sorto, M. Alejandra; Wilkerson, Trena L.

    2015-01-01

    There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the "Algebra for All" movement. In light of this…

  10. UCSMP Algebra. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2007

    2007-01-01

    "University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…

  11. Constraint-Referenced Analytics of Algebra Learning

    ERIC Educational Resources Information Center

    Sutherland, Scot M.; White, Tobin F.

    2016-01-01

    The development of the constraint-referenced analytics tool for monitoring algebra learning activities presented here came from the desire to firstly, take a more quantitative look at student responses in collaborative algebra activities, and secondly, to situate those activities in a more traditional introductory algebra setting focusing on…

  12. Embedding Algebraic Thinking throughout the Mathematics Curriculum

    ERIC Educational Resources Information Center

    Vennebush, G. Patrick; Marquez, Elizabeth; Larsen, Joseph

    2005-01-01

    This article explores the algebra that can be uncovered in many middle-grades mathematics tasks that, on first inspection, do not appear to be algebraic. It shows connections to the other four Standards that occur in traditional algebra problems, and it offers strategies for modifying activities so that they can be used to foster algebraic…

  13. Teaching Strategies to Improve Algebra Learning

    ERIC Educational Resources Information Center

    Zbiek, Rose Mary; Larson, Matthew R.

    2015-01-01

    Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…

  14. Build an Early Foundation for Algebra Success

    ERIC Educational Resources Information Center

    Knuth, Eric; Stephens, Ana; Blanton, Maria; Gardiner, Angela

    2016-01-01

    Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…

  15. Teacher Actions to Facilitate Early Algebraic Reasoning

    ERIC Educational Resources Information Center

    Hunter, Jodie

    2015-01-01

    In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an…

  16. Difficulties in Initial Algebra Learning in Indonesia

    ERIC Educational Resources Information Center

    Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

    2014-01-01

    Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was…

  17. Cyclic homology for Hom-associative algebras

    NASA Astrophysics Data System (ADS)

    Hassanzadeh, Mohammad; Shapiro, Ilya; Sütlü, Serkan

    2015-12-01

    In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology and cohomology for this class of algebras generalizing these theories from the associative to the Hom-associative setting.

  18. Temporal Large-Eddy Simulation

    NASA Technical Reports Server (NTRS)

    Pruett, C. D.; Thomas, B. C.

    2004-01-01

    In 1999, Stolz and Adams unveiled a subgrid-scale model for LES based upon approximately inverting (defiltering) the spatial grid-filter operator and termed .the approximate deconvolution model (ADM). Subsequently, the utility and accuracy of the ADM were demonstrated in a posteriori analyses of flows as diverse as incompressible plane-channel flow and supersonic compression-ramp flow. In a prelude to the current paper, a parameterized temporal ADM (TADM) was developed and demonstrated in both a priori and a posteriori analyses for forced, viscous Burger's flow. The development of a time-filtered variant of the ADM was motivated-primarily by the desire for a unifying theoretical and computational context to encompass direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds averaged Navier-Stokes simulation (RANS). The resultant methodology was termed temporal LES (TLES). To permit exploration of the parameter space, however, previous analyses of the TADM were restricted to Burger's flow, and it has remained to demonstrate the TADM and TLES methodology for three-dimensional flow. For several reasons, plane-channel flow presents an ideal test case for the TADM. Among these reasons, channel flow is anisotropic, yet it lends itself to highly efficient and accurate spectral numerical methods. Moreover, channel-flow has been investigated extensively by DNS, and a highly accurate data base of Moser et.al. exists. In the present paper, we develop a fully anisotropic TADM model and demonstrate its utility in simulating incompressible plane-channel flow at nominal values of Re(sub tau) = 180 and Re(sub tau) = 590 by the TLES method. The TADM model is shown to perform nearly as well as the ADM at equivalent resolution, thereby establishing TLES as a viable alternative to LES. Moreover, as the current model is suboptimal is some respects, there is considerable room to improve TLES.

  19. Transformed eddy-PV flux and positive synoptic eddy feedback onto low-frequency flow

    NASA Astrophysics Data System (ADS)

    Ren, Hong-Li; Jin, Fei-Fei; Kug, Jong-Seong; Gao, Li

    2011-06-01

    Interaction between synoptic eddy and low-frequency flow (SELF) has been the subject of many studies. In this study, we further examine the interaction by introducing a transformed eddy-potential-vorticity (TEPV) flux that is obtained from eddy-potential-vorticity flux through a quasi-geostrophic potential-vorticity inversion. The main advantage of using the TEPV flux is that it combines the effects of the eddy-vorticity and heat fluxes into the net acceleration of the low-frequency flow in such a way that the TEPV flux tends to be analogous to the eddy-vorticity fluxes in the barotropic framework. We show that the anomalous TEPV fluxes are preferentially directed to the left-hand side of the low-frequency flow in all vertical levels throughout the troposphere for monthly flow anomalies and for climate modes such as the Arctic Oscillation (AO). Furthermore, this left-hand preference of the TEPV flux direction is a convenient three-dimensional indicator of the positive reinforcement of the low-frequency flow by net eddy-induced acceleration. By projecting the eddy-induced net accelerations onto the low-frequency flow anomalies, we estimate the eddy-induced growth rates for the low frequency flow anomalies. This positive eddy-induced growth rate is larger (smaller) in the lower (upper) troposphere. The stronger positive eddy feedback in the lower troposphere may play an important role in maintaining an equivalent barotropic structure of the low-frequency atmospheric flow by balancing some of the strong damping effect of surface friction.

  20. Transformed Eddy-PV Flux and Positive Synoptic Eddy Feedback onto Low-Frequency Flow

    NASA Astrophysics Data System (ADS)

    Ren, H.; Jin, F.; Kug, J.; Gao, L.

    2010-12-01

    Interaction between synoptic eddy and low-frequency flow (SELF) has been the subject of many studies. In this study, we further examine the interaction by introducing a transformed eddy-potential-vorticity (TEPV) flux that is obtained from eddy-potential-vorticity flux through a quasi-geostrophic potential-vorticity inversion. The main advantage of using the TEPV flux is that it combines the effects of the eddy-vorticity and heat fluxes into the net acceleration of the low-frequency flow in such a way that the TEPV flux tends to be analogous to the eddy-vorticity fluxes in the barotropic framework. We show that the anomalous TEPV fluxes are preferentially directed to the left-hand side of the low-frequency flow in all vertical levels throughout the troposphere for monthly flow anomalies and for climate modes such as the Arctic Oscillation (AO). Furthermore, this left-hand preference of the TEPV flux direction is a convenient three-dimensional indicator of the positive reinforcement of the low-frequency flow by net eddy-induced acceleration. By projecting the eddy-induced net accelerations onto the low-frequency flow anomalies, we estimate the eddy-induced growth rates for the low frequency flow anomalies. This positive eddy-induced growth rate is larger (smaller) in the lower (upper) troposphere. The stronger positive eddy feedback in the lower troposphere may play an important role in maintaining an equivalent barotropic structure of the low-frequency atmospheric flow by balancing some of the strong damping effect of surface friction.

  1. Underlying mechanism of numerical instability in large-eddy simulation of turbulent flows

    NASA Astrophysics Data System (ADS)

    Ida, Masato; Taniguchi, Nobuyuki

    2004-04-01

    This paper extends our recent theoretical work concerning the feasibility of stable and accurate computation of turbulence using a large eddy simulation [

    M. Ida and N. Taniguchi, Phys. Rev. E 68, 036705 (2003)
    ]. In our previous paper, it was shown, based on a simple assumption regarding the instantaneous streamwise velocity, that the application of the Gaussian filter to the incompressible Navier-Stokes equations can result in the appearance of a numerically unstable term that can be decomposed into positive and negative viscosities. That result raises the question as to whether an accurate solution can be achieved by a numerically stable subgrid-scale model. In the present paper, based on assumptions regarding the statistically averaged velocity, we present similar theoretical investigations to show that in several situations, the shears appearing in the statistically averaged velocity field numerically destabilize the fluctuation components because of the derivation of a numerically unstable term that represents negative diffusion in a fixed direction. This finding can explain the problematic numerical instability that has been encountered in large eddy simulations of wall-bounded flows. The present result suggests that this numerical problem is universal in large eddy simulations, and that if there is no failure in modeling, the resulting subgrid-scale model can still have unstable characteristics; that is, the known instability problems of several existing subgrid-scale models are not something that one may remove simply by an artificial technique, but must be taken seriously so as to treat them accurately.

  2. Quartz resonator fluid density and viscosity monitor

    DOEpatents

    Martin, Stephen J.; Wiczer, James J.; Cernosek, Richard W.; Frye, Gregory C.; Gebert, Charles T.; Casaus, Leonard; Mitchell, Mary A.

    1998-01-01

    A pair of thickness-shear mode resonators, one smooth and one with a textured surface, allows fluid density and viscosity to be independently resolved. A textured surface, either randomly rough or regularly patterned, leads to trapping of liquid at the device surface. The synchronous motion of this trapped liquid with the oscillating device surface allows the device to weigh the liquid; this leads to an additional response that depends on liquid density. This additional response enables a pair of devices, one smooth and one textured, to independently resolve liquid density and viscosity; the difference in responses determines the density while the smooth device determines the density-viscosity product, and thus, the pair determines both density and viscosity.

  3. Neoclassical Viscosities and Anomalous Flows in Stellarators

    NASA Astrophysics Data System (ADS)

    Ware, A. S.; Spong, D. A.; Breyfogle, M.; Marine, T.

    2009-05-01

    We present initial work to use neoclassical viscosities calculated with the PENTA code [1] in a transport model that includes Reynolds stress generation of flows [2]. The PENTA code uses a drift kinetic equation solver to calculate neoclassical viscosities and flows in general three-dimensional geometries over a range of collisionalities. The predicted neoclassical viscosities predicted by PENTA can be flux-surfaced average and applied in a 1-D transport model that includes anomalous flow generation. This combination of codes can be used to test the impact of stellarator geometry on anomalous flow generation. As a test case, we apply the code to modeling flows in the HSX stellarator. Due to variations in the neoclassical viscosities, HSX can have strong neoclassical flows in the core region. In turn, these neoclassical flows can provide a seed for anomalous flow generation. [1] D. A. Spong, Phys. Plasmas 12, 056114 (2005). [2] D. E. Newman, et al., Phys. Plasmas 5, 938 (1998).

  4. Sludge based Bacillus thuringiensis biopesticides: viscosity impacts.

    PubMed

    Brar, S K; Verma, M; Tyagi, R D; Valéro, J R; Surampalli, R Y

    2005-08-01

    Viscosity studies were performed on raw, pre-treated (sterilised and thermal alkaline hydrolysed or both types of treatment) and Bacillus thuringiensis (Bt) fermented sludges at different solids concentration (10-40 g/L) for production of biopesticides. Correlations were established among rheological parameter (viscosity), solids (total and dissolved) concentration and entomotoxicity (Tx) of Bt fermented sludges. Exponential and power laws were preferentially followed by hydrolysed fermented compared to raw fermented sludge. Soluble chemical oxygen demand variation corroborated with increase in dissolved solids concentration on pre-treatments, contributing to changes in viscosity. Moreover, Tx was higher for hydrolysed fermented sludge in comparison to raw fermented sludge owing to increased availability of nutrients and lower viscosity that improved oxygen transfer. The shake flask results were reproducible in fermenter. This study will have major impact on selecting fermentation, harvesting and formulation techniques of Bt fermented sludges for biopesticide production.

  5. Viscosity of Sheared Helical filament Suspensions

    NASA Astrophysics Data System (ADS)

    Sartucci, Matthew; Urbach, Jeff; Blair, Dan; Schwenger, Walter

    The viscosity of suspensions can be dramatically affected by high aspect ratio particles. Understanding these systems provides insight into key biological functions and can be manipulated for many technological applications. In this talk, the viscosity as a function of shear rate of suspensions of helical filaments is compared to that of suspensions of straight rod-like filaments. Our goal is to determine the impact of filament geometry on low volume fraction colloidal suspensions in order to identify strategies for altering viscosity with minimal volume fraction. In this research, the detached flagella of the bacteria Salmonella Typhimurium are used as a model system of helical filaments and compared to mutated straight flagella of the Salmonella. We compare rheological measurements of the suspension viscosity in response to shear flow and use a combination of the rheology and fluorescence microscopy to identify the microstructural changes responsible for the observed rheological response.

  6. Large-eddy simulation of stable atmospheric boundary layers to develop better turbulence closures for climate and weather models

    NASA Astrophysics Data System (ADS)

    Bou-Zeid, Elie; Huang, Jing; Golaz, Jean-Christophe

    2011-11-01

    A disconnect remains between our improved physical understanding of boundary layers stabilized by buoyancy and how we parameterize them in coarse atmospheric models. Most operational climate models require excessive turbulence mixing in such conditions to prevent decoupling of the atmospheric component from the land component, but the performance of such a model is unlikely to be satisfactory under weakly and moderately stable conditions. Using Large-eddy simulation, we revisit some of the basic challenges in parameterizing stable atmospheric boundary layers: eddy-viscosity closure is found to be more reliable due to an improved alignment of vertical Reynolds stresses and mean strains under stable conditions, but the dependence of the magnitude of the eddy viscosity on stability is not well represented by several models tested here. Thus, we propose a new closure that reproduces the different stability regimes better. Subsequently, tests of this model in the GFDL's single-column model (SCM) are found to yield good agreement with LES results in idealized steady-stability cases, as well as in cases with gradual and sharp changes of stability with time.

  7. Automated eddy current analysis of materials

    NASA Technical Reports Server (NTRS)

    Workman, Gary L.

    1990-01-01

    This research effort focused on the use of eddy current techniques for characterizing flaws in graphite-based filament-wound cylindrical structures. A major emphasis was on incorporating artificial intelligence techniques into the signal analysis portion of the inspection process. Developing an eddy current scanning system using a commercial robot for inspecting graphite structures (and others) has been a goal in the overall concept and is essential for the final implementation for expert system interpretation. Manual scans, as performed in the preliminary work here, do not provide sufficiently reproducible eddy current signatures to be easily built into a real time expert system. The expert systems approach to eddy current signal analysis requires that a suitable knowledge base exist in which correct decisions as to the nature of the flaw can be performed. In eddy current or any other expert systems used to analyze signals in real time in a production environment, it is important to simplify computational procedures as much as possible. For that reason, we have chosen to use the measured resistance and reactance values for the preliminary aspects of this work. A simple computation, such as phase angle of the signal, is certainly within the real time processing capability of the computer system. In the work described here, there is a balance between physical measurements and finite element calculations of those measurements. The goal is to evolve into the most cost effective procedures for maintaining the correctness of the knowledge base.

  8. The direct viscosity enhancement of carbon dioxide

    SciTech Connect

    Iezzi, A.; Enick, R.; Brady, J. . Dept. of Chemistry)

    1988-01-01

    A high pressure viscometer has been constructed for use over a wide range of temperatures and pressures, including near-critical and supercritical conditions. An aluminum cylinder falls through a tube containing a stationary column of fluid, enabling viscosities to be determined from terminal velocity measurements. Preliminary results are presented on the search for an additive which can enhance the viscosity of carbon dioxide when present in low (less than 1%) concentrations.

  9. Modified Chaplygin gas cosmology with bulk viscosity

    NASA Astrophysics Data System (ADS)

    Benaoum, H. B.

    2014-09-01

    In this paper, we investigate the viscous modified Chaplygin gas cosmological model. Solutions for different values of the viscosity parameter are obtained using both analytical and numerical methods. We have calculated the deceleration and defined newly statefinder {r, s} pair in D dimensions. It is shown that when D = 4, the usual statefinder parameters are recovered. Furthermore, we apply the statefinder diagnostic to the MCG model with and without viscosity in D dimensions and explore these parameters graphically.

  10. Carry Groups: Abstract Algebra Projects

    ERIC Educational Resources Information Center

    Miller, Cheryl Chute; Madore, Blair F.

    2004-01-01

    Carry Groups are a wonderful collection of groups to introduce in an undergraduate Abstract Algebra course. These groups are straightforward to define but have interesting structures for students to discover. We describe these groups and give examples of in-class group projects that were developed and used by Miller.

  11. Algebra, Home Mortgages, and Recessions

    ERIC Educational Resources Information Center

    Mariner, Jean A. Miller; Miller, Richard A.

    2009-01-01

    The current financial crisis and recession in the United States present an opportunity to discuss relevant applications of some topics in typical first-and second-year algebra and precalculus courses. Real-world applications of percent change, exponential functions, and sums of finite geometric sequences can help students understand the problems…

  12. Exploring Algebraic Misconceptions with Technology

    ERIC Educational Resources Information Center

    Sakow, Matthew; Karaman, Ruveyda

    2015-01-01

    Many students struggle with algebra, from simplifying expressions to solving systems of equations. Students also have misconceptions about the meaning of variables. In response to the question "Can x + y + z ever equal x + p + z?" during a student interview, the student claimed, "Never . . . because p has to have a different value…

  13. Easing Students' Transition to Algebra

    ERIC Educational Resources Information Center

    Baroudi, Ziad

    2006-01-01

    Traditionally, students learn arithmetic throughout their primary schooling, and this is seen as the ideal preparation for the learning of algebra in the junior secondary school. The four operations are taught and rehearsed in the early years and from this, it is assumed, "children will induce the fundamental structure of arithmetic" (Warren &…

  14. Algebra for All. Research Brief

    ERIC Educational Resources Information Center

    Bleyaert, Barbara

    2009-01-01

    The call for "algebra for all" is not a recent phenomenon. Concerns about the inadequacy of math (and science) preparation in America's high schools have been a steady drumbeat since the 1957 launch of Sputnik; a call for raising standards and the number of math (and science) courses required for graduation has been a part of countless…

  15. Algebraic methods in system theory

    NASA Technical Reports Server (NTRS)

    Brockett, R. W.; Willems, J. C.; Willsky, A. S.

    1975-01-01

    Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.

  16. Inequalities, Assessment and Computer Algebra

    ERIC Educational Resources Information Center

    Sangwin, Christopher J.

    2015-01-01

    The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…

  17. Adventures in Flipping College Algebra

    ERIC Educational Resources Information Center

    Van Sickle, Jenna

    2015-01-01

    This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…

  18. Elementary Algebra Connections to Precalculus

    ERIC Educational Resources Information Center

    Lopez-Boada, Roberto; Daire, Sandra Arguelles

    2013-01-01

    This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…

  19. Celestial mechanics with geometric algebra

    NASA Technical Reports Server (NTRS)

    Hestenes, D.

    1983-01-01

    Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.

  20. Math Sense: Algebra and Geometry.

    ERIC Educational Resources Information Center

    Howett, Jerry

    This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…

  1. Weaving Geometry and Algebra Together

    ERIC Educational Resources Information Center

    Cetner, Michelle

    2015-01-01

    When thinking about student reasoning and sense making, teachers must consider the nature of tasks given to students along with how to plan to use the tasks in the classroom. Students should be presented with tasks in a way that encourages them to draw connections between algebraic and geometric concepts. This article focuses on the idea that it…

  2. Algebraic Activities Aid Discovery Lessons

    ERIC Educational Resources Information Center

    Wallace-Gomez, Patricia

    2013-01-01

    After a unit on the rules for positive and negative numbers and the order of operations for evaluating algebraic expressions, many students believe that they understand these principles well enough, but they really do not. They clearly need more practice, but not more of the same kind of drill. Wallace-Gomez provides three graphing activities that…

  3. A local dynamic model for large eddy simulation

    NASA Technical Reports Server (NTRS)

    Ghosal, Sandip; Lund, Thomas S.; Moin, Parviz

    1993-01-01

    The dynamic model is a method for computing the coefficient C in Smagorinsky's model for the subgrid-scale stress tensor as a function of position from the information already contained in the resolved velocity field rather than treating it as an adjustable parameter. A variational formulation of the dynamic model is described that removes the inconsistency associated with taking C out of the filtering operation. This model, however, is still unstable due to the negative eddy-viscosity. Next, three models are presented that are mathematically consistent as well as numerically stable. The first two are applicable to homogeneous flows and flows with at least one homogeneous direction, respectively, and are, in fact, a rigorous derivation of the ad hoc expressions used by previous authors. The third model in this set can be applied to arbitrary flows, and it is stable because the C it predicts is always positive. Finally, a model involving the subgrid-scale kinetic energy is presented which attempts to model backscatter. This last model has some desirable theoretical features. However, even though it gives results in LES that are qualitatively correct, it is outperformed by the simpler constrained variational models. It is suggested that one of the constrained variational models should be used for actual LES while theoretical investigation of the kinetic energy approach should be continued in an effort to improve its predictive power and to understand more about backscatter.

  4. Teachers' Understanding of Algebraic Generalization

    NASA Astrophysics Data System (ADS)

    Hawthorne, Casey Wayne

    Generalization has been identified as a cornerstone of algebraic thinking (e.g., Lee, 1996; Sfard, 1995) and is at the center of a rich conceptualization of K-8 algebra (Kaput, 2008; Smith, 2003). Moreover, mathematics teachers are being encouraged to use figural-pattern generalizing tasks as a basis of student-centered instruction, whereby teachers respond to and build upon the ideas that arise from students' explorations of these activities. Although more and more teachers are engaging their students in such generalizing tasks, little is known about teachers' understanding of generalization and their understanding of students' mathematical thinking in this domain. In this work, I addressed this gap, exploring the understanding of algebraic generalization of 4 exemplary 8th-grade teachers from multiple perspectives. A significant feature of this investigation is an examination of teachers' understanding of the generalization process, including the use of algebraic symbols. The research consisted of two phases. Phase I was an examination of the teachers' understandings of the underlying quantities and quantitative relationships represented by algebraic notation. In Phase II, I observed the instruction of 2 of these teachers. Using the lens of professional noticing of students' mathematical thinking, I explored the teachers' enacted knowledge of algebraic generalization, characterizing how it supported them to effectively respond to the needs and queries of their students. Results indicated that teachers predominantly see these figural patterns as enrichment activities, disconnected from course content. Furthermore, in my analysis, I identified conceptual difficulties teachers experienced when solving generalization tasks, in particular, connecting multiple symbolic representations with the quantities in the figures. Moreover, while the teachers strived to overcome the challenges of connecting different representations, they invoked both productive and unproductive

  5. Effects of surface roughness on shear viscosity

    NASA Astrophysics Data System (ADS)

    Papanikolaou, Michail; Frank, Michael; Drikakis, Dimitris

    2017-03-01

    This paper investigates the effect of surface roughness on fluid viscosity using molecular dynamics simulations. The three-dimensional model consists of liquid argon flowing between two solid walls whose surface roughness was modeled using fractal theory. In tandem with previously published experimental work, our results show that, while the viscosity in smooth channels remains constant across the channel width, in the presence of surface roughness it increases close to the walls. The increase of the boundary viscosity is further accentuated by an increase in the depth of surface roughness. We attribute this behavior to the increased momentum transfer at the boundary, a result of the irregular distribution of fluid particles near rough surfaces. Furthermore, although the viscosity in smooth channels has previously been shown to be independent of the strength of the solid-liquid interaction, here we show that in the presence of surface roughness, the boundary viscosity increases with the solid's wettability. The paper concludes with an analytical description of the viscosity as a function of the distance from the channel walls, the walls' surface roughness, and the solid's wetting properties. The relation can potentially be used to adjust the fluid dynamics equations for a more accurate description of microfluidic systems.

  6. Viscosity effects in wind wave generation

    NASA Astrophysics Data System (ADS)

    Paquier, A.; Moisy, F.; Rabaud, M.

    2016-12-01

    We investigate experimentally the influence of the liquid viscosity on the problem of the generation of waves by a turbulent wind at the surface of a liquid, extending the results of Paquier et al. [A. Paquier et al., Phys. Fluids 27, 122103 (2015), 10.1063/1.4936395] over nearly three decades of viscosity. The surface deformations are measured with micrometer accuracy using the free-surface synthetic schlieren method. We recover the two regimes of surface deformations previously identified: the wrinkle regime at small wind velocity, resulting from the viscous imprint on the liquid surface of the turbulent fluctuations in the boundary layer, and the regular wave regime at large wind velocity. Below the wave threshold, we find that the characteristic amplitude of the wrinkles scales as ν-1 /2u*3 /2 over nearly the whole range of viscosities, whereas their size is essentially unchanged. We propose a simple model for this scaling, which compares well with the data. We show that the critical friction velocity u* for the onset of regular waves slowly increases with viscosity as ν0.2. Whereas the transition between wrinkles and waves is smooth at low viscosity, including for water, it becomes rather abrupt at high viscosity. A third wave regime is found at ν >(100 -200 ) ×10-6m2s-1 , characterized by a slow, nearly periodic emission of large-amplitude isolated fluid bumps.

  7. Viscosity of mafic magmas at high pressures

    NASA Astrophysics Data System (ADS)

    Cochain, B.; Sanloup, C.; Leroy, C.; Kono, Y.

    2017-01-01

    While it is accepted that silica-rich melts behave anomalously with a decrease of their viscosity at increased pressures (P), the viscosity of silica-poor melts is much less constrained. However, modeling of mantle melts dynamics throughout Earth's history, including the magma ocean era, requires precise knowledge of the viscous properties of silica-poor magmas. We extend here our previous measurements on fayalite melt to natural end-members pyroxenite melts (MgSiO3 and CaSiO3) using in situ X-ray radiography up to 8 GPa. For all compositions, viscosity decreases with P, rapidly below 5 GPa and slowly above. The magnitude of the viscosity decrease is larger for pyroxene melts than for fayalite melt and larger for the Ca end-member within pyroxene melts. The anomalous viscosity decrease appears to be a universal behavior for magmas up to 13 GPa, while the P dependence of viscosity beyond this remains to be measured. These results imply that mantle melts are very pervasive at depth.

  8. Explicit field realizations of W algebras

    NASA Astrophysics Data System (ADS)

    Wei, Shao-Wen; Liu, Yu-Xiao; Zhang, Li-Jie; Ren, Ji-Rong

    2009-06-01

    The fact that certain nonlinear W2,s algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize W2,s algebras from linear W1,2,s algebras. In this paper, we first construct the explicit field realizations of linear W1,2,s algebras with double scalar and double spinor, respectively. Then, after a change of basis, the realizations of W2,s algebras are presented. The results show that all these realizations are Romans-type realizations.

  9. Array algebra estimation in signal processing

    NASA Astrophysics Data System (ADS)

    Rauhala, U. A.

    A general theory of linear estimators called array algebra estimation is interpreted in some terms of multidimensional digital signal processing, mathematical statistics, and numerical analysis. The theory has emerged during the past decade from the new field of a unified vector, matrix and tensor algebra called array algebra. The broad concepts of array algebra and its estimation theory cover several modern computerized sciences and technologies converting their established notations and terminology into one common language. Some concepts of digital signal processing are adopted into this language after a review of the principles of array algebra estimation and its predecessors in mathematical surveying sciences.

  10. On special classes of n-algebras

    NASA Astrophysics Data System (ADS)

    Vainerman, L.; Kerner, R.

    1996-05-01

    We define n-algebras as linear spaces on which the internal composition law involves n elements: m:V⊗n■V. It is known that such algebraic structures are interesting for their applications to problems of modern mathematical physics. Using the notion of a commutant of two subalgebras of an n-algebra, we distinguish certain classes of n-algebras with reasonable properties: semisimple, Abelian, nilpotent, solvable. We also consider a few examples of n-algebras of different types, and show their properties.

  11. Eddy analysis in the Eastern China Sea using altimetry data

    NASA Astrophysics Data System (ADS)

    Qin, Dandi; Wang, Jianhong; Liu, Yu; Dong, Changming

    2015-12-01

    Statistical characteristics of mesoscale eddies in the Eastern China Sea (ECS) are analyzed using altimetry sea surface height anomaly (SSHA) data from 1993 to 2010. A velocity geometry-based automated eddy detection scheme is employed to detect eddies from the SSHA data to generate an eddy data set. About 1,096 eddies (one lifetime of eddies is counted as one eddy) with a lifetime longer than or equal to 4 weeks are identified in this region. The average lifetime and radius of eddies are 7 weeks and 55 km, respectively, and there is no significant difference between cyclonic eddies (CEs) and anticyclonic eddies (AEs) in this respect. Eddies' lifetimes are generally longer in deep water than in shallow water. Most eddies propagate northeastward along the Kuroshio (advected by the Kuroshio), with more CEs generated on its western side and AEs on its eastern side. The variation of the Kuroshio transport is one of the major mechanisms for eddy genesis, however the generation of AEs on the eastern side of the Kuroshio (to the open ocean) is also subject to other factors, such as the wind stress curl due to the presence of the Ryukyu Islands and the disturbance from the open ocean.

  12. Solitonlike solutions in loop current eddies

    NASA Technical Reports Server (NTRS)

    Nakamoto, Shoichiro

    1989-01-01

    The application of the nonlinear quasi-geostrophic equations to an isolated eddy in the western continental slope region in the Gulf of Mexico is examined for a two-layer ocean model with bottom topography. In the linear limit, solutions are topographic nondispersive waves. Form-preserving solutions, or solitons, have been found. The solution is shown to be a limiting form for a nonlinear dispersive system propagating northward along the topographic waveguide in the western continental slope region in the Gulf of Mexico. Using satellite-tracked drifter data, a linear relationship is found between the amplitude of the deduced stream function of the eddy and its observed translational velocity over the continental slope, which supports the hypothesis that some mesoscale eddies interacting with the continental slope behave as solitons.

  13. Deep Eddies in the Gulf of Mexico

    NASA Astrophysics Data System (ADS)

    Furey, H. H.; Bower, A. S.; Perez-Brunius, P.; Hamilton, P.

    2014-12-01

    A major Lagrangian program is currently underway to map the deep (1500-2500 m) circulation of the entire Gulf of Mexico. Beginning in 2011, more than 120 acoustically tracked RAFOS floats have been released in the eastern, central and western Gulf, many in pairs and triplets. Most floats are programmed to drift for two years, obtaining position fixes and temperature/pressure measurements three times daily. More than 80 floats have completed their missions, and results from the trajectories will be described with a focus on mesoscale eddying behavior. In particular, the first-ever observations of deep energetic anticyclonic eddies (possibly lenses) forming at and separating from a northeastward-flowing boundary current west of Campeche Bank will be discussed. The existence of these eddies has major implications for exchange between the continental slope and interior Gulf. The project is being supported by the U.S. Bureau of Ocean Energy Management (BOEM).

  14. Turbulent fluxes by "Conditional Eddy Sampling"

    NASA Astrophysics Data System (ADS)

    Siebicke, Lukas

    2015-04-01

    Turbulent flux measurements are key to understanding ecosystem scale energy and matter exchange, including atmospheric trace gases. While the eddy covariance approach has evolved as an invaluable tool to quantify fluxes of e.g. CO2 and H2O continuously, it is limited to very few atmospheric constituents for which sufficiently fast analyzers exist. High instrument cost, lack of field-readiness or high power consumption (e.g. many recent laser-based systems requiring strong vacuum) further impair application to other tracers. Alternative micrometeorological approaches such as conditional sampling might overcome major limitations. Although the idea of eddy accumulation has already been proposed by Desjardin in 1972 (Desjardin, 1977), at the time it could not be realized for trace gases. Major simplifications by Businger and Oncley (1990) lead to it's widespread application as 'Relaxed Eddy Accumulation' (REA). However, those simplifications (flux gradient similarity with constant flow rate sampling irrespective of vertical wind velocity and introduction of a deadband around zero vertical wind velocity) have degraded eddy accumulation to an indirect method, introducing issues of scalar similarity and often lack of suitable scalar flux proxies. Here we present a real implementation of a true eddy accumulation system according to the original concept. Key to our approach, which we call 'Conditional Eddy Sampling' (CES), is the mathematical formulation of conditional sampling in it's true form of a direct eddy flux measurement paired with a performant real implementation. Dedicated hardware controlled by near-real-time software allows full signal recovery at 10 or 20 Hz, very fast valve switching, instant vertical wind velocity proportional flow rate control, virtually no deadband and adaptive power management. Demonstrated system performance often exceeds requirements for flux measurements by orders of magnitude. The system's exceptionally low power consumption is ideal

  15. Recursion and feedback in image algebra

    NASA Astrophysics Data System (ADS)

    Ritter, Gerhard X.; Davidson, Jennifer L.

    1991-04-01

    Recursion and feedback are two important processes in image processing. Image algebra, a unified algebraic structure developed for use in image processing and image analysis, provides a common mathematical environment for expressing image processing transforms. It is only recently that image algebra has been extended to include recursive operations [1]. Recently image algebra was shown to incorporate neural nets [2], including a new type of neural net, the morphological neural net [3]. This paper presents the relationship of the recursive image algebra to the field of fractions of the ring of matrices, and gives the two dimensional moving average filter as an example. Also, the popular multilayer perceptron with back propagation and a morphology neural network with learning rule are presented in image algebra notation. These examples show that image algebra can express these important feedback concepts in a succinct way.

  16. Deformed Kac Moody and Virasoro algebras

    NASA Astrophysics Data System (ADS)

    Balachandran, A. P.; Queiroz, A. R.; Marques, A. M.; Teotonio-Sobrinho, P.

    2007-07-01

    Whenever the group {\\bb R}^n acts on an algebra {\\cal A} , there is a method to twist \\cal A to a new algebra {\\cal A}_\\theta which depends on an antisymmetric matrix θ (θμν = -θνμ = constant). The Groenewold-Moyal plane {\\cal A}_\\theta({\\bb R}^{d+1}) is an example of such a twisted algebra. We give a general construction to realize this twist in terms of {\\cal A} itself and certain 'charge' operators Qμ. For {\\cal A}_\\theta({\\bb R}^{d+1}), Q_\\mu are translation generators. This construction is then applied to twist the oscillators realizing the Kac-Moody (KM) algebra as well as the KM currents. They give different deformations of the KM algebra. From one of the deformations of the KM algebra, we construct, via the Sugawara construction, the Virasoro algebra. These deformations have an implication for statistics as well.

  17. A spin-orbit constraint on the viscosity of a Mercurian liquid core

    NASA Technical Reports Server (NTRS)

    Peale, S. J.; Boss, A. P.

    1977-01-01

    The escape of Mercury from the stable spin-orbit resonance in which the spin angular velocity is twice the orbital mean motion (2n) requires that the kinematic viscosity of a molten core with a laminar boundary layer be comparable to that of water (0.01 sq cm/s) and the tidal Q be less than about 100. If the boundary layer is turbulent, escape from the resonance is only consistent with a liquid core of low viscosity if the critical Reynolds number for the onset of turbulence is above about 500, the moment difference (B - A)/C is below about 0.00001, and the tidal dissipation factor Q is less than about 40. These conclusions depend on the assumptions that Mercury's obliquity was near 0 deg at the time of resonance passage, that the liquid core was not stably stratified at the time at which Mercury passed through the resonance, that a turbulent boundary layer can be characterized by a turbulent or eddy viscosity coefficient, and that the most important coupling between core and mantle is a viscous coupling at a smooth spherical boundary.

  18. Eddy parameterization challenge suite I: Eady spindown

    NASA Astrophysics Data System (ADS)

    Bachman, S.; Fox-Kemper, B.

    2013-04-01

    The first set of results in a suite of eddy-resolving Boussinesq, hydrostatic simulations is presented. Each set member consists of an initially linear stratification and shear as in the Eady problem, but this profile occupies only a limited region of a channel and is allowed to spin-down via baroclinic instability. The diagnostic focus is on the spatial structure and scaling of the eddy transport tensor, which is the array of coefficients in a linear flux-gradient relationship. The advective (antisymmetric) and diffusive (symmetric) components of the tensor are diagnosed using passive tracers, and the resulting diagnosed tensor reproduces the horizontal transport of the active tracer (buoyancy) to within ± 7% and the vertical transport to within ± 12%. The derived scalings are shown to be close in form to the standard Gent-McWilliams (antisymmetric) and Redi diffusivity (symmetric) tensors with a magnitude that varies in space (concentrated in the horizontal and vertical near the center of the frontal shear) and time as the eddies energize. The Gent-McWilliams eddy coefficient is equal to the Redi isopycnal diffusivity to within ± 6%, even as these coefficients vary with depth. The scaling for the magnitude of simulation parameters is determined empirically to within ± 28%. To achieve this accuracy, the eddy velocities are diagnosed directly and used in the tensor scalings, rather than assuming a correlation between eddy velocity and the mean flow velocity where ± 97% is the best accuracy achievable. Plans for the next set of models in the challenge suite are described.

  19. Tracking the PRIME eddy using satellite altimetry

    NASA Astrophysics Data System (ADS)

    Wade, Ian P.; Heywood, Karen J.

    The PRIME cruise to the North Atlantic during June/July 1996 surveyed and sampled an extremely vigorous and deep-reaching eddy with a significant barotropic component. Although it exhibited anticyclonic flow and featured a warm core at depth, it had been capped at some point during its lifetime, so appeared as a cold feature in the upper 500 m. Satellite-derived sea-surface temperatures (SST) showed it to have moved little during the few weeks prior to the cruise. In this paper we discuss the origin of the PRIME eddy including where and when it is likely to have formed. Consistently large amounts of cloud cover restrict the use of SST imagery to track such features. Altimetry provides a better method to trace this eddy back in time and space since microwave radiation is not significantly affected by cloud cover. Sea-level anomaly (SLA) data from the TOPEX/POSEIDON and European Remote Sensing (ERS) satellites were used. Results show that the eddy remained almost stationary in the Iceland Basin since first being detected in late 1995 and that it almost certainly formed locally, probably as a result of an instability in the current flow around the northwest of the Hatton Bank. Comparisons between satellite SLAs and hydrographic estimates of sea-surface elevation confirm that the eddy had a substantial barotropic flow. Both the altimeter data and the sea-surface height derived from the acoustic Doppler current profiler agree that the PRIME eddy had a sea-surface elevation of about 20 cm and that its diameter was about 120 km.

  20. Large Eddy Simulation ... Where Do We Stand? International Workshop Held in St. Petersburg Beach, Florida on 19-21 December 1990.

    DTIC Science & Technology

    1990-01-01

    Contribution of Two-Point Closure to Large-Eddy Simulation. 3. A. J. Chorin Accesion For Application of Statistical Mechanics to Turbulence Modeling ...and DNS of Reacting Homogeneous Turbulence , 3. C. E. Leith Stochastic Backscatter in a Subgrid-Scale Model : 3D Compressible Flows. 4. G. Erlebacher and... models and non- linear viscosities. REFERENCES Bass, J., 1949: Sur les bases mathdmatiques de la thdorie de la turbulence d’Heisenberg. C. R. Acad. Sci

  1. Development of magnetic eddy current testing techniques

    NASA Astrophysics Data System (ADS)

    Tada, Toyokazu; Suetsugu, Hidehiko

    2017-02-01

    IRIS (Internal Rotary Inspection System) has become a major maintenance inspection technique for the heat exchanger and reactor tubes. It is known that IRIS has a high precision of evaluation thickness, however there are a few disadvantages, such as slow inspection speed. Therefore, we have developed a magnetic eddy current flaw testing technique which combines a magnetic array forming a strong magnetic field, 4 coil structures for controlling the generation area of the eddy currents, and a desorption yoke structure to control the magnetizing force. In this presentation, details of this technique and practical application will be elaborated.

  2. Parameterisation of Eddies in Coarse Resolution Models

    DTIC Science & Technology

    2001-01-19

    quasi-Stokes ve - varying, e.g. on seasonal scales . (Should seasonal varia- locities in parameterizations. J. Phys. Oceanogr., 31, tion be included within...length scale in Fig. 1 is proportional to eddy amplitude. For linear theory, it appears as a delta- 7 function boundary layer. When the eddies have...finite amplitude, the vertical length scale over which the two -1.5 densities differ noticeably is of order z/ ’ a IVH /-2 - 0 1 2 which is the typical

  3. Eddy Correlation Flux Measurement System (ECOR) Handbook

    SciTech Connect

    Cook, DR

    2011-01-31

    The eddy correlation (ECOR) flux measurement system provides in situ, half-hour measurements of the surface turbulent fluxes of momentum, sensible heat, latent heat, and carbon dioxide (CO2) (and methane at one Southern Great Plains extended facility (SGP EF) and the North Slope of Alaska Central Facility (NSA CF). The fluxes are obtained with the eddy covariance technique, which involves correlation of the vertical wind component with the horizontal wind component, the air temperature, the water vapor density, and the CO2 concentration.

  4. Visualization and analysis of eddies in a global ocean simulation

    SciTech Connect

    Williams, Sean J; Hecht, Matthew W; Petersen, Mark; Strelitz, Richard; Maltrud, Mathew E; Ahrens, James P; Hlawitschka, Mario; Hamann, Bernd

    2010-10-15

    Eddies at a scale of approximately one hundred kilometers have been shown to be surprisingly important to understanding large-scale transport of heat and nutrients in the ocean. Due to difficulties in observing the ocean directly, the behavior of eddies below the surface is not very well understood. To fill this gap, we employ a high-resolution simulation of the ocean developed at Los Alamos National Laboratory. Using large-scale parallel visualization and analysis tools, we produce three-dimensional images of ocean eddies, and also generate a census of eddy distribution and shape averaged over multiple simulation time steps, resulting in a world map of eddy characteristics. As expected from observational studies, our census reveals a higher concentration of eddies at the mid-latitudes than the equator. Our analysis further shows that mid-latitude eddies are thicker, within a range of 1000-2000m, while equatorial eddies are less than 100m thick.

  5. Viscosity of Xenon Examined in Microgravity

    NASA Technical Reports Server (NTRS)

    Zimmerli, Gregory A.; Berg, Robert F.; Moldover, Michael R.

    1999-01-01

    Why does water flow faster than honey? The short answer, that honey has a greater viscosity, merely rephrases the question. The fundamental answer is that viscosity originates in the interactions between a fluid s molecules. These interactions are so complicated that, except for low-density gases, the viscosity of a fluid cannot be accurately predicted. Progress in understanding viscosity has been made by studying moderately dense gases and, more recently, fluids near the critical point. Modern theories predict a universal behavior for all pure fluids near the liquid-vapor critical point, and they relate the increase in viscosity to spontaneous fluctuations in density near this point. The Critical Viscosity of Xenon (CVX) experiment tested these theories with unprecedented precision when it flew aboard the Space Shuttle Discovery (STS-85) in August 1997. Near the critical point, xenon is a billion times more compressible than water, yet it has about the same density. Because the fluid is so "soft," it collapses under its own weight when exposed to the force of Earth s gravity - much like a very soft spring. Because the CVX experiment is conducted in microgravity, it achieves a very uniform fluid density even very close to the critical point. At the heart of the CVX experiment is a novel viscometer built around a small nickel screen. An oscillating electric field forces the screen to oscillate between pairs of electrodes. Viscosity, which dampens the oscillations, can be calculated by measuring the screen motion and the force applied to the screen. So that the fluid s delicate state near the critical point will not be disrupted, the screen oscillations are set to be both slow and small.

  6. Estimating the Kinematic Viscosity of Petroleum Fractions

    NASA Astrophysics Data System (ADS)

    AlMulla, Hessa A.; Albahri, Tareq A.

    2017-04-01

    Kinematic viscosity correlation has been developed for liquid petroleum fractions at 37.78°C and 98.89°C (100 and 210°F) standard temperatures using a large variety of experimental data. The only required inputs are the specific gravity and the average boiling point temperature. The accuracy of the correlation was compared with several other correlations available in the literature. The proposed correlations proved to be more accurate in predicting the viscosity at 37.78°C and 98.89°C with average absolute deviations of 0.39 and 0.72 mm2/s, respectively. Another objective was to develop a relation for the variation of viscosity with temperature to predict the viscosity of petroleum fraction at a certain temperature from the knowledge of the viscosity for the same liquid at two other temperatures. The newly developed correlation represents a wide array of temperatures from 20°C to 150°C and viscosities from 0.14 mm2/s to 343.64 mm2/s. The results have been validated with experimental data consisting of 9558 data points, yielding an overall deviation of 0.248 mm2/s and R2 of 0.998. In addition, new formulas were developed to interconvert the viscosity of petroleum fractions from one unit of measure to another based on finding the best fit for a set of experimental data from the literature with R2 as high as 1.0 for many cases. Detailed analysis showed good agreement between the predicted values and the experimental data.

  7. Sub-grid scale modeling for large eddy simulations in analysis of shock-turbulence interactions

    NASA Astrophysics Data System (ADS)

    Buckingham, A. C.; Grun, J.

    1992-12-01

    We continue to study the influence of dynamic shock wave interactions on turbulence. The interactions may significantly increase turbulent energy and Reynolds stress. Strong support for tensor amplification is supplied by the sharp, transiently distorted strain field in the immediate neighborhood of the shock. Beyond this, there develops a gradual decay to a new, more modestly amplified state relative to the pre-shocked level. Practical interest is centered on the significantly altered, albeit shock localized, post-shock turbulent kinetic energy, eddy transport, eddy component mixing and diffusion, wall shear, and heat transfer. In the shock interaction and post-shock region, compressible two dimensional large eddy simulations (LES) are applied. A compressibility modified Smagorinsky model is adapted to represent the non-resolved sub-grid scales. Favre mass-weighted average space and time discretized compressible Navier-Stokes equations are used to represent the explicitly resolved grid scale motions. Predicted amplification levels, modal energy partition, shock translational to turbulence kinetic energy transfer, and viscoelastic response of turbulence to shock interaction are examined in comparison with available experimental evidence. A two-band dynamic eddy viscosity model representing the unresolved subgrid scale field is a possible replacement for the Smagorinsky model. Improvement is sought for predictions in the near wall region, under the influence of stochastic subgrid scale backscatter, and in the neighborhood of the shock. Wall-bounded supersonic compression comer flow experiments and hypersonic cylindrical shock wave turbulence interaction experiments are used as trial cases for test and comparison of the two classes of subgrid scale models.

  8. Algebraic complexities and algebraic curves over finite fields

    PubMed Central

    Chudnovsky, D. V.; Chudnovsky, G. V.

    1987-01-01

    We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields. For infinite fields minimal complexities are known [Winograd, S. (1977) Math. Syst. Theory 10, 169-180]. We prove lower and upper bounds on minimal complexities over finite fields, both linear in the number of inputs, using the relationship with linear coding theory and algebraic curves over finite fields. PMID:16593816

  9. Effective viscosity of dilute bacterial suspensions

    NASA Astrophysics Data System (ADS)

    Haines, Brian M.

    This dissertation explores the bulk (volume averaged) properties of suspensions of microswimmers in a fluid. A microswimmer is a microscopic object that propels itself through a fluid. A common example of a microswimmer is a bacterium, such as Bacillus subtilis. Our particular interest is the bulk rheological properties of suspensions of bacteria -- that is, studying how such a suspension deforms under the application of an external force. In the simplest case, the rheology of a fluid can be described by a scalar effective viscosity. The goal of this dissertation is to find explicit formulae for the effective viscosity in terms of known geometric and physical parameters characterizing bacteria and use them to explain experimental observations. Throughout the dissertation, we consider bacterial suspensions in the dilute limit, where bacteria are assumed to be so far apart that interactions between them are negligible. This simplifies calculations significantly and is the regime in which the most striking experimental results have been observed. We first study suspensions of self-propelled particles using a two-dimensional (2D) Partial Differential Equation (PDE) model. A bacterium is modeled as a disk in 2D with self-propulsion provided by a point force in the fluid. A formula is obtained for the effective viscosity of such suspensions in the dilute limit. This formula includes the two terms that are found in the 2D version of Einstein's classical result for a passive suspension of spheres. To this, our main contribution is added, an additional term due to self-propulsion which depends on the physical and geometric properties of the suspension. This work demonstrates how bacterial self-propulsion can alter the viscosity of a fluid and highlights the importance of bacterial orientation. Next, we present a more realistic PDE model for dilute suspensions of swimming bacteria in a three-dimensional fluid. In this work, a bacterium is modeled as a prolate spheroid with

  10. Viscosity of Campi Flregrei (Italy) magmas

    NASA Astrophysics Data System (ADS)

    Misiti, Valeria; Vetere, Francesco; Scarlato, Piergiorgio; Behrens, Harald; Mangiacapra, Annarita; Freda, Carmela

    2010-05-01

    Viscosity is an important factor governing both intrusive and volcanic processes. The most important parameters governing silicate melts viscosity are bulk composition of melt and temperature. Pressure has only minor effect at crustal depths, whereas crystals and bubbles have significant influence. Among compositional parameters, the water content is critical above all in terms of rheological behaviour of melts and explosive style of an eruption. Consequently, without an appropriate knowledge of magma viscosity depending on the amount of dissolved volatiles, it is not possible to model the processes (i.e., magma ascent, fragmentation, and dispersion) required to predict realistic volcanic scenarios and thus forecast volcanic hazards. The Campi Flegrei are a large volcanic complex (~150 km2) located west of the city of Naples, Italy, that has been the site of volcanic activity for more than 60 ka and represents a potential volcanic hazard owing to the large local population. In the frame of a INGV-DPC (Department of Civil Protection) project devoted to design a multidisciplinary system for short-term volcano hazard evaluation, we performed viscosity measurements, under dry and hydrous conditions, of primitive melt compositions representative of two Campi Flegrei eruptions (Minopoli-shoshonite and Fondo Riccio-latite). Viscosity of the two melts have been investigated in the high temperature/low viscosity range at atmospheric pressure in dry samples and at 0.5 GPa in runs having water content from nominally anhydrous to about 3 wt%. Data in the low temperature/high viscosity range were obtained near the glass transition temperature at atmospheric pressure on samples whose water contents vary from 0.3 up to 2.43 wt%. The combination of high- and low-viscosity data permits a general description of the viscosity as a function of temperature and water content using a modified Tamman-Vogel-Fulcher equation. logν = a+ --b--+ --d--×exp(g × w-) (T - c) (T - e) T (1) where

  11. Study of Near-Surface Models in Large-Eddy Simulations of a Neutrally Stratified Atmospheric Boundary Layer

    NASA Technical Reports Server (NTRS)

    Senocak, I.; Ackerman, A. S.; Kirkpatrick, M. P.; Stevens, D. E.; Mansour, N. N.

    2004-01-01

    Large-eddy simulation (LES) is a widely used technique in armospheric modeling research. In LES, large, unsteady, three dimensional structures are resolved and small structures that are not resolved on the computational grid are modeled. A filtering operation is applied to distinguish between resolved and unresolved scales. We present two near-surface models that have found use in atmospheric modeling. We also suggest a simpler eddy viscosity model that adopts Prandtl's mixing length model (Prandtl 1925) in the vicinity of the surface and blends with the dynamic Smagotinsky model (Germano et al, 1991) away from the surface. We evaluate the performance of these surface models by simulating a neutraly stratified atmospheric boundary layer.

  12. A dynamic mixed subgrid-scale model for large eddy simulation on unstructured grids: application to turbulent pipe flows

    NASA Astrophysics Data System (ADS)

    Lampitella, P.; Colombo, E.; Inzoli, F.

    2014-04-01

    The paper presents a consistent large eddy simulation (LES) framework which is particularly suited for implicitly filtered LES with unstructured finite volume (FV) codes. From the analysis of the subgrid-scale (SGS) stress tensor arising in this new LES formulation, a novel form of scale-similar SGS model is proposed and combined with a classical eddy viscosity term. The constants in the resulting mixed model are then computed trough a new, cheaper, dynamic procedure based on a consistent redefinition of the Germano identity within the new LES framework. The dynamic mixed model is implemented in a commercial, unstructured, finite volume solver and numerical tests are performed on the turbulent pipe flow at Reτ = 320-1142, showing the flexibility and improvements of the approach over classical modeling strategies. Some limitations of the proposed implementation are also highlighted.

  13. Gulf Stream eddies - Recent observations in the western Sargasso Sea.

    NASA Technical Reports Server (NTRS)

    Richardson, P. L.; Knauss, J. A.; Strong, A. E.

    1973-01-01

    A cyclonic Gulf Stream eddy was observed in the western Sargasso Sea by satellite infrared measurements and later confirmed by ship measurements. Fourteen months of observations indicate that the eddy moved southwestward at an average rate of 1 mile per day. The evidence suggests that the eddy was absorbed by the Gulf Stream off Florida.

  14. Viscosity and electric properties of water aerosols

    NASA Astrophysics Data System (ADS)

    Shavlov, A. V.; Sokolov, I. V.; Dzhumandzhi, V. A.

    2016-09-01

    The flow of water mist in a narrow duct has been studied experimentally. The profile of the velocity of drops has been measured, and the viscosity of the mist has been calculated using the Navier-Stokes equation. It has been found that at low gradients of the rate of shear the viscosity of the mist can exceed that of clean air by tens and even hundreds of times. The electric charge of the drops has been measured. It has been found that the viscosity of the mist differs from that of clean air at gradients of the rate of shear that are less than the frequency of the establishment of electric equilibrium between the drops. A comparative analysis of the viscosities of the mist and a drop cluster has been carried out, and the dependence of the viscosity of the water aerosol on the radius and the charge of the drops has been predicted. The possible role of aerosols that contain submicron drops in the known "clear air turbulence" problem has been shown.

  15. Predicting slag viscosity from coal ash composition

    SciTech Connect

    Laumb, J.; Benson, S.A.; Katrinak, K.A.; Schwalbe, R.; McCollor, D.P.

    1999-07-01

    Management of slag flow from cyclone-fired utility boilers requires accurate prediction of viscosity. Cyclones tend to build up slag when the cyclone combustion temperature is less than the temperature required to melt and tap the ash from the coal being fired. Cyclone-fired boilers designed for lignite are equipped with predry systems, which remove 6-9% of the moisture from the coal. Cyclones tend to slag when the as-received heating value of the fuel is less than 6350 Btu/lb and T250 (temperature where viscosity equals 250 poise) is greater than 2350 F. The T250 value, as well as the rest of the viscosity-temperature relationship, can be predicted using models based on coal ash composition. The focus of this work is to evaluate several models in terms of their agreement with measured viscosities. Viscosity measurements were made for ten samples, including nine lignite coals and one lignite-derived slag. Model performance is related to the SiO{sub 2}, CaO, and Fe{sub 2}O{sub 3} contents of the slag. The Sage and McIlroy and Kalmanovitch models worked best for high SiO{sub 2} and low Fe{sub 2}O{sub 3} fuels. The Senior model worked best when Fe{sub 2}O{sub 3} content was moderate to high.

  16. Viscosity Measurement Using Drop Coalescence in Microgravity

    NASA Technical Reports Server (NTRS)

    Antar, Basil N.; Ethridge, Edwin C.; Maxwell, Daniel; Curreri, Peter A. (Technical Monitor)

    2002-01-01

    We present in here validation studies of a new method for application in microgravity environment which measures the viscosity of highly viscous undercooled liquids using drop coalescence. The method has the advantage of avoiding heterogeneous nucleation at container walls caused by crystallization of undercooled liquids during processing. Homogeneous nucleation can also be avoided due to the rapidity of the measurement using this method. The technique relies on measurements from experiments conducted in near zero gravity environment as well as highly accurate analytical formulation for the coalescence process. The viscosity of the liquid is determined by allowing the computed free surface shape relaxation time to be adjusted in response to the measured free surface velocity for two coalescing drops. Results are presented from two sets of validation experiments for the method which were conducted on board aircraft flying parabolic trajectories. In these tests the viscosity of a highly viscous liquid, namely glycerin, was determined at different temperatures using the drop coalescence method described in here. The experiments measured the free surface velocity of two glycerin drops coalescing under the action of surface tension alone in low gravity environment using high speed photography. The liquid viscosity was determined by adjusting the computed free surface velocity values to the measured experimental data. The results of these experiments were found to agree reasonably well with the known viscosity for the test liquid used.

  17. Entropy viscosity method applied to Euler equations

    SciTech Connect

    Delchini, M. O.; Ragusa, J. C.; Berry, R. A.

    2013-07-01

    The entropy viscosity method [4] has been successfully applied to hyperbolic systems of equations such as Burgers equation and Euler equations. The method consists in adding dissipative terms to the governing equations, where a viscosity coefficient modulates the amount of dissipation. The entropy viscosity method has been applied to the 1-D Euler equations with variable area using a continuous finite element discretization in the MOOSE framework and our results show that it has the ability to efficiently smooth out oscillations and accurately resolve shocks. Two equations of state are considered: Ideal Gas and Stiffened Gas Equations Of State. Results are provided for a second-order time implicit schemes (BDF2). Some typical Riemann problems are run with the entropy viscosity method to demonstrate some of its features. Then, a 1-D convergent-divergent nozzle is considered with open boundary conditions. The correct steady-state is reached for the liquid and gas phases with a time implicit scheme. The entropy viscosity method correctly behaves in every problem run. For each test problem, results are shown for both equations of state considered here. (authors)

  18. Alternative algebraic approaches in quantum chemistry

    SciTech Connect

    Mezey, Paul G.

    2015-01-22

    Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed.

  19. Algebraic Methods to Design Signals

    DTIC Science & Technology

    2015-08-27

    group theory are employed to investigate the theory of their construction methods leading to new families of these arrays and some generalizations...sequences and arrays with desirable correlation properties. The methods used are very algebraic and number theoretic. Many new families of sequences...context of optical quantum computing, we prove that infinite families of anticirculant block weighing matrices can be obtained from generic weighing

  20. Methane fluxes above the Hainich forest by True Eddy Accumulation and Eddy Covariance

    NASA Astrophysics Data System (ADS)

    Siebicke, Lukas; Gentsch, Lydia; Knohl, Alexander

    2016-04-01

    Understanding the role of forests for the global methane cycle requires quantifying vegetation-atmosphere exchange of methane, however observations of turbulent methane fluxes remain scarce. Here we measured turbulent fluxes of methane (CH4) above a beech-dominated old-growth forest in the Hainich National Park, Germany, and validated three different measurement approaches: True Eddy Accumulation (TEA, closed-path laser spectroscopy), and eddy covariance (EC, open-path and closed-path laser spectroscopy, respectively). The Hainich flux tower is a long-term Fluxnet and ICOS site with turbulent fluxes and ecosystem observations spanning more than 15 years. The current study is likely the first application of True Eddy Accumulation (TEA) for the measurement of turbulent exchange of methane and one of the very few studies comparing open-path and closed-path eddy covariance (EC) setups side-by-side. We observed uptake of methane by the forest during the day (a methane sink with a maximum rate of 0.03 μmol m-2 s-1 at noon) and no or small fluxes of methane from the forest to the atmosphere at night (a methane source of typically less than 0.01 μmol m-2 s-1) based on continuous True Eddy Accumulation measurements in September 2015. First results comparing TEA to EC CO2 fluxes suggest that True Eddy Accumulation is a valid option for turbulent flux quantifications using slow response gas analysers (here CRDS laser spectroscopy, other potential techniques include mass spectroscopy). The TEA system was one order of magnitude more energy efficient compared to closed-path eddy covariance. The open-path eddy covariance setup required the least amount of user interaction but is often constrained by low signal-to-noise ratios obtained when measuring methane fluxes over forests. Closed-path eddy covariance showed good signal-to-noise ratios in the lab, however in the field it required significant amounts of user intervention in addition to a high power consumption. We conclude

  1. Large-Eddy Simulation and Multigrid Methods

    SciTech Connect

    Falgout,R D; Naegle,S; Wittum,G

    2001-06-18

    A method to simulate turbulent flows with Large-Eddy Simulation on unstructured grids is presented. Two kinds of dynamic models are used to model the unresolved scales of motion and are compared with each other on different grids. Thereby the behavior of the models is shown and additionally the feature of adaptive grid refinement is investigated. Furthermore the parallelization aspect is addressed.

  2. Investigations of eddy coherence in jet flows

    NASA Technical Reports Server (NTRS)

    Yule, A. J.

    1980-01-01

    In turbulent shear flow the term coherent structures refers to eddies which are both spatially coherent, i.e., large eddies, aand also temporally coherent, i.e., they retain their identities for times which are long compared with their time scales in fixed point measurements. In transitional flows, the existence of such structures is evident from flow visualizations. In many other flows, such structures are not so evident. The reasons for the existence of these two classes of flows are discussed and attention is focused upon the more difficult flows, where coherent structures are not so evident. Techniques by which the existence (or nonexistence) of such structures in these flows can be established from point measurements, are also discussed. A major problem is shown to be the need to discriminate between real losses in eddy coherence and apparent losses in coherence introduced by phase scrambling effects which 'smear' multipoint correlations. The analysis of multiprobe time dependent data in cold and reacting round turbulent jets is described and it is shown how evidence of strong eddy coherence can be extracted from data.

  3. The turbulent cascade of individual eddies

    NASA Astrophysics Data System (ADS)

    Huertas-Cerdeira, Cecilia; Lozano-Durán, Adrián; Jiménez, Javier

    2014-11-01

    The merging and splitting processes of Reynolds-stress carrying structures in the inertial range of scales are studied through their time-resolved evolution in channels at Reλ = 100 - 200 . Mergers and splits coexist during the whole life of the structures, and are responsible for a substantial part of their growth and decay. Each interaction involves two or more eddies and results in little overall volume loss or gain. Most of them involve a small eddy that merges with, or splits from, a significantly larger one. Accordingly, if merge and split indexes are respectively defined as the maximum number of times that a structure has merged from its birth or will split until its death, the mean eddy volume grows linearly with both indexes, suggesting an accretion process rather than a hierarchical fragmentation. However, a non-negligible number of interactions involve eddies of similar scale, with a second probability peak of the volume of the smaller parent or child at 0.3 times that of the resulting or preceding structure. Funded by the Multiflow project of the ERC.

  4. Algerian Eddies lifetime can near 3 years

    NASA Astrophysics Data System (ADS)

    Puillat, I.; Taupier-Letage, I.; Millot, C.

    2002-01-01

    The Algerian Current (AC) is unstable and generates mesoscale meanders and eddies. Only anticyclonic eddies can develop and reach diameters over 200 km with vertical extents down to the bottom (˜3000 m). Algerian Eddies (AEs) first propagate eastward along the Algerian slope at few kilometers per day. In the vicinity of the Channel of Sardinia, a few AEs detach from the Algerian slope and propagate along the Sardinian one. It was hypothesized that AEs then followed a counter-clockwise circuit in the eastern part of the basin. Maximum recorded lifetimes were known to exceed 9 months. Within the framework of the 1-year Eddies and Leddies Interdisciplinary Study off Algeria (ELISA) experiment (1997-1998), we exhaustively tracked two AEs, using mainly an ˜3-year time series of NOAA/AVHRR satellite images. We show that AEs lifetimes can near 3 years, exceeding 33 months at least. We also confirm the long-lived AEs preferential circuit in the eastern part of the Algerian Basin, and specify that it may include several loops (at least three).

  5. Computer algebra and transport theory.

    SciTech Connect

    Warsa, J. S.

    2004-01-01

    Modern symbolic algebra computer software augments and complements more traditional approaches to transport theory applications in several ways. The first area is in the development and enhancement of numerical solution methods for solving the Boltzmann transport equation. Typically, special purpose computer codes are designed and written to solve specific transport problems in particular ways. Different aspects of the code are often written from scratch and the pitfalls of developing complex computer codes are numerous and well known. Software such as MAPLE and MATLAB can be used to prototype, analyze, verify and determine the suitability of numerical solution methods before a full-scale transport application is written. Once it is written, the relevant pieces of the full-scale code can be verified using the same tools I that were developed for prototyping. Another area is in the analysis of numerical solution methods or the calculation of theoretical results that might otherwise be difficult or intractable. Algebraic manipulations are done easily and without error and the software also provides a framework for any additional numerical calculations that might be needed to complete the analysis. We will discuss several applications in which we have extensively used MAPLE and MATLAB in our work. All of them involve numerical solutions of the S{sub N} transport equation. These applications encompass both of the two main areas in which we have found computer algebra software essential.

  6. BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.

    1994-01-01

    The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.

  7. Introduction to Image Algebra Ada

    NASA Astrophysics Data System (ADS)

    Wilson, Joseph N.

    1991-07-01

    Image Algebra Ada (IAA) is a superset of the Ada programming language designed to support use of the Air Force Armament Laboratory's image algebra in the development of computer vision application programs. The IAA language differs from other computer vision languages is several respects. It is machine independent, and an IAA translator has been implemented in the military standard Ada language. Its image operands and operations can be used to program a range of both low- and high-level vision algorithms. This paper provides an overview of the image algebra constructs supported in IAA and describes the embodiment of these constructs in the IAA extension of Ada. Examples showing the use of IAA for a range of computer vision tasks are given. The design of IAA as a superset of Ada and the implementation of the initial translator in Ada represent critical choices. The authors discuss the reasoning behind these choices as well as the benefits and drawbacks associated with them. Implementation strategies associated with the use of Ada as an implementation language for IAA are also discussed. While one can look on IAA as a program design language (PDL) for specifying Ada programs, it is useful to consider IAA as a separate language superset of Ada. This admits the possibility of directly translating IAA for implementation on special purpose architectures. This paper explores strategies for porting IAA to various architectures and notes the critical language and implementation features for porting to different architectures.

  8. Polyfunctional dispersants for controlling viscosity of phyllosilicates

    DOEpatents

    Chaiko, David J.

    2006-07-25

    This invention provides phyllosilicates and polyfunctional dispersants which can be manipulated to selectively control the viscosity of phyllosilicate slurries. The polyfunctional dispersants used in the present invention, which include at least three functional groups, increase the dispersion and exfoliation of phyllosilicates in polymers and, when used in conjunction with phyllosilicate slurries, significantly reduce the viscosity of slurries having high concentrations of phyllosilicates. The functional groups of the polyfunctional dispersants are capable of associating with multivalent metal cations and low molecular weight organic polymers, which can be manipulated to substantially increase or decrease the viscosity of the slurry in a concentration dependent manner. The polyfunctional dispersants of the present invention can also impart desirable properties on the phyllosilicate dispersions including corrosion inhibition and enhanced exfoliation of the phyllosilicate platelets.

  9. Viscosity near Earth's solid inner core

    PubMed

    Smylie

    1999-04-16

    Anomalous splitting of the two equatorial translational modes of oscillation of Earth's solid inner core is used to estimate the effective viscosity just outside its boundary. Superconducting gravimeter observations give periods of 3.5822 +/- 0.0012 (retrograde) and 4.0150 +/- 0.0010 (prograde) hours. With the use of Ekman layer theory to estimate viscous drag forces, an inferred single viscosity of 1.22 x 10(11) Pascal seconds gives calculated periods of 3.5839 and 4.0167 hours for the two modes, close to the observed values. The large effective viscosity is consistent with a fluid, solid-liquid mixture surrounding the inner core associated with the "compositional convection" that drives Earth's geodynamo.

  10. Neoclassical Viscosities and Anomalous Flows in Stellarators

    NASA Astrophysics Data System (ADS)

    Ware, A. S.; Spong, D. A.

    2008-11-01

    We discuss initial work to use neoclassical viscosities calculated with the PENTA code [1,2] in a transport model that includes Reynolds stress generation of flows [3]. The PENTA code uses a drift kinetic equation solver to calculate neoclassical viscosities and flows in general three-dimensional geometries over a range of collisionalities. The predicted neoclassical viscosities predicted by PENTA can be flux-surfaced average and applied in a 1-D transport model that includes anomalous flow generation. This combination of codes can be used to test the impact of stellarator geometry on anomalous flow generation. [1] D. A. Spong, Phys. Plasmas 12, 056114 (2005). [2] D. A. Spong, Fusion Sci. Technology 50, 343 (2006). [3] D. E. Newman, et al., Phys. Plasmas 5, 938 (1998).

  11. Viscosity of fluids in subduction zones.

    PubMed

    Audétat, Andreas; Keppler, Hans

    2004-01-23

    The viscosities of aqueous fluids with 10 to 80 weight percent dissolved silicates have been measured at 600 degrees to 950 degrees C and 1.0 to 2.0 gigapascals by in situ observation of falling spheres in the diamond anvil cell. The viscosities at 800 degrees C range from 10(-4) to 10(0.5) pascal seconds. The combination of low viscosities with a favorable wetting angle makes silicate-rich fluid an efficient agent for material transport at low-volume fractions. Our results therefore suggest that there may be a direct relationship between the position of the volcanic front and the onset of complete miscibility between water and silicate melt in the subducting slab.

  12. Diffusion, Viscosity and Crystal Growth in Microgravity

    NASA Technical Reports Server (NTRS)

    Myerson, Allan S.

    1996-01-01

    The diffusivity of TriGlycine Sulfate (TGS), Potassium Dihydrogen Phosphate (KDP), Ammonium Dihydrogen Phosphate (ADF) and other compounds of interest to microgravity crystal growth, in supersaturated solutions as a function of solution concentration, 'age' and 'history was studied experimentally. The factors that affect the growth of crystals from water solutions in microgravity have been examined. Three non-linear optical materials have been studied, potassium dihydrogen phosphate (KDP), ammonium dihydrogen phosphate (ADP) and triglycine sulfate (TGC). The diffusion coefficient and viscosity of supersaturated water solutions were measured. Also theoretical model of diffusivity and viscosity in a metastable state, model of crystal growth from solution including non-linear time dependent diffusivity and viscosity effect and computer simulation of the crystal growth process which allows simulation of the microgravity crystal growth were developed.

  13. Evaluation of SpectroVisc Q3000 for Viscosity Determination

    DTIC Science & Technology

    2013-11-14

    The Navy routinely measures the viscosity of lubricating oils and hydraulic fluids. Viscosity measurements typically are conducted in a land based...BACKGROUND The Navy routinely measures the viscosity of lubricating oils and hydraulic fluids. Viscosity measurements that are lower than expected... viscosity at 40°C in lubricating oils and hydraulic fluids. 3.0 APPROACH The accuracy and repeatability of the SpectroVisc Q3000 was evaluated using

  14. Viscosity properties of sodium borophosphate glasses

    SciTech Connect

    Gaylord, S.; Tincher, B.; Petit, L. Richardson, K.

    2009-05-06

    The viscosity behavior of (1 - x)NaPO{sub 3}-xNa{sub 2}B{sub 4}O{sub 7} glasses (x = 0.05-0.20) have been measured as a function of temperature using beam-bending and parallel-plate viscometry. The viscosity was found to shift to higher temperatures with increasing sodium borate content. The kinetic fragility parameter, m, estimated from the viscosity curve, decreases from 52 to 33 when x increases from 0.05 to 0.20 indicating that the glass network transforms from fragile to strong with the addition of Na{sub 2}B{sub 4}O{sub 7}. The decrease in fragility with increasing x is due to the progressive depolymerization of the phosphate network by the preferred four-coordinated boron atoms present in the low alkali borate glasses. As confirmed by Raman spectroscopy increasing alkali borate leads to enhanced B-O-P linkages realized with the accompanying transition from solely four-coordinated boron (in BO{sub 4} units) to mixed BO{sub 4}/BO{sub 3} structures. The glass viscosity characteristics of the investigated glasses were compared to those of P-SF67 and N-FK5 commercial glasses from SCHOTT. We showed that the dependence of the viscosity of P-SF67 was similar to the investigated glasses due to similar phosphate network organization confirmed by Raman spectroscopy, whereas N-FK5 exhibited a very different viscosity curve and fragility parameter due to its highly coordinated silicate network.

  15. Viscosity Meaurement Technique for Metal Fuels

    SciTech Connect

    Ban, Heng; Kennedy, Rory

    2015-02-09

    Metallic fuels have exceptional transient behavior, excellent thermal conductivity, and a more straightforward reprocessing path, which does not separate out pure plutonium from the process stream. Fabrication of fuel containing minor actinides and rare earth (RE) elements for irradiation tests, for instance, U-20Pu-3Am-2Np-1.0RE-15Zr samples at the Idaho National Laboratory, is generally done by melt casting in an inert atmosphere. For the design of a casting system and further scale up development, computational modeling of the casting process is needed to provide information on melt flow and solidification for process optimization. Therefore, there is a need for melt viscosity data, the most important melt property that controls the melt flow. The goal of the project was to develop a measurement technique that uses fully sealed melt sample with no Americium vapor loss to determine the viscosity of metallic melts and at temperatures relevant to the casting process. The specific objectives of the project were to: develop mathematical models to establish the principle of the measurement method, design and build a viscosity measurement prototype system based on the established principle, and calibrate the system and quantify the uncertainty range. The result of the project indicates that the oscillation cup technique is applicable for melt viscosity measurement. Detailed mathematical models of innovative sample ampoule designs were developed to not only determine melt viscosity, but also melt density under certain designs. Measurement uncertainties were analyzed and quantified. The result of this project can be used as the initial step toward the eventual goal of establishing a viscosity measurement system for radioactive melts.

  16. Algebra: A Challenge at the Crossroads of Policy and Practice

    ERIC Educational Resources Information Center

    Stein, Mary Kay; Kaufman, Julia Heath; Sherman, Milan; Hillen, Amy F.

    2011-01-01

    The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier.…

  17. Obituary: John Allen Eddy (1931-2009)

    NASA Astrophysics Data System (ADS)

    Gingerich, Owen

    2011-12-01

    Jack Eddy, who was born 25 March 1931 in Pawnee City in southeastern Nebraska, died after a long battle with cancer in Tucson, Arizona, on 10 June 2009. Best known for his work on the long-term instability of the sun, described in a landmark paper in Science titled "The Maunder Minimum," he also deserves recognition as one of the triumvirate who founded the Historical Astronomy Division of the AAS. His father ran a cooperative farm store where Jack worked as a teenager; his parents were of modest means and there were concerns whether he could afford college, but one of the state senators, also from Pawnee City, nominated him for the U.S. Naval Academy. A course in celestial navigation gave him a love of the sky. After graduation in 1953, he served four years on aircraft carriers in the Pacific during the Korean War and then as a navigator and operations officer on a destroyer in the Persian Gulf. In 1957, he left the Navy and entered graduate school at the University of Colorado in Boulder, where in 1962 he received a Ph.D. in astro-geophysics. His thesis, supervised by Gordon Newkirk, dealt with light scattering in the upper atmosphere, based on data from stratospheric balloon flights. He then worked as teacher and researcher at the High Altitude Observatory in Boulder. Always adventuresome and willing to explore new frontiers, on his own time Eddy examined an Amerindian stone circle in the Big Horn mountains of Wyoming, a so-called medicine wheel, concluding that there were alignments with both the solstitial sun and Aldebaran. His conjectures became a cover story on Science magazine in June of 1974. In 1971 Jack privately reproduced for his friends a small collection of his own hilarious cartoons titled "Job Opportunities for Out-of-work Astronomers," with an abstract beginning, "Contrary to popular belief, a PhD in Astronomy/Astrophysics need not be a drawback in locating work in this decade." For example, under merchandising, a used car salesman advertises

  18. ANTI-INFLAMMATORY ACTIVITY OF DODONAEA VISCOSE

    PubMed Central

    Mahadevan, N.; Venkatesh, Sama; Suresh, B.

    1998-01-01

    Dodonaea viscose, Linn is a widely grown plant of Nilgiris district of Tamil and is commonly used by the tribals of Nilgiris as a traditional medicine for done fracture and joint sprains. Since it is generally believed tat fractures are accompanied by either some degree of injury or inflammations, it was felt desirable to carry our anti inflammatory activity of Dodonaea viscose. Anti-inflammatory activity of the plant was carried out by carrageenin induced paw edema method in Wister albino rats. PMID:22556883

  19. Shear Viscosity in a Gluon Gas

    SciTech Connect

    Xu Zhe; Greiner, Carsten

    2008-05-02

    The relation of the shear viscosity coefficient to the recently introduced transport rate is derived within relativistic kinetic theory. We calculate the shear viscosity over entropy ratio {eta}/s for a gluon gas, which involves elastic gg{yields}gg perturbative QCD (PQCD) scatterings as well as inelastic gg{r_reversible}ggg PQCD bremsstrahlung. For {alpha}{sub s}=0.3 we find {eta}/s=0.13 and for {alpha}{sub s}=0.6, {eta}/s=0.076. The small {eta}/s values, which suggest strongly coupled systems, are due to the gluon bremsstrahlung incorporated.

  20. Measuring Viscosities of Gases at Atmospheric Pressure

    NASA Technical Reports Server (NTRS)

    Singh, Jag J.; Mall, Gerald H.; Hoshang, Chegini

    1987-01-01

    Variant of general capillary method for measuring viscosities of unknown gases based on use of thermal mass-flowmeter section for direct measurement of pressure drops. In technique, flowmeter serves dual role, providing data for determining volume flow rates and serving as well-characterized capillary-tube section for measurement of differential pressures across it. New method simple, sensitive, and adaptable for absolute or relative viscosity measurements of low-pressure gases. Suited for very complex hydrocarbon mixtures where limitations of classical theory and compositional errors make theoretical calculations less reliable.

  1. Shock capturing by the spectral viscosity method

    NASA Technical Reports Server (NTRS)

    Tadmor, Eitan

    1989-01-01

    A main disadvantage of using spectral methods for nonlinear conservation laws lies in the formation of Gibbs phenomenon, once spontaneous shock discontinuities appear in the solution. The global nature of spectral methods than pollutes the unstable Gibbs oscillations overall the computational domain, and the lack of entropy dissipation prevents convergences in these cases. The Spectral Viscosity method, which is based on high frequency dependent vanishing viscosity regularization of the classical spectral methods is discussed. It is shown that this method enforces the convergence of nonlinear spectral approximations without sacrificing their overall spectral accuracy.

  2. Viscosity of a nanoconfined liquid during compression

    NASA Astrophysics Data System (ADS)

    Khan, Shah H.; Kramkowski, Edward L.; Ochs, Peter J.; Wilson, David M.; Hoffmann, Peter M.

    2014-01-01

    The viscous behavior of liquids under nanoconfinement is not well understood. Using a small-amplitude atomic force microscope, we found bulk-like viscosity in a nanoconfined, weakly interacting liquid. A further decrease in viscosity was observed at confinement sizes of a just few molecular layers. Overlaid over the continuum viscous behavior, we measured non-continuum stiffness and damping oscillations. The average stiffness of the confined liquid was found to scale linearly with the size of the confining tip, while the damping scales with the radius of curvature of the tip end.

  3. Gravimetric capillary method for kinematic viscosity measurements

    NASA Technical Reports Server (NTRS)

    Rosenberger, Franz; Iwan, J.; Alexander, D.; Jin, Wei-Qing

    1992-01-01

    A novel version of the capillary method for viscosity measurements of liquids is presented. Viscosity data can be deduced in a straightforward way from mass transfer data obtained by differential weighing during the gravity-induced flow of the liquid between two cylindrical chambers. Tests of this technique with water, carbon tetrachloride, and ethanol suggest that this arrangement provides an accuracy of about +/- 1 percent. The technique facilitates operation under sealed, isothermal conditions and, thus can readily be applied to reactive and/or high vapor pressure liquids.

  4. Low shear viscosity of dilute polymer solutions

    SciTech Connect

    Chiou, C.S.; Gordon, R.J.

    1980-09-01

    A modification of a viscometer originally proposed by Zimm and Crothers is studied, which may be used to measure ultra low shear viscosity for highly dilute polymer solutions. This may provide useful information on polymer coil dimensions and relaxation time. Use of the low shear viscosity data leads to large value of relaxation time induced by polymer addition to a concentration of only 2 to 3 ppM by wt. This finding is consistent with the marked viscoelastic effects exhibited by these solutions.

  5. Apparatus and method for measuring viscosity

    DOEpatents

    Murphy, Jr., Robert J.

    1986-01-01

    The present invention is directed to an apparatus and method for measuring the viscosity of a fluid. This apparatus and method is particularly useful for the measurement of the viscosity of a liquid in a harsh environment characterized by high temperature and the presence of corrosive or deleterious gases and vapors which adversely affect conventional ball or roller bearings. The apparatus and method of the present invention employ one or more flexural or torsional bearings to suspend a bob capable of limited angular motion within a rotatable sleeve suspended from a stationary frame.

  6. Apparatus and method for measuring viscosity

    DOEpatents

    Murphy, R.J. Jr.

    1986-02-25

    The present invention is directed to an apparatus and method for measuring the viscosity of a fluid. This apparatus and method is particularly useful for the measurement of the viscosity of a liquid in a harsh environment characterized by high temperature and the presence of corrosive or deleterious gases and vapors which adversely affect conventional ball or roller bearings. The apparatus and method of the present invention employ one or more flexural or torsional bearings to suspend a bob capable of limited angular motion within a rotatable sleeve suspended from a stationary frame. 7 figs.

  7. Shear viscosity coefficient of liquid lanthanides

    SciTech Connect

    Patel, H. P. Thakor, P. B. Prajapati, A. V.; Sonvane, Y. A.

    2015-05-15

    Present paper deals with the computation of shear viscosity coefficient (η) of liquid lanthanides. The effective pair potential v(r) is calculated through our newly constructed model potential. The Pair distribution function g(r) is calculated from PYHS reference system. To see the influence of local field correction function, Hartree (H), Tailor (T) and Sarkar et al (S) local field correction function are used. Present results are compared with available experimental as well as theoretical data. Lastly, we found that our newly constructed model potential successfully explains the shear viscosity coefficient (η) of liquid lanthanides.

  8. Large-eddy simulation of unidirectional turbulent flow over dunes

    NASA Astrophysics Data System (ADS)

    Omidyeganeh, Mohammad

    We performed large eddy simulation of the flow over a series of two- and three-dimensional dune geometries at laboratory scale using the Lagrangian dynamic eddy-viscosity subgrid-scale model. First, we studied the flow over a standard 2D transverse dune geometry, then bedform three-dimensionality was imposed. Finally, we investigated the turbulent flow over barchan dunes. The results are validated by comparison with simulations and experiments for the 2D dune case, while the results of the 3D dunes are validated qualitatively against experiments. The flow over transverse dunes separates at the dune crest, generating a shear layer that plays a crucial role in the transport of momentum and energy, as well as the generation of coherent structures. Spanwise vortices are generated in the separated shear; as they are advected, they undergo lateral instabilities and develop into horseshoe-like structures and finally reach the surface. The ejection that occurs between the legs of the vortex creates the upwelling and downdrafting events on the free surface known as "boils". The three-dimensional separation of flow at the crestline alters the distribution of wall pressure, which may cause secondary flow across the stream. The mean flow is characterized by a pair of counter-rotating streamwise vortices, with core radii of the order of the flow depth. Staggering the crestlines alters the secondary motion; two pairs of streamwise vortices appear (a strong one, centred about the lobe, and a weaker one, coming from the previous dune, centred around the saddle). The flow over barchan dunes presents significant differences to that over transverse dunes. The flow near the bed, upstream of the dune, diverges from the centerline plane; the flow close to the centerline plane separates at the crest and reattaches on the bed. Away from the centerline plane and along the horns, flow separation occurs intermittently. The flow in the separation bubble is routed towards the horns and leaves

  9. Bilinear forms on fermionic Novikov algebras

    NASA Astrophysics Data System (ADS)

    Chen, Zhiqi; Zhu, Fuhai

    2007-05-01

    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in formal variational calculus. Fermionic Novikov algebras correspond to a certain Hamiltonian super-operator in a super-variable. In this paper, we show that there is a remarkable geometry on fermionic Novikov algebras with non-degenerate invariant symmetric bilinear forms, which we call pseudo-Riemannian fermionic Novikov algebras. They are related to pseudo-Riemannian Lie algebras. Furthermore, we obtain a procedure to classify pseudo-Riemannian fermionic Novikov algebras. As an application, we give the classification in dimension <=4. Motivated by the one in dimension 4, we construct some examples in high dimensions.

  10. Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Tianjie; Gao, Xing; Guo, Li

    2016-10-01

    The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.

  11. A comparison of three approaches to compute the effective Reynolds number of the implicit large-eddy simulations

    SciTech Connect

    Zhou, Ye; Thornber, Ben

    2016-04-12

    Here, the implicit large-eddy simulation (ILES) has been utilized as an effective approach for calculating many complex flows at high Reynolds number flows. Richtmyer–Meshkov instability (RMI) induced flow can be viewed as a homogeneous decaying turbulence (HDT) after the passage of the shock. In this article, a critical evaluation of three methods for estimating the effective Reynolds number and the effective kinematic viscosity is undertaken utilizing high-resolution ILES data. Effective Reynolds numbers based on the vorticity and dissipation rate, or the integral and inner-viscous length scales, are found to be the most self-consistent when compared to the expected phenomenology and wind tunnel experiments.

  12. Numerical linear algebra algorithms and software

    NASA Astrophysics Data System (ADS)

    Dongarra, Jack J.; Eijkhout, Victor

    2000-11-01

    The increasing availability of advanced-architecture computers has a significant effect on all spheres of scientific computation, including algorithm research and software development in numerical linear algebra. Linear algebra - in particular, the solution of linear systems of equations - lies at the heart of most calculations in scientific computing. This paper discusses some of the recent developments in linear algebra designed to exploit these advanced-architecture computers. We discuss two broad classes of algorithms: those for dense, and those for sparse matrices.

  13. Symbolic Lie algebras manipulations using COMMON LISP

    NASA Astrophysics Data System (ADS)

    Cecchini, R.; Tarlini, M.

    1989-01-01

    We present a description and an implementation of a program in COMMON LISP to perform symbolic computations in a given Lie algebra. Using the general definitions of vector space Lie algebra and enveloping algebra, the program is able to compute commutators, to evaluate similarity transformations and the general Baker-Campbell-Hausdorff formula. All the computations are exact, including numerical coefficients. For the interactive user an optional menu facility and online help are available. LISP knowledge is unnecessary.

  14. Lie algebras of classical and stochastic electrodynamics

    NASA Astrophysics Data System (ADS)

    Neto, J. J. Soares; Vianna, J. D. M.

    1994-03-01

    The Lie algebras associated with infinitesimal symmetry transformations of third-order differential equations of interest to classical electrodynamics and stochastic electrodynamics have been obtained. The structure constants for a general case are presented and the Lie algebra for each particular application is easily achieved. By the method used here it is not necessary to know the explicit expressions of the infinitesimal generators in order to determine the structure constants of the Lie algebra.

  15. Large eddy simulation model for wind-driven sea circulation in coastal areas

    NASA Astrophysics Data System (ADS)

    Petronio, A.; Roman, F.; Nasello, C.; Armenio, V.

    2013-12-01

    In the present paper a state-of-the-art large eddy simulation model (LES-COAST), suited for the analysis of water circulation and mixing in closed or semi-closed areas, is presented and applied to the study of the hydrodynamic characteristics of the Muggia bay, the industrial harbor of the city of Trieste, Italy. The model solves the non-hydrostatic, unsteady Navier-Stokes equations, under the Boussinesq approximation for temperature and salinity buoyancy effects, using a novel, two-eddy viscosity Smagorinsky model for the closure of the subgrid-scale momentum fluxes. The model employs: a simple and effective technique to take into account wind-stress inhomogeneity related to the blocking effect of emerged structures, which, in turn, can drive local-scale, short-term pollutant dispersion; a new nesting procedure to reconstruct instantaneous, turbulent velocity components, temperature and salinity at the open boundaries of the domain using data coming from large-scale circulation models (LCM). Validation tests have shown that the model reproduces field measurement satisfactorily. The analysis of water circulation and mixing in the Muggia bay has been carried out under three typical breeze conditions. Water circulation has been shown to behave as in typical semi-closed basins, with an upper layer moving along the wind direction (apart from the anti-cyclonic veering associated with the Coriolis force) and a bottom layer, thicker and slower than the upper one, moving along the opposite direction. The study has shown that water vertical mixing in the bay is inhibited by a large level of stable stratification, mainly associated with vertical variation in salinity and, to a minor extent, with temperature variation along the water column. More intense mixing, quantified by sub-critical values of the gradient Richardson number, is present in near-coastal regions where upwelling/downwelling phenomena occur. The analysis of instantaneous fields has detected the presence of

  16. Algebraic logic of concepts and its machine implementation in the algebras of deontic and axiological notions

    NASA Astrophysics Data System (ADS)

    Manerowska, Anna; Nieznański, Edward; Mulawka, Jan

    2013-10-01

    Our aim is to present the algebra of concepts in two formal languages. First, after introducing a primary relation between concepts, which is subsumption, we shall specify in a language that uses quantifiers, the Boolean algebra of general concepts. Next, we shall note down the same algebra in simplified non-quantifying language, in order to use it as basis for two specific implementations, i.e. to create the Boolean algebras of deontic concepts and axiological concepts.

  17. Dynamically consistent parameterization of mesoscale eddies. Part I: Simple model

    NASA Astrophysics Data System (ADS)

    Berloff, Pavel

    2015-03-01

    This work aims at developing a framework for dynamically consistent parameterization of mesoscale eddy effects for use in non-eddy-resolving ocean circulation models. The proposed eddy parameterization framework is successfully tested on the classical, wind-driven double-gyre model, which is solved both with explicitly resolved vigorous eddy field and in the non-eddy-resolving configuration with the eddy parameterization replacing the eddy effects. The parameterization locally approximates transient eddy flux divergence by spatially localized and temporally periodic forcing, referred to as the plunger, and focuses on the linear-dynamics flow solution induced by it. The nonlinear self-interaction of this solution, referred to as the footprint, characterizes and quantifies the induced cumulative eddy forcing exerted on the large-scale flow. We find that spatial pattern and amplitude of the footprint strongly depend on the underlying large-scale and the corresponding relationships provide the basis for the eddy parameterization and its closure on the large-scale flow properties. Dependencies of the footprints on other important parameters of the problem are also systematically analyzed. The parameterization utilizes the local large-scale flow information, constructs and scales the corresponding footprints, and then sums them up over the gyres to produce the resulting eddy forcing field, which is interactively added to the model as an extra forcing. The parameterization framework is implemented in the simplest way, but it provides a systematic strategy for improving the implementation algorithm.

  18. Random-forcing model of the mesoscale oceanic eddies

    NASA Astrophysics Data System (ADS)

    Berloff, Pavel S.

    2005-04-01

    The role of mesoscale oceanic eddies in driving large-scale currents is studied in an eddy-resolving midlatitude double-gyre ocean model. The reference solution is decomposed into large-scale and eddy components in a way which is dynamically consistent with a non-eddy-resolving ocean model. That is, the non-eddy-resolving solution driven by this eddy-forcing history, calculated on the basis of this decomposition, correctly approximates the original flow. The main effect of the eddy forcing on the large-scale flow is to enhance the eastward-jet extension of the subtropical western boundary current. This is an anti-diffusive process, which cannot be represented in terms of turbulent diffusion. It is shown that the eddy-forcing history can be approximated as a space-time correlated, random-forcing process in such a way that the non-eddy-resolving solution correctly approximates the reference solution. Thus, the random-forcing model can potentially replace the diffusion model, which is commonly used to parameterize eddy effects on the large-scale currents. The eddy-forcing statistics are treated as spatially inhomogeneous but stationary, and the dynamical roles of space-time correlations and spatial inhomogeneities are systematically explored. The integral correlation time, oscillations of the space correlations, and inhomogeneity of the variance are found to be particularly important for the flow response.

  19. Projected changes to Tasman Sea eddies in a future climate

    NASA Astrophysics Data System (ADS)

    Oliver, Eric C. J.; O'Kane, Terence J.; Holbrook, Neil J.

    2015-11-01

    The Tasman Sea is a hot spot of ocean warming, that is linked to the increased poleward influence of the East Australian Current (EAC) over recent decades. Specifically, the EAC produces mesoscale eddies which have significant impacts on the physical, chemical, and biological properties of the Tasman Sea. To effectively consider and explain potential eddy changes in the next 50 years, we use high-resolution dynamically downscaled climate change simulations to characterize the projected future marine climate and mesoscale eddies in the Tasman Sea through the 2060s. We assess changes in the marine climate and the eddy field using bulk statistics and by detecting and tracking individual eddies. We find that the eddy kinetic energy is projected to increase along southeast Australia. In addition, we find that eddies in the projected future climate are composed of a higher proportion of anticyclonic eddies in this region and that these eddies are longer lived and more stable. This amounts to nearly a doubling of eddy-related southward temperature transport in the upper 200 m of the Tasman Sea. These changes are concurrent with increases in baroclinic and barotropic instabilities focused around the EAC separation point. This poleward transport and increase in eddy activity would be expected to also increase the frequency of sudden warming events, including ocean temperature extremes, with potential impacts on marine fisheries, aquaculture, and biodiversity off Tasmania's east coast, through direct warming or competition/predation from invasive migrating species.

  20. Do East Australian Current anticyclonic eddies leave the Tasman Sea?

    NASA Astrophysics Data System (ADS)

    Pilo, Gabriela S.; Oke, Peter R.; Rykova, Tatiana; Coleman, Richard; Ridgway, Ken

    2015-12-01

    Using satellite altimetry and high-resolution model output we analyze the pathway of large, long-lived anticyclonic eddies that originate near the East Australian Current (EAC) separation point. We show that 25-30% of these eddies propagate southward, around Tasmania, leave the Tasman Sea, and decay in the Great Australian Bight. This pathway has not been previously documented owing to poor satellite sampling off eastern Tasmania. As eddies propagate southward, they often "stall" for several months at near-constant latitude. Along the pathway eddies become increasingly barotropic. Eddy intensity is primarily influenced by merging with other eddies and a gradual decay otherwise. Surface temperature anomaly associated with anticyclonic eddies changes as they propagate, while surface salinity anomaly tends to remain relatively unchanged as they propagate.

  1. Biogeochemical properties of eddies in the California Current System

    NASA Astrophysics Data System (ADS)

    Chenillat, Fanny; Franks, Peter J. S.; Combes, Vincent

    2016-06-01

    The California Current System (CCS) has intense mesoscale activity that modulates and exports biological production from the coastal upwelling system. To characterize and quantify the ability of mesoscale eddies to affect the local and regional planktonic ecosystem of the CCS, we analyzed a 10 year-long physical-biological model simulation, using eddy detection and tracking to isolate the dynamics of cyclonic and anticyclonic eddies. As they propagate westward across the shelf, cyclonic eddies efficiently transport coastal planktonic organisms and maintain locally elevated production for up to 1 year (800 km offshore). Anticyclonic eddies, on the other hand, have a limited impact on local production over their ~6 month lifetime as they propagate 400 km offshore. At any given time ~8% of the model domain was covered by eddy cores. Though the eddies cover a small area, they explain ~50 and 20% of the transport of nitrate and plankton, respectively.

  2. A True Eddy Accumulation - Eddy Covariance hybrid for measurements of turbulent trace gas fluxes

    NASA Astrophysics Data System (ADS)

    Siebicke, Lukas

    2016-04-01

    Eddy covariance (EC) is state-of-the-art in directly and continuously measuring turbulent fluxes of carbon dioxide and water vapor. However, low signal-to-noise ratios, high flow rates and missing or complex gas analyzers limit it's application to few scalars. True eddy accumulation, based on conditional sampling ideas by Desjardins in 1972, requires no fast response analyzers and is therefore potentially applicable to a wider range of scalars. Recently we showed possibly the first successful implementation of True Eddy Accumulation (TEA) measuring net ecosystem exchange of carbon dioxide of a grassland. However, most accumulation systems share the complexity of having to store discrete air samples in physical containers representing entire flux averaging intervals. The current study investigates merging principles of eddy accumulation and eddy covariance, which we here refer to as "true eddy accumulation in transient mode" (TEA-TM). This direct flux method TEA-TM combines true eddy accumulation with continuous sampling. The TEA-TM setup is simpler than discrete accumulation methods while avoiding the need for fast response gas analyzers and high flow rates required for EC. We implemented the proposed TEA-TM method and measured fluxes of carbon dioxide (CO2), methane (CH4) and water vapor (H2O) above a mixed beech forest at the Hainich Fluxnet and ICOS site, Germany, using a G2301 laser spectrometer (Picarro Inc., USA). We further simulated a TEA-TM sampling system using measured high frequency CO2 time series from an open-path gas analyzer. We operated TEA-TM side-by-side with open-, enclosed- and closed-path EC flux systems for CO2, H2O and CH4 (LI-7500, LI-7200, LI-6262, LI-7700, Licor, USA, and FGGA LGR, USA). First results show that TEA-TM CO2 fluxes were similar to EC fluxes. Remaining differences were similar to those between the three eddy covariance setups (open-, enclosed- and closed-path gas analyzers). Measured TEA-TM CO2 fluxes from our physical

  3. Dispersion Operators Algebra and Linear Canonical Transformations

    NASA Astrophysics Data System (ADS)

    Andriambololona, Raoelina; Ranaivoson, Ravo Tokiniaina; Hasimbola Damo Emile, Randriamisy; Rakotoson, Hanitriarivo

    2017-04-01

    This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.

  4. Dispersion Operators Algebra and Linear Canonical Transformations

    NASA Astrophysics Data System (ADS)

    Andriambololona, Raoelina; Ranaivoson, Ravo Tokiniaina; Hasimbola Damo Emile, Randriamisy; Rakotoson, Hanitriarivo

    2017-02-01

    This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.

  5. Banach Algebras Associated to Lax Pairs

    NASA Astrophysics Data System (ADS)

    Glazebrook, James F.

    2015-04-01

    Lax pairs featuring in the theory of integrable systems are known to be constructed from a commutative algebra of formal pseudodifferential operators known as the Burchnall- Chaundy algebra. Such pairs induce the well known KP flows on a restricted infinite-dimensional Grassmannian. The latter can be exhibited as a Banach homogeneous space constructed from a Banach *-algebra. It is shown that this commutative algebra of operators generating Lax pairs can be associated with a commutative C*-subalgebra in the C*-norm completion of the *-algebra. In relationship to the Bose-Fermi correspondence and the theory of vertex operators, this C*-algebra has an association with the CAR algebra of operators as represented on Fermionic Fock space by the Gelfand-Naimark-Segal construction. Instrumental is the Plücker embedding of the restricted Grassmannian into the projective space of the associated Hilbert space. The related Baker and tau-functions provide a connection between these two C*-algebras, following which their respective state spaces and Jordan-Lie-Banach algebras structures can be compared.

  6. Difficulties in initial algebra learning in Indonesia

    NASA Astrophysics Data System (ADS)

    Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

    2014-12-01

    Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.

  7. Multicloning and Multibroadcasting in Operator Algebras

    NASA Astrophysics Data System (ADS)

    Kaniowski, Krzysztof; Lubnauer, Katarzyna; Łuczak, Andrzej

    2015-12-01

    We investigate multicloning and multibroadcasting in the general operator algebra framework in arbitrary dimension, generalizing thus results obtained in this framework for simple cloning and broadcasting.

  8. Prospective Teachers' Views on the Use of Calculators with Computer Algebra System in Algebra Instruction

    ERIC Educational Resources Information Center

    Ozgun-Koca, S. Ash

    2010-01-01

    Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This…

  9. An Arithmetic-Algebraic Work Space for the Promotion of Arithmetic and Algebraic Thinking: Triangular Numbers

    ERIC Educational Resources Information Center

    Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos

    2016-01-01

    This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…

  10. LARGE EDDY SIMULATION OF TURBULENT FLOW OVER MARGINALLY RESOLVED THREE BLUFF BODIES USING AN IMMERSED BOUNDARY METHOD AND LAGRANGIAN DYNAMIC EDDY-VISCOSITY MODELS. (R828771C004)

    EPA Science Inventory

    The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...

  11. Entropy-viscosity based LES of turbulent flow in a flexible pipe

    NASA Astrophysics Data System (ADS)

    Wang, Zhicheng; Xie, Fangfang; Triantafyllou, Michael; Constantinides, Yiannis; Karniadakis, George

    2016-11-01

    We present large-eddy simulations (LES) of turbulent flow in a flexible pipe conveying incompressible fluid. We are interested in quantifying the flow-structure interaction in terms of mean quantities and their variances. For the LES, we employ an Entropy Viscosity Method (EVM), implemented in a spectral element code. In previous work, we investigated laminar flow and studied the complex interaction between structural and internal flow dynamics and obtained a phase diagram of the transition between states as function of three non-dimensional quantities: the fluid-tension parameter, the dimensionless fluid velocity, and the Reynolds number. Here we extend our studies in the turbulence regime, Re from 5,000 to 50,000. The motion of the flexible pipe affects greatly the turbulence statistics of the pipe flow, with substantial differences for free (self-sustained) vibrations and prescribed (forced) vibrations.

  12. Effect of Viscosity on Liquid Curtain Stability

    NASA Astrophysics Data System (ADS)

    Mohammad Karim, Alireza; Suszynski, Wieslaw; Francis, Lorraine; Carvalho, Marcio; Dow Chemical Company Collaboration; PUC Rio Collaboration; University of Minnesota, Twin Cities Collaboration

    2016-11-01

    The effect of viscosity on the stability of Newtonian liquid curtains was explored by high-speed visualization. Glycerol/water solutions with viscosity ranging from 19.1 to 210 mPa.s were used as coating liquids. The experimental set-up used a slide die delivery and steel tube edge guides. The velocity along curtain at different positions was measured by tracking small particles at different flow conditions. The measurements revealed that away from edge guides, velocity is well described by free fall effect. However, close to edge guides, liquid moves slower, revealing formation of a viscous boundary layer. The size of boundary layer and velocity near edge guides are strong function of viscosity. The critical condition was determined by examining flow rate below which curtain broke. Curtain failure was initiated by growth of a hole within liquid curtain, close to edge guides. Visualization results showed that the hole forms in a circular shape then becomes elliptical as it grows faster in vertical direction compared to horizontal direction. As viscosity rises, minimum flow rate for destabilization of curtain increased, indicating connection between interaction with edge guides and curtain stability. We would like to acknowledge the financial support from the Dow Chemical Company.

  13. Viscosity Measurement using Drop Coalescence in Microgravity

    NASA Technical Reports Server (NTRS)

    Antar, Basil N.; Ethridge, Edwin; Maxwell, Daniel

    1999-01-01

    We present in here details of a new method, using drop coalescence, for application in microgravity environment for determining the viscosity of highly viscous undercooled liquids. The method has the advantage of eliminating heterogeneous nucleation at container walls caused by crystallization of undercooled liquids during processing. Also, due to the rapidity of the measurement, homogeneous nucleation would be avoided. The technique relies on both a highly accurate solution to the Navier-Stokes equations as well as on data gathered from experiments conducted in near zero gravity environment. The liquid viscosity is determined by allowing the computed free surface shape relaxation time to be adjusted in response to the measured free surface velocity of two coalescing drops. Results are presented from two validation experiments of the method which were conducted recently on board the NASA KC-135 aircraft. In these tests the viscosity of a highly viscous liquid, such as glycerine at different temperatures, was determined to reasonable accuracy using the liquid coalescence method. The experiments measured the free surface velocity of two glycerine drops coalescing under the action of surface tension alone in low gravity environment using high speed photography. The free surface velocity was then compared with the computed values obtained from different viscosity values. The results of these experiments were found to agree reasonably well with the calculated values.

  14. Viscosity in accretion discs. [for binary stars

    NASA Technical Reports Server (NTRS)

    Katz, J. I.

    1980-01-01

    Both HerX-1 and SS433 may contain accretion disks slaved to a precessing companion star. If so, it is possible to bound the effective viscosity in these disks. The results, in terms of the disk parameter alpha, are lower bounds of 0.01 for HerX-1 and of 0.1 for SS433.

  15. Bulk viscosity effects on ultrasonic thermoacoustic instability

    NASA Astrophysics Data System (ADS)

    Lin, Jeffrey; Scalo, Carlo; Hesselink, Lambertus

    2016-11-01

    We have carried out unstructured fully-compressible Navier-Stokes simulations of a minimal-unit traveling-wave ultrasonic thermoacoustic device in looped configuration. The model comprises a thermoacoustic stack with 85% porosity and a tapered area change to suppress the fundamental standing-wave mode. A bulk viscosity model, which accounts for vibrational and rotational molecular relaxation effects, is derived and implemented via direct modification of the viscous stress tensor, τij ≡ 2 μSij +λ/2 μ ∂uk/∂xk δij , where the bulk viscosity is defined by μb ≡ λ +2/3 μ . The effective bulk viscosity coefficient accurately captures acoustic absorption from low to high ultrasonic frequencies and matches experimental wave attenuation rates across five decades. Using pressure-based similitude, the model was downscaled from total length L = 2 . 58 m to 0 . 0258 m, corresponding to the frequency range f = 242 - 24200 Hz, revealing the effects of bulk viscosity and direct modification of the thermodynamic pressure. Simulations are carried out to limit cycle and exhibit growth rates consistent with linear stability analyses, based on Rott's theory.

  16. Modeling the Viscosity of Aluminosilicate Melts

    NASA Astrophysics Data System (ADS)

    Decterov, Sergei A.; Grundy, A. Nicholas; Jung, In-Ho; Pelton, Arthur D.

    2007-12-01

    Silicate systems are of fundamental importance for many metallurgical processes, for the glass industry and also for many aspects of geology. In addition to the phase relations, there are many properties of the liquid phase such as molar volume, surface tension, absorption coefficient, thermal conductivity and viscosity that are important for understanding, simulating and modeling processes involving silicate liquids. Over the past several years, through critical evaluation of all available thermodynamic and phase equilibrium data, we have developed a quantitative thermodynamic description of multicomponent silicate melts using the Modified Quasichemical Model for short-range ordering. We find that the local structure of the liquid, in terms of the bridging behavior of oxygen, calculated using our thermodynamic description allows us to link the viscosity and the thermodynamics of the silicate liquid. We can thus simultaneously calculate phase relations, thermodynamics and viscosity of the liquid over a wide composition and temperature range. In the present work we outline the viscosity model using selected binary and ternary systems as examples. The model has successfully been applied to melts in the multicomponent Na2O-K2O-MgO-CaO-MnO-FeO-ZnO-PbO-Al2O3-SiO2 system and more elements are currently being added to the database.

  17. Sensor for Viscosity and Shear Strength Measurement

    SciTech Connect

    Dillon, J.; Moore, J.E. Jr.; Ebadian, M.A.; Jones, W.K.

    1998-10-20

    Measurement of the physical properties (viscosity and density) of waste slurries is critical in evaluating transport parameters to ensure turbulent flow through transport pipes. The environment for measurement and sensor exposure is extremely harsh; therefore, reliability and ruggedness are critical in the sensor design. The work for this project will be performed in three phases. The first phase, carried out in FY96, involved (1) an evaluation of acoustic and other methods for viscosity measurement; (2) measurement of the parameters of slurries over the range of percent solids found in tanks and transport systems; (3) a comparison of physical properties (e.g., viscosity and density) to percent solids found composition; and (4) the design of a prototype sensor. The second phase (FY97) will involve the fabrication of a prototype hybrid sensor to measure the viscosity and mechanical properties of slurries in remote, high-radiation environments. Two different viscometer designs are being investigated in this study: a magnetostrictive pulse wave guide viscometer; an oscillating cylinder viscometer. In FY97, the Hemispheric Center for Environmental Technology (HCET) at Florida International University (FIU), which has printed circuit, thick film, thin film, and co-fired ceramic fabrication capability, will fabricate five probes for demonstration after technology selection and evaluation.

  18. Heat flux viscosity in collisional magnetized plasmas

    SciTech Connect

    Liu, C.; Fox, W.; Bhattacharjee, A.

    2015-05-15

    Momentum transport in collisional magnetized plasmas due to gradients in the heat flux, a “heat flux viscosity,” is demonstrated. Even though no net particle flux is associated with a heat flux, in a plasma there can still be momentum transport owing to the velocity dependence of the Coulomb collision frequency, analogous to the thermal force. This heat-flux viscosity may play an important role in numerous plasma environments, in particular, in strongly driven high-energy-density plasma, where strong heat flux can dominate over ordinary plasma flows. The heat flux viscosity can influence the dynamics of the magnetic field in plasmas through the generalized Ohm's law and may therefore play an important role as a dissipation mechanism allowing magnetic field line reconnection. The heat flux viscosity is calculated directly using the finite-difference method of Epperlein and Haines [Phys. Fluids 29, 1029 (1986)], which is shown to be more accurate than Braginskii's method [S. I. Braginskii, Rev. Plasma Phys. 1, 205 (1965)], and confirmed with one-dimensional collisional particle-in-cell simulations. The resulting transport coefficients are tabulated for ease of application.

  19. Spiders Tune Glue Viscosity to Maximize Adhesion.

    PubMed

    Amarpuri, Gaurav; Zhang, Ci; Diaz, Candido; Opell, Brent D; Blackledge, Todd A; Dhinojwala, Ali

    2015-11-24

    Adhesion in humid conditions is a fundamental challenge to both natural and synthetic adhesives. Yet, glue from most spider species becomes stickier as humidity increases. We find the adhesion of spider glue, from five diverse spider species, maximizes at very different humidities that matches their foraging habitats. By using high-speed imaging and spreading power law, we find that the glue viscosity varies over 5 orders of magnitude with humidity for each species, yet the viscosity at maximal adhesion for each species is nearly identical, 10(5)-10(6) cP. Many natural systems take advantage of viscosity to improve functional response, but spider glue's humidity responsiveness is a novel adaptation that makes the glue stickiest in each species' preferred habitat. This tuning is achieved by a combination of proteins and hygroscopic organic salts that determines water uptake in the glue. We therefore anticipate that manipulation of polymer-salts interaction to control viscosity can provide a simple mechanism to design humidity responsive smart adhesives.

  20. Pressure-viscosity coefficient of biobased lubricants

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Film thickness is an important tribological property that is dependent on the combined effect of lubricant properties, material property of friction surfaces, and the operating conditions of the tribological process. Pressure-viscosity coefficient (PVC) is one of the lubricant properties that influe...

  1. Constraints on Crustal Viscosity from Geodetic Observations

    NASA Astrophysics Data System (ADS)

    Houseman, Gregory

    2015-04-01

    Laboratory measurements of the ductile deformation of crustal rocks demonstrate a range of crystal deformation mechanisms that may be represented by a viscous deformation law, albeit one in which the effective viscosity may vary by orders of magnitude, depending on temperature, stress, grain size, water content and other factors. In such measurements these factors can be separately controlled and effective viscosities can be estimated more or less accurately, though the measured deformation occurs on much shorter time scales and length scales than are typical of geological deformation. To obtain bulk measures of the in situ crustal viscosity law for actual geological processes, estimated stress differences are balanced against measured surface displacement or strain rates: at the continental scale, surface displacement and strain rates can be effectively measured using GPS, and stress differences can be estimated from the distribution of gravitational potential energy; this method has provided constraints on a depth-averaged effective viscosity for the lithosphere as a whole in regions that are actively deforming. Another technique measures the post-seismic displacements that are interpreted to occur in the aftermath of a large crustal earthquake. Stress-differences here are basically constrained by the co-seismic deformation and the elastic rigidity (obtained from seismic velocity) and the strain rates are again provided by GPS. In this technique the strain is a strong function of position relative to the fault, so in general the interpretation of this type of data depends on a complex calculation in which various simplifying assumptions must be made. The spatial variation of displacement history on the surface in this case contains information about the spatial variation of viscosity within the crust. Recent post-seismic studies have shown the potential for obtaining measurements of both depth variation and lateral variation of viscosity in the crust beneath

  2. Effects of eddy initial conditions on nonlinear forcing of planetary scale waves by amplifying baroclinic eddies

    NASA Technical Reports Server (NTRS)

    Young, Richard E.

    1986-01-01

    The previous study of Young and Villere concerning growth of planetary scale waves forced by wave-wave interactions of amplifying intermediate scale baroclinic eddies is extended to investigate effects of different eddy initial conditions. A global, spectral, primitive equation model is used for the calculations. For every set of eddy initial conditions considered, growth rates of planetary modes are considerably greater than growth rates computed from linear instability theory for a fixed zonally independent basic state. However, values of growth rates ranged over a factor of 3 depending on the particular set of eddy initial conditions used. Nonlinear forcing of planetary modes via wave-wave coupling becomes more important than baroclinic growth on the basic state at small values of the intermediate-scale modal amplitudes. The relative importance of direct transfer of kinetic energy from intermediate scales of motion to a planetary mode, compared to baroclinic conversion of available potential energy to kinetic energy within that planetary mode, depends on the individual case. In all cases, however, the transfer of either kinetic or available potential energy to the planetary modes was accomplished principally by wave-wave transfer from intermediate scale eddies, rather than from the zonally averaged state. The zonal wavenumber 2 planetary mode was prominent in all solutions, even in those for which eddy initial conditions were such that a different planetary mode was selectively forced at the start. General characteristics of the structural evolution of the planetary wave components of total heat and momentum flux, and modal structures themselves, were relatively insensitive to variations in eddy initial conditions, even though quantitative details varied from case to case.

  3. Reference Correlation for the Viscosity of Ethane

    NASA Astrophysics Data System (ADS)

    Vogel, Eckhard; Span, Roland; Herrmann, Sebastian

    2015-12-01

    A new representation of the viscosity for the fluid phase of ethane includes a zero-density correlation and a contribution for the critical enhancement, initially both developed separately, but based on experimental data. The higher-density contributions are correlated as a function of the reduced density δ = ρ/ρc and of the reciprocal reduced temperature τ = Tc/T (ρc—critical density and Tc—critical temperature). The final formulation contains 14 coefficients obtained using a state-of-the-art linear optimization algorithm. The evaluation and choice of the selected primary data sets is reviewed, in particular with respect to the assessment used in earlier viscosity correlations. The new viscosity surface correlation makes use of the reference equation of state for the thermodynamic properties of ethane by Bücker and Wagner [J. Phys. Chem. Ref. Data 35, 205 (2006)] and is valid in the fluid region from the melting line to temperatures of 675 K and pressures of 100 MPa. The viscosity in the limit of zero density is described with an expanded uncertainty of 0.5% (coverage factor k = 2) for temperatures 290 < T/K < 625, increasing to 1.0% at temperatures down to 212 K. The uncertainty of the correlated values is 1.5% in the range 290 < T/K < 430 at pressures up to 30 MPa on the basis of recent measurements judged to be very reliable as well as 4.0% and 6.0% in further regions. The uncertainty in the near-critical region (1.001 < 1/τ < 1.010 and 0.8 < δ < 1.2) increases with decreasing temperature up to 3.0% considering the available reliable data. Tables of the viscosity calculated from the correlation are listed in an appendix for the single-phase region, for the vapor-liquid phase boundary, and for the near-critical region.

  4. Classification of filiform Lie algebras of order 3

    NASA Astrophysics Data System (ADS)

    Navarro, Rosa María

    2016-12-01

    Lie algebras of order 3 constitute a generalization of Lie algebras and superalgebras. Throughout this paper the classification problem of filiform Lie algebras of order 3 is considered and therefore this work is a continuation papers seen in the literature. We approach this classification by extending Vergne's result for filiform Lie algebras and by considering algebras of order 3 of high nilindex. We find the expression of the law to which any elementary filiform Lie algebra of order 3 is isomorphic.

  5. The Algebra of Lexical Semantics

    NASA Astrophysics Data System (ADS)

    Kornai, András

    The current generative theory of the lexicon relies primarily on tools from formal language theory and mathematical logic. Here we describe how a different formal apparatus, taken from algebra and automata theory, resolves many of the known problems with the generative lexicon. We develop a finite state theory of word meaning based on machines in the sense of Eilenberg [11], a formalism capable of describing discrepancies between syntactic type (lexical category) and semantic type (number of arguments). This mechanism is compared both to the standard linguistic approaches and to the formalisms developed in AI/KR.

  6. Conditions of viscosity measurement for detecting irradiated peppers

    NASA Astrophysics Data System (ADS)

    Hayashi, Toru; Todoriki, Setsuko; Okadome, Hiroshi; Kohyama, Kaoru

    1995-04-01

    Viscosity of gelatinized suspensions of black and white peppers decreased depending upon dose. The viscosity was influenced by gelatinization and viscosity measurement conditions. The difference between unirradiated pepper and an irradiated one was larger at a higher pH and temperature for gelatinization. A viscosity parameter normalized with the starch content of pepper sample and the viscosity of a 5% suspension of corn starch could get rid of the influence of the conditions for viscosity measurement such as a type of viscometer, shear rate and temperature.

  7. Effects of the mean velocity field on the renormalized turbulent viscosity and correlation function

    NASA Astrophysics Data System (ADS)

    Kumar, Abhishek; Verma, Mahendra

    2015-11-01

    We perform renormalization group analysis of the Navier Stokes equation in the Eulerian framework in the presence of mean velocity field U0, and observe that that the renormalized viscosity ν (k) is independent of U0, where k is the wavenumber. Thus we show that ν (k) in the Eulerian field theory is Galilean invariant. We also compute ν (k) using numerical simulations and verify the above theoretical prediction. The velocity-velocity correlation function however exhibits damped oscillations whose time period of oscillation and damping time scales are given by 1 / kU0 and 1 / (ν (k) k2) respectively. In a modified form of Kraichnan's direct interaction approximation (DIA), the ``random mean velocity field'' of the large eddies sweeps the small-scale fluctuations. The DIA calculations also reveal that in the weak turbulence limit, the energy spectrum E (k) ~k - 3 / 2 , but for the strong turbulence limit, the random velocity field of the large-scale eddies is scale-dependent that leads to Kolmogorov's energy spectrum.

  8. Oceanic mass transport by mesoscale eddies.

    PubMed

    Zhang, Zhengguang; Wang, Wei; Qiu, Bo

    2014-07-18

    Oceanic transports of heat, salt, fresh water, dissolved CO2, and other tracers regulate global climate change and the distribution of natural marine resources. The time-mean ocean circulation transports fluid as a conveyor belt, but fluid parcels can also be trapped and transported discretely by migrating mesoscale eddies. By combining available satellite altimetry and Argo profiling float data, we showed that the eddy-induced zonal mass transport can reach a total meridionally integrated value of up to 30 to 40 sverdrups (Sv) (1 Sv = 10(6) cubic meters per second), and it occurs mainly in subtropical regions, where the background flows are weak. This transport is comparable in magnitude to that of the large-scale wind- and thermohaline-driven circulation.

  9. Eddy current signal comparison for tube identification

    SciTech Connect

    Glass, S. W. E-mail: Ratko.Vojvodic@areva.com; Vojvodic, R. E-mail: Ratko.Vojvodic@areva.com

    2015-03-31

    Inspection of nuclear power plant steam generator tubes is required to justify continued safe plant operation. The steam generators consist of thousands of tubes with nominal diameters of 15 to 22mm, approximately 1mm wall thickness, and 20 to 30m in length. The tubes are inspected by passing an eddy current probe through the tubes from tube end to tube end. It is critical to know exactly which tube identification (row and column) is associated with each tube's data. This is controlled by a precision manipulator that provides the tube ID to the eddy current system. Historically there have been some instances where the manipulator incorrectly reported the tube ID. This can have serious consequences including lack of inspection of a tube, or if a pluggable indication is detected, the tube is likely to be mis-plugged thereby risking a primary to secondary leak.

  10. Contoured Surface Eddy Current Inspection System

    DOEpatents

    Batzinger, Thomas James; Fulton, James Paul; Rose, Curtis Wayne; Perocchi, Lee Cranford

    2003-04-08

    Eddy current inspection of a contoured surface of a workpiece is performed by forming a backing piece of flexible, resiliently yieldable material with a contoured exterior surface conforming in shape to the workpiece contoured surface. The backing piece is preferably cast in place so as to conform to the workpiece contoured surface. A flexible eddy current array probe is attached to the contoured exterior surface of the backing piece such that the probe faces the contoured surface of the workpiece to be inspected when the backing piece is disposed adjacent to the workpiece. The backing piece is then expanded volumetrically by inserting at least one shim into a slot in the backing piece to provide sufficient contact pressure between the probe and the workpiece contoured surface to enable the inspection of the workpiece contoured surface to be performed.

  11. Eddy current signal comparison for tube identification

    NASA Astrophysics Data System (ADS)

    Glass, S. W.; Vojvodic, R.

    2015-03-01

    Inspection of nuclear power plant steam generator tubes is required to justify continued safe plant operation. The steam generators consist of thousands of tubes with nominal diameters of 15 to 22mm, approximately 1mm wall thickness, and 20 to 30m in length. The tubes are inspected by passing an eddy current probe through the tubes from tube end to tube end. It is critical to know exactly which tube identification (row and column) is associated with each tube's data. This is controlled by a precision manipulator that provides the tube ID to the eddy current system. Historically there have been some instances where the manipulator incorrectly reported the tube ID. This can have serious consequences including lack of inspection of a tube, or if a pluggable indication is detected, the tube is likely to be mis-plugged thereby risking a primary to secondary leak.

  12. Strengthening Effect Algebras in a Logical Perspective: Heyting-Wajsberg Algebras

    NASA Astrophysics Data System (ADS)

    Konig, Martinvaldo

    2014-10-01

    Heyting effect algebras are lattice-ordered pseudoboolean effect algebras endowed with a pseudocomplementation that maps on the center (i.e. Boolean elements). They are the algebraic counterpart of an extension of both Łukasiewicz many-valued logic and intuitionistic logic. We show that Heyting effect algebras are termwise equivalent to Heyting-Wajsberg algebras where the two different logical implications are defined as primitive operators. We prove this logic to be decidable, to be strongly complete and to have the deduction-detachment theorem.

  13. Large Eddy Simulation of Turbulent Combustion

    DTIC Science & Technology

    2006-03-15

    Application to an HCCI Engine . Proceedings of the 4th Joint Meeting of the U.S. Sections of the Combustion Institute, 2005. [34] K. Fieweger...LARGE EDDY SIMULATION OF TURBULENT COMBUSTION Principle Investigator: Heinz Pitsch Flow Physics and Computation Department of Mechanical Engineering ...burners and engines found in modern, industrially relevant equipment. In the course of this transition of LES from a scientifically interesting method

  14. INNOVATIVE EDDY CURRENT PROBE FOR MICRO DEFECTS

    SciTech Connect

    Santos, Telmo G.; Vilaca, Pedro; Quintino, Luisa; Santos, Jorge dos; Rosado, Luis

    2010-02-22

    This paper reports the development of an innovative eddy current (EC) probe, and its application to micro-defects on the root of the Friction Stir Welding (FSW). The new EC probe presents innovative concept issues, allowing 3D induced current in the material, and a lift-off independence. Validation experiments were performed on aluminium alloys processed by FSW. The results clearly show that the new EC probe is able to detect and sizing surface defects about 60 microns depth.

  15. HYCOM High-resolution Eddying Simulations

    DTIC Science & Technology

    2014-07-01

    number of vertical profiles of temperature and salinity in place of XBT temperature profiles. The reanalysis was completed in February 2014. As noted...10.1016/j.ocemod.2011.02.011. Metzger, E. J., and Coauthors, 2014a: US Navy operational global ocean and Arctic ice prediction systems. Oceanography...has collaborated on developing and demonstrating the performance and application of eddy-resolving, real-time global and basin-scale ocean prediction

  16. Anisotropic Mesoscale Eddy Transport in Ocean General Circulation Models

    NASA Astrophysics Data System (ADS)

    Reckinger, S. J.; Fox-Kemper, B.; Bachman, S.; Bryan, F.; Dennis, J.; Danabasoglu, G.

    2014-12-01

    Modern climate models are limited to coarse-resolution representations of large-scale ocean circulation that rely on parameterizations for mesoscale eddies. The effects of eddies are typically introduced by relating subgrid eddy fluxes to the resolved gradients of buoyancy or other tracers, where the proportionality is, in general, governed by an eddy transport tensor. The symmetric part of the tensor, which represents the diffusive effects of mesoscale eddies, is universally treated isotropically in general circulation models. Thus, only a single parameter, namely the eddy diffusivity, is used at each spatial and temporal location to impart the influence of mesoscale eddies on the resolved flow. However, the diffusive processes that the parameterization approximates, such as shear dispersion, potential vorticity barriers, oceanic turbulence, and instabilities, typically have strongly anisotropic characteristics. Generalizing the eddy diffusivity tensor for anisotropy extends the number of parameters to three: a major diffusivity, a minor diffusivity, and the principal axis of alignment. The Community Earth System Model (CESM) with the anisotropic eddy parameterization is used to test various choices for the newly introduced parameters, which are motivated by observations and the eddy transport tensor diagnosed from high resolution simulations. Simply setting the ratio of major to minor diffusivities to a value of five globally, while aligning the major axis along the flow direction, improves biogeochemical tracer ventilation and reduces global temperature and salinity biases. These effects can be improved even further by parameterizing the anisotropic transport mechanisms in the ocean.

  17. Interface Exchange as an Indicator for Eddy Heat Transport

    SciTech Connect

    Petersen, Mark R.; Williams, Sean J.; Hecht, Matthew W.; Maltrud, Mathew E.; Hamann, Bernd; Patchett, John M.; Ahrens, James P.

    2012-06-12

    The ocean contains many large-scale, long-lived vortices, called mesoscale eddies, that are believed to have a role in the transport and redistribution of salt, heat, and nutrients throughout the ocean. Determining this role, however, has proven to be a challenge, since the mechanics of eddies are only partly understood; a standard definition for these ocean eddies does not exist and, therefore, scientifically meaningful, robust methods for eddy extraction, characterization, tracking and visualization remain a challenge. In order to shed light on the nature and potential roles of eddies, we have combined our previous research on eddy identification and tracking, and have used those approaches as the basis for analysis-driven computational experiments on the nature of eddies. Based on the resulting visualizations of eddy behavior, we have devised a new metric to characterize the transfer of water into and out of eddies across their boundary, and have developed visualization methods for this new metric to provide clues about the role eddies play in the global ocean and, potentially, climate change.

  18. Eddy current inspection tool. [Patent application

    DOEpatents

    Petrini, R.R.; Van Lue, D.F.

    1980-10-29

    A miniaturized inspection tool, for testing and inspection of metal objects in locations with difficult accessibility, which comprises eddy current sensing equipment with a probe coil, and associated coaxial coil cable, oil energizing means, and circuit means responsive to impedance changes in the coil as effected by induced eddy currents in a test object to produce a data output signal proportional to such changes. The coil and cable are slideably received in the utility channel of the flexible insertion tube of a fiberoptic scope. The scope is provided with light transmitting and receiving fiberoptics for viewing through the flexible tube, and articulation means for articulating the distal end of the tube and permitting close control of coil placement relative to a test object. The eddy current sensing equipment includes a tone generator for generating audible signals responsive to the data output signal. In one selected mode of operation, the tone generator responsive to the output signal above a selected level generates a constant single frequency tone for signalling detection of a discontinuity and, in a second selected mode, generates a tone whose frequency is proportional to the difference between the output signal and a predetermined selected threshold level.

  19. Algebraic Thinking: A Problem Solving Approach

    ERIC Educational Resources Information Center

    Windsor, Will

    2010-01-01

    Algebraic thinking is a crucial and fundamental element of mathematical thinking and reasoning. It initially involves recognising patterns and general mathematical relationships among numbers, objects and geometric shapes. This paper will highlight how the ability to think algebraically might support a deeper and more useful knowledge, not only of…

  20. Learning from Student Approaches to Algebraic Proofs

    ERIC Educational Resources Information Center

    D'Ambrosio, Beatriz S.; Kastberg, Signe E.; Viola dos Santos, Joao Ricardo

    2010-01-01

    Many mathematics teachers struggle to support their students' developing understanding of proof as an essential element in investigations of mathematics. The area of mathematics where the development of an understanding of proof is most challenging is algebra. In the case of algebraic proof, analysis of student written work on tasks that demand…

  1. From operator algebras to superconformal field theory

    SciTech Connect

    Kawahigashi, Yasuyuki

    2010-01-15

    We survey operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory of Jones, and certain aspects of noncommutative geometry of Connes.

  2. A Technology-Intensive Approach to Algebra.

    ERIC Educational Resources Information Center

    Heid, M. Kathleen; Zbiek, Rose Mary

    1995-01-01

    Computer-Intensive Algebra (CIA) focuses on the use of technology to help develop a rich understanding of fundamental algebraic concepts in real-world settings using computing tools for easy access to numerical, graphical, and symbolic representations of mathematical ideas. (MKR)

  3. Focus on Fractions to Scaffold Algebra

    ERIC Educational Resources Information Center

    Ooten, Cheryl Thomas

    2013-01-01

    Beginning algebra is a gatekeeper course into the pipeline to higher mathematics courses required for respected professions in engineering, science, statistics, mathematics, education, and technology. Beginning algebra can also be a perfect storm if the necessary foundational skills are not within a student's grasp. What skills ensure beginning…

  4. Post-Lie Algebras and Isospectral Flows

    NASA Astrophysics Data System (ADS)

    Ebrahimi-Fard, Kurusch; Lundervold, Alexander; Mencattini, Igor; Munthe-Kaas, Hans Z.

    2015-11-01

    In this paper we explore the Lie enveloping algebra of a post-Lie algebra derived from a classical R-matrix. An explicit exponential solution of the corresponding Lie bracket flow is presented. It is based on the solution of a post-Lie Magnus-type differential equation.

  5. Teaching Modeling and Axiomatization with Boolean Algebra.

    ERIC Educational Resources Information Center

    De Villiers, Michael D.

    1987-01-01

    Presented is an alternative approach to the traditional teaching of Boolean algebra for secondary school mathematics. The main aim of the approach is to use Boolean algebra to teach pupils such mathematical processes as modeling and axiomatization. A course using the approach is described. (RH)

  6. Arithmetic and Cognitive Contributions to Algebra

    ERIC Educational Resources Information Center

    Cirino, Paul T.; Tolar, Tammy D.; Fuchs, Lynn S.

    2013-01-01

    Algebra is a prerequisite for access to STEM careers and occupational success (NMAP, 2008a), yet algebra is difficult for students through high school (US DOE, 2008). Growth in children's conceptual and procedural arithmetical knowledge is reciprocal, although conceptual knowledge has more impact on procedural knowledge than the reverse…

  7. Algebraic Thinking through Koch Snowflake Constructions

    ERIC Educational Resources Information Center

    Ghosh, Jonaki B.

    2016-01-01

    Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…

  8. Calif. Laws Shift Gears on Algebra, Textbooks

    ERIC Educational Resources Information Center

    Robelen, Erik W.

    2012-01-01

    New laws in California have set the state on a course for some potentially significant changes to the curriculum, including a measure that revisits the matter of teaching Algebra 1 in 8th grade and another that revamps the state's textbook-adoption process and hands districts greater leeway in choosing instructional materials. The algebra-related…

  9. Using Students' Interests as Algebraic Models

    ERIC Educational Resources Information Center

    Whaley, Kenneth A.

    2012-01-01

    Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…

  10. An algebraic approach to the scattering equations

    NASA Astrophysics Data System (ADS)

    Huang, Rijun; Rao, Junjie; Feng, Bo; He, Yang-Hui

    2015-12-01

    We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.

  11. THE RADICAL OF A JORDAN ALGEBRA

    PubMed Central

    McCrimmon, Kevin

    1969-01-01

    In this paper we define a Jacobson radical for Jordan algebras analogous to that for associative algebras and show that it enjoys many of the properties of the associative radical. We then relate the corresponding notion of “semisimplicity” to the previously defined notion of “nondegeneracy” (Jacobson, N., these Proceedings, 55, 243-251 (1966)). PMID:16591736

  12. Cartan calculus on quantum Lie algebras

    SciTech Connect

    Schupp, P.; Watts, P.; Zumino, B.

    1993-12-09

    A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions au into one big algebra, the ``Cartan Calculus.``

  13. The operator algebra approach to quantum groups

    PubMed Central

    Kustermans, Johan; Vaes, Stefaan

    2000-01-01

    A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory. PMID:10639116

  14. Using the Internet To Investigate Algebra.

    ERIC Educational Resources Information Center

    Sherwood, Walter

    The lesson plans in this book engage students by using a tool they enjoy--the Internet--to explore key concepts in algebra. Working either individually or in groups, students learn to approach algebra from a problem solving perspective. Each lesson shows learners how to use the Internet as a resource for gathering facts, data, and other…

  15. Teaching Algebra to Students with Learning Disabilities

    ERIC Educational Resources Information Center

    Impecoven-Lind, Linda S.; Foegen, Anne

    2010-01-01

    Algebra is a gateway to expanded opportunities, but it often poses difficulty for students with learning disabilities. Consequently, it is essential to identify evidence-based instructional strategies for these students. The authors begin by identifying three areas of algebra difficulty experienced by students with disabilities: cognitive…

  16. Gary M. Klingler Algebra Teacher Assistance Packages

    ERIC Educational Resources Information Center

    Klingler, Gary

    2005-01-01

    Several packages designed by Elizabeth Marquez for mathematics teachers of grades 6-12, officially entitled the Teacher Assistance Package in Support of Better Algebra Assessment, is a series of resources developed to accompany ET's End-of-Course Algebra Assessment. It is designed to enhance teachers classroom assessment by providing examples of…

  17. Just Say Yes to Early Algebra!

    ERIC Educational Resources Information Center

    Stephens, Ana; Blanton, Maria; Knuth, Eric; Isler, Isil; Gardiner, Angela Murphy

    2015-01-01

    Mathematics educators have argued for some time that elementary school students are capable of engaging in algebraic thinking and should be provided with rich opportunities to do so. Recent initiatives like the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) have taken up this call by reiterating the place of early algebra in…

  18. Symbolic Notations and Students' Achievements in Algebra

    ERIC Educational Resources Information Center

    Peter, Ebiendele E.; Olaoye, Adetunji A.

    2013-01-01

    This study focuses on symbolic notations and its impact on students' achievement in Algebra. The main reason for this study rests on the observation from personal and professional experiences on students' increasing hatred for Algebra. One hundred and fifty (150) Senior Secondary School Students (SSS) from Ojo Local Education District, Ojo, Lagos,…

  19. SAYD Modules over Lie-Hopf Algebras

    NASA Astrophysics Data System (ADS)

    Rangipour, Bahram; Sütlü, Serkan

    2012-11-01

    In this paper a general van Est type isomorphism is proved. The isomorphism is between the Lie algebra cohomology of a bicrossed sum Lie algebra and the Hopf cyclic cohomology of its Hopf algebra. We first prove a one to one correspondence between stable-anti-Yetter-Drinfeld (SAYD) modules over the total Lie algebra and those modules over the associated Hopf algebra. In contrast to the non-general case done in our previous work, here the van Est isomorphism is proved at the first level of a natural spectral sequence, rather than at the level of complexes. It is proved that the Connes-Moscovici Hopf algebras do not admit any finite dimensional SAYD modules except the unique one-dimensional one found by Connes-Moscovici in 1998. This is done by extending our techniques to work with the infinite dimensional Lie algebra of formal vector fields. At the end, the one to one correspondence is applied to construct a highly nontrivial four dimensional SAYD module over the Schwarzian Hopf algebra. We then illustrate the whole theory on this example. Finally explicit representative cocycles of the cohomology classes for this example are calculated.

  20. Algebraic Formulas for Areas between Curves.

    ERIC Educational Resources Information Center

    Gabai, Hyman

    1982-01-01

    Korean secondary school students preparing for college learn about a simple algebraic formula for area bounded by a parabola and line. The approach does not seem well-known among American students. It is noted that, while the formula derivations rely on integration, algebra students could use the formulas without proofs. (MP)

  1. Some Applications of Algebraic System Solving

    ERIC Educational Resources Information Center

    Roanes-Lozano, Eugenio

    2011-01-01

    Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact…

  2. An Inquiry-Based Linear Algebra Class

    ERIC Educational Resources Information Center

    Wang, Haohao; Posey, Lisa

    2011-01-01

    Linear algebra is a standard undergraduate mathematics course. This paper presents an overview of the design and implementation of an inquiry-based teaching material for the linear algebra course which emphasizes discovery learning, analytical thinking and individual creativity. The inquiry-based teaching material is designed to fit the needs of a…

  3. Practicing Algebraic Skills: A Conceptual Approach

    ERIC Educational Resources Information Center

    Friedlander, Alex; Arcavi, Abraham

    2012-01-01

    Traditionally, a considerable part of teaching and learning algebra has focused on routine practice and the application of rules, procedures, and techniques. Although today's computerized environments may have decreased the need to master algebraic skills, procedural competence is still a central component in any mathematical activity. However,…

  4. Success in Algebra among Community College Students

    ERIC Educational Resources Information Center

    Reyes, Czarina

    2010-01-01

    College algebra is a required course for most majors, but is viewed by many as a gatekeeper course for degree completion by students. With almost half a million students taking college algebra each year, faculty are experimenting with new course lengths of time that might result in higher success, completion, and retention rates for college…

  5. Is Algebra Really Difficult for All Students?

    ERIC Educational Resources Information Center

    Egodawatte, Gunawardena

    2009-01-01

    Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…

  6. Estimating the effective Reynolds number in implicit large-eddy simulation.

    PubMed

    Zhou, Ye; Grinstein, Fernando F; Wachtor, Adam J; Haines, Brian M

    2014-01-01

    In implicit large-eddy simulation (ILES), energy-containing large scales are resolved, and physics capturing numerics are used to spatially filter out unresolved scales and to implicitly model subgrid scale effects. From an applied perspective, it is highly desirable to estimate a characteristic Reynolds number (Re)-and therefore a relevant effective viscosity-so that the impact of resolution on predicted flow quantities and their macroscopic convergence can usefully be characterized. We argue in favor of obtaining robust Re estimates away from the smallest scales of the simulated flow-where numerically controlled dissipation takes place and propose a theoretical basis and framework to determine such measures. ILES examples include forced turbulence as a steady flow case, the Taylor-Green vortex to address transition and decaying turbulence, and simulations of a laser-driven reshock experiment illustrating a fairly complex turbulence problem of current practical interest.

  7. MODEL IDENTIFICATION AND COMPUTER ALGEBRA.

    PubMed

    Bollen, Kenneth A; Bauldry, Shawn

    2010-10-07

    Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods.

  8. LINPACK. Simultaneous Linear Algebraic Equations

    SciTech Connect

    Miller, M.A.

    1990-05-01

    LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE General, GB General band, PO Positive definite, PP Positive definite packed, PB Positive definite band, SI Symmetric indefinite, SP Symmetric indefinite packed, HI Hermitian indefinite, HP Hermitian indefinite packed, TR Triangular, GT General tridiagonal, PT Positive definite tridiagonal, CH Cholesky decomposition, QR Orthogonal-triangular decomposition, SV Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA Factor, CO Factor and estimate condition, SL Solve, DI Determinant and/or inverse and/or inertia, DC Decompose, UD Update, DD Downdate, EX Exchange. The LINPACK package also includes a set of routines to perform basic vector operations called the Basic Linear Algebra Subprograms (BLAS).

  9. LINPACK. Simultaneous Linear Algebraic Equations

    SciTech Connect

    Dongarra, J.J.

    1982-05-02

    LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE General, GB General band, PO Positive definite, PP Positive definite packed, PB Positive definite band, SI Symmetric indefinite, SP Symmetric indefinite packed, HI Hermitian indefinite, HP Hermitian indefinite packed, TR Triangular, GT General tridiagonal, PT Positive definite tridiagonal, CH Cholesky decomposition, QR Orthogonal-triangular decomposition, SV Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA Factor, CO Factor and estimate condition, SL Solve, DI Determinant and/or inverse and/or inertia, DC Decompose, UD Update, DD Downdate, EX Exchange. The LINPACK package also includes a set of routines to perform basic vector operations called the Basic Linear Algebra Subprograms (BLAS).

  10. Hexagonal tessellations in image algebra

    NASA Astrophysics Data System (ADS)

    Eberly, David H.; Wenzel, Dennis J.; Longbotham, Harold G.

    1990-11-01

    In image algebra '' the concept of a coordinate set X is general in that such a set is simply a subset of ndimensional Euclidean space . The standard applications in 2-dimensional image processing use coordinate sets which are rectangular arrays X 72 x ZZm. However some applications may require other geometries for the coordinate set. We look at three such related applications in the context of image algebra. The first application is the modeling of photoreceptors in primate retinas. These receptors are inhomogeneously distributed on the retina. The largest receptor density occurs in the center of the fovea and decreases radially outwards. One can construct a hexagonal tessellation of the retina such that each hexagon contains approximately the same number of receptors. The resulting tessellation called a sunflower heart2 consists of concentric rings of hexagons whose sizes increase as the radius of the ring increases. The second application is the modeling of the primary visual . The neurons are assumed to be uniformly distributed as a regular hexagonal lattice. Cortical neural image coding is modeled by a recursive convolution of the retinal neural image using a special set of filters. The third application involves analysis of a hexagonally-tessellated image where the pixel resolution is variable .

  11. Verification and calibration of Energy- and Flux-Budget (EFB) turbulence closure model through large eddy simulations and direct numerical simulations

    NASA Astrophysics Data System (ADS)

    Kadantsev, Evgeny; Fortelius, Carl; Druzhinin, Oleg; Mortikov, Evgeny; Glazunov, Andrey; Zilitinkevich, Sergej

    2016-04-01

    We examine and validate the EFB turbulence closure model (Zilitinkevich et al., 2013), which is based on the budget equations for basic second moments, namely, two energies: turbulent kinetic energy EK and turbulent potential energy EP, and vertical turbulent fluxes of momentum and potential temperature, τi (i = 1, 2) and Fz. Instead of traditional postulation of down-gradient turbulent transport, the EFB closure determines the eddy viscosity and eddy conductivity from the steady-state version of the budget equations for τi and Fz. Furthermore, the EFB closure involves new prognostic equation for turbulent dissipation time scale tT, and extends the theory to non-steady turbulence regimes accounting for non-gradient and non-local turbulent transports (when the traditional concepts of eddy viscosity and eddy conductivity become generally inconsistent). Our special interest is in asymptotic behavior of the EFB closure in strongly stable stratification. For this purpose, we consider plane Couette flow, namely, the flow between two infinite parallel plates, one of which is moving relative to another. We use a set of Direct Numerical Simulation (DNS) experiments at the highest possible Reynolds numbers for different bulk Richardson numbers (Druzhinin et al., 2015). To demonstrate potential improvements in Numerical Weather Prediction models, we test the new closure model in various idealized cases, varying stratification from the neutral and conventionally neutral to stable (GABLS1) running a test RANS model and HARMONIE/AROME model in single-column mode. Results are compared with DNS and LES (Large Eddy Simulation) runs and different numerical weather prediction models.

  12. Novel residual-based large eddy simulation turbulence models for incompressible magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Sondak, David

    The goal of this work was to develop, introduce, and test a promising computational paradigm for the development of turbulence models for incompressible magnetohydrodynamics (MHD). MHD governs the behavior of an electrically conducting fluid in the presence of an external electromagnetic (EM) field. The incompressible MHD model is used in many engineering and scientific disciplines from the development of nuclear fusion as a sustainable energy source to the study of space weather and solar physics. Many interesting MHD systems exhibit the phenomenon of turbulence which remains an elusive problem from all scientific perspectives. This work focuses on the computational perspective and proposes techniques that enable the study of systems involving MHD turbulence. Direct numerical simulation (DNS) is not a feasible approach for studying MHD turbulence. In this work, turbulence models for incompressible MHD were developed from the variational multiscale (VMS) formulation wherein the solution fields were decomposed into resolved and unresolved components. The unresolved components were modeled with a term that is proportional to the residual of the resolved scales. Two additional MHD models were developed based off of the VMS formulation: a residual-based eddy viscosity (RBEV) model and a mixed model that partners the VMS formulation with the RBEV model. These models are endowed with several special numerical and physics features. Included in the numerical features is the internal numerical consistency of each of the models. Physically, the new models are able to capture desirable MHD physics such as the inverse cascade of magnetic energy and the subgrid dynamo effect. The models were tested with a Fourier-spectral numerical method and the finite element method (FEM). The primary test problem was the Taylor-Green vortex. Results comparing the performance of the new models to DNS were obtained. The performance of the new models was compared to classic and cutting

  13. Generalization of n-ary Nambu algebras and beyond

    SciTech Connect

    Ataguema, H.; Makhlouf, A.; Silvestrov, S.

    2009-08-15

    The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type including n-ary Nambu algebras, n-ary Nambu-Lie algebras and n-ary Lie algebras, and n-ary algebras of associative type including n-ary totally associative and n-ary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an n-ary Hom-algebra structure starting from an n-ary algebra and an n-ary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three-dimensional Hom-Nambu-Lie structures with diagonal homomorphism.

  14. Molten Composition B Viscosity at Elevated Temperature

    NASA Astrophysics Data System (ADS)

    Zerkle, David K.; Núñez, Marcel P.; Zucker, Jonathan M.

    2016-10-01

    A shear-thinning viscosity model is developed for molten Composition B at elevated temperature from analysis of falling ball viscometer data. Results are reported with the system held at 85, 110, and 135°C. Balls of densities of 2.7, 8.0, and 15.6 g/cm3 are dropped to generate a range of strain rates in the material. Analysis of video recordings gives the speed at which the balls fall. Computer simulation of the viscometer is used to determine parameters for a non-Newtonian model calibrated to measured speeds. For the first time, viscosity is shown to be a function of temperature and strain rate-dependent maximum RDX (cyclotrimethylenetrinitramine) particle volume fraction.

  15. Viscosity function in polymer-modified asphalts.

    PubMed

    Stastna, J; Zanzotto, L; Vacin, O J

    2003-03-01

    Asphalt is a multidisperse micellar system with rheological behavior resembling that of a low-molecular-weight polymer. Nowadays, asphalt is frequently modified by blending it with various polymers. Such modified asphalt has rheological properties that differ from the properties of the base asphalt. It is quite common to study asphalt in dynamic experiments. Such studies, however useful, cannot reveal all characteristic features of polymer-modified asphalts. Asphalt modification by polymers is strongly manifested in the region of transitions from a viscoelastic fluid to the Newtonian fluid. The viscosity study in this region can reveal behavior characteristic of the used polymer modifier, thus complementing the dynamic studies of these materials. The viscosity of base asphalt modified by styrene-butadiene-styrene and by ethylene-vinyl acetate polymers (in several concentrations) is studied and discussed in this note.

  16. Prediction of viscosity of dense fluid mixtures

    NASA Astrophysics Data System (ADS)

    Royal, Damian D.; Vesovic, Velisa; Trusler, J. P. Martin; Wakeham, William. A.

    The Vesovic-Wakeham (VW) method of predicting the viscosity of dense fluid mixtures has been improved by implementing new mixing rules based on the rigid sphere formalism. The proposed mixing rules are based on both Lebowitz's solution of the Percus-Yevick equation and on the Carnahan-Starling equation. The predictions of the modified VW method have been compared with experimental viscosity data for a number of diverse fluid mixtures: natural gas, hexane + hheptane, hexane + octane, cyclopentane + toluene, and a ternary mixture of hydrofluorocarbons (R32 + R125 + R134a). The results indicate that the proposed improvements make possible the extension of the original VW method to liquid mixtures and to mixtures containing polar species, while retaining its original accuracy.

  17. A brief review on viscosity of nanofluids

    NASA Astrophysics Data System (ADS)

    Mishra, Purna Chandra; Mukherjee, Sayantan; Nayak, Santosh Kumar; Panda, Arabind

    2014-10-01

    Since the past decade, rapid development in nanotechnology has produced several aspects for the scientists and technologists to look into. Nanofluid is one of the incredible outcomes of such advancement. Nanofluids (colloidal suspensions of metallic and nonmetallic nanoparticles in conventional base fluids) are best known for their remarkable change to enhanced heat transfer abilities. Earlier research work has already acutely focused on thermal conductivity of nanofluids. However, viscosity is another important property that needs the same attention due to its very crucial impact on heat transfer. Therefore, viscosity of nanofluids should be thoroughly investigated before use for practical heat transfer applications. In this contribution, a brief review on theoretical models is presented precisely. Furthermore, the effects of nanoparticles' shape and size, temperature, volume concentration, pH, etc. are organized together and reviewed.

  18. Effective viscosity of magnetic nanofluids through capillaries.

    PubMed

    Patel, Rajesh

    2012-02-01

    The simultaneous effect of magnetic field and temperature on the capillary viscosity of magnetic nanofluid is an important parameter for a new class of applications such as nanoduct flow, nanomotors, micro- and nanofluidic devices, for transformer cooling, magnetic targeted drug delivery, etc. The effective viscosity of a nanofluid is explained based on the rotation of the particles and the effect of torque on it due to an externally applied magnetic field. Two types of fluids are used here, temperature-sensitive and non-temperature-sensitive magnetic nanofluids. In both types of fluids, decrease in effective viscosity with temperature is observed, but in both cases the mechanism for the decrement is quite different. One is due to temperature dependence of the magnetic moment and the other is due to removal of the secondary surfactant. For temperature-sensitive magnetic nanofluids, a Curie temperature of ~80 °C is extracted from this study. For non-temperature-sensitive magnetic nanofluids ~65% of the secondary surfactant is removed for a change in temperature, ΔT = 40 °C. This is analogous with removal of a drug from magnetic particles for targeted drug delivery. Further, a linear dependence of effective viscosity with different capillary size and ξ (angle between magnetic field and flow direction, ξε[0,π/2]) is also observed. This linear dependence can also be a good approximation for the study of magnetic drug targeting, as in the human body the capillaries are of different sizes, and the externally applied magnetic field is not always parallel or perpendicular to the drug flow direction.

  19. Effective viscosity of magnetic nanofluids through capillaries

    NASA Astrophysics Data System (ADS)

    Patel, Rajesh

    2012-02-01

    The simultaneous effect of magnetic field and temperature on the capillary viscosity of magnetic nanofluid is an important parameter for a new class of applications such as nanoduct flow, nanomotors, micro- and nanofluidic devices, for transformer cooling, magnetic targeted drug delivery, etc. The effective viscosity of a nanofluid is explained based on the rotation of the particles and the effect of torque on it due to an externally applied magnetic field. Two types of fluids are used here, temperature-sensitive and non-temperature-sensitive magnetic nanofluids. In both types of fluids, decrease in effective viscosity with temperature is observed, but in both cases the mechanism for the decrement is quite different. One is due to temperature dependence of the magnetic moment and the other is due to removal of the secondary surfactant. For temperature-sensitive magnetic nanofluids, a Curie temperature of ˜80 ∘C is extracted from this study. For non-temperature-sensitive magnetic nanofluids ˜65% of the secondary surfactant is removed for a change in temperature, ΔT = 40 ∘C. This is analogous with removal of a drug from magnetic particles for targeted drug delivery. Further, a linear dependence of effective viscosity with different capillary size and ξ (angle between magnetic field and flow direction, ξ∈[0,π/2]) is also observed. This linear dependence can also be a good approximation for the study of magnetic drug targeting, as in the human body the capillaries are of different sizes, and the externally applied magnetic field is not always parallel or perpendicular to the drug flow direction.

  20. A dynamic wall model for Large-Eddy simulations of wind turbine dedicated airfoils

    NASA Astrophysics Data System (ADS)

    J, Calafell; O, Lehmkuhl; A, Carmona; D, Pérez-Segarra C.; A, Oliva

    2014-06-01

    This work aims at modelling the flow behavior past a wind turbine dedicated airfoil at high Reynolds number and large angle of attack (AoA). The DU-93-W-210 airfoil has been selected. To do this, Large Eddy Simulations (LES) have been performed. Momentum equations have been solved with a parallel unstructured symmetry preserving formulation while the wall-adapting local-eddy viscosity model within a variational multi-scale framework (VMS- WALE) is used as the subgrid-scales model. Since LES calculations are still very expensive at high Reynolds Number, specially at the near-wall region, a dynamic wall model has been implemented in order to overcome this limitation. The model has been validated with a very unresolved Channel Flow case at Reτ = 2000. Afterwards, the model is also tested with the Ahmed Car case, that from the flow physics point of view is more similar to an stalled airfoil than the Channel Flow is, including flow features as boundary layer detachment and recirculations. This case has been selected because experimental results of mean velocity profiles are available. Finally, a flow around a DU-93-W-210 airfoil is computed at Re = 3 x 106 and with an AoA of 15°. Numerical results are presented in comparison with Direct Numerical Simulation (DNS) or experimental data for all cases.