Identifying finite-time coherent sets from limited quantities of Lagrangian data.
Williams, Matthew O; Rypina, Irina I; Rowley, Clarence W
2015-08-01
A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that "leak" from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, "data rich" test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or "mesh-free" methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea. PMID:26328579
Identifying finite-time coherent sets from limited quantities of Lagrangian data
NASA Astrophysics Data System (ADS)
Williams, Matthew O.; Rypina, Irina I.; Rowley, Clarence W.
2015-08-01
A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that "leak" from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, "data rich" test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or "mesh-free" methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.
Identifying finite-time coherent sets from limited quantities of Lagrangian data
Williams, Matthew O.; Rypina, Irina I.; Rowley, Clarence W.
2015-08-15
A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that “leak” from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, “data rich” test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or “mesh-free” methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.
Transitory Transport Between Lagrangian Coherent Structures
NASA Astrophysics Data System (ADS)
Mosovsky, B. A.; Meiss, J. D.
2011-12-01
In recent years, the geophysical and dynamical systems communities have developed numerous novel techniques for identifying structures that remain coherent in the Lagrangian sense in aperiodic time-dependent flows. The existence and persistence of these structures is intimately tied to the dynamical time scales of the flow, and as such, they can lend valuable insight into finite-time transport and mixing processes. Geophysical examples in the recent literature include eddy interaction and transport across ocean currents, transport of water-borne pollutants off the coast of California, and mixing and transport within the stratospheric polar vortex. However, in many cases the identification of the coherent structures themselves is a difficult task, making any further quantification of transport between them over a finite time interval either prohibitively expensive or imprecise. In this talk we consider transitory systems, those that experience time-dependent behavior only on a compact interval in time, and present a method for rigorously quantifying transport between Lagrangian coherent structures over this transition interval. In the systems we consider, this transport is effected by the exchange of "lobes" of fluid particles resulting from the intersection of the invariant manifolds bounding the coherent structures. We provide a method for computing the volumes of these lobes that relies on knowing only the trajectories at the intersections of the manifolds, and we present, as applications of our theory, a 2D rotating double-gyre flow and a 3D transitory version of the classical Arnold-Beltrami-Childress (ABC) flow. These flows can be viewed as simplified kinematic descriptions of eddy-eddy interactions and three-dimensional turbulence, respectively. For the 2D case, we compare our results to a common technique employing finite-time Lyapunov exponents, and discuss the benefits and limitations of both methods.
Lagrangian coherent structures and plasma transport processes
NASA Astrophysics Data System (ADS)
Falessi, M. V.; Pegoraro, F.; Schep, T. J.
2015-10-01
> A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom, the Poincaré map provides a splitting of the phase space into regions where particles have different kinds of motion: periodic, quasi-periodic or chaotic. The boundaries of these regions are transport barriers, i.e. a trajectory cannot cross such boundaries throughout the evolution of the system. Lagrangian coherent structures generalize this method to systems with the most general time dependence, splitting the phase space into regions with different qualitative behaviours. This leads to the definition of finite-time transport barriers, i.e. trajectories cannot cross the barrier for a finite amount of time. This methodology can be used to identify fast recirculating regions in the dynamical system and to characterize the transport between them.
Lagrangian transport properties of pulmonary interfacial flows
Smith, Bradford J.; Lukens, Sarah; Yamaguchi, Eiichiro; Gaver, Donald P.
2012-01-01
Disease states characterized by airway fluid occlusion and pulmonary surfactant insufficiency, such as respiratory distress syndrome, have a high mortality rate. Understanding the mechanics of airway reopening, particularly involving surfactant transport, may provide an avenue to increase patient survival via optimized mechanical ventilation waveforms. We model the occluded airway as a liquid-filled rigid tube with the fluid phase displaced by a finger of air that propagates with both mean and sinusoidal velocity components. Finite-time Lyapunov exponent (FTLE) fields are employed to analyse the convective transport characteristics, taking note of Lagrangian coherent structures (LCSs) and their effects on transport. The Lagrangian perspective of these techniques reveals flow characteristics that are not readily apparent by observing Eulerian measures. These analysis techniques are applied to surfactant-free velocity fields determined computationally, with the boundary element method, and measured experimentally with micro particle image velocimetry (μ-PIV). We find that the LCS divides the fluid into two regimes, one advected upstream (into the thin residual film) and the other downstream ahead of the advancing bubble. At higher oscillatory frequencies particles originating immediately inside the LCS experience long residence times at the air–liquid interface, which may be conducive to surfactant transport. At high frequencies a well-mixed attractor region is identified; this volume of fluid cyclically travels along the interface and into the bulk fluid. The Lagrangian analysis is applied to velocity data measured with 0.01 mg ml−1 of the clinical pulmonary surfactant Infasurf in the bulk fluid, demonstrating flow field modifications with respect to the surfactant-free system that were not visible in the Eulerian frame. PMID:23049141
A practical Lagrangian transport model
Jobson, Harvey E.
1980-01-01
An unconditionally stable and practical transport model for use in upland streams and rivers has been developed and verified. Basing the model on the Lagrangian, rather than the Eulerian, reference frame greatly reduces the numerical problems associated with solving the advective terms of the convective-diffusion equation. The model contains almost no numerical dispersion, is conceptually simple, and is relatively easy to code. Model results closely simulated dye concentrations measured in the Chattahoochee River near Atlanta, Ga. under highly unsteady flow conditions. (USGS)
Lagrangian coherent structures as mesoscale transport barriers in atmospheric flows
NASA Astrophysics Data System (ADS)
Naik, Shibabrat; Ross, Shane
2015-11-01
Coherent structures in two-dimensional flows have long been studied in the context of transport in fluid dynamics. However, for geophysical systems a small vertical velocity can lead to nontrivial three-dimensional motion of airborne biological populations affecting agriculture or hazardous outputs from natural disasters. The pathways and barriers in the lower atmosphere, from ground level to a kilometer altitude and over a horizontal scale of several kilometers-which bridge the scale of, for example, local farmlands to the larger regional scale-are still unclear. This requires exploring relevant spatiotemporal scales related to advection in the space of 3D + time. In this talk, we will present the application of finite-time Lyapunov exponent based three-dimensional Lagrangian coherent structures (LCS) to address questions of transport using historical data sets from satellite observations, field measurements and the Weather Research and Forecasting (WRF) model.
Challenges in Lagrangian transport and predictability in 3D flows
NASA Astrophysics Data System (ADS)
Branicki, M.; Wiggins, S.; Kirwan, A. D.; Malek-Madani, R.
2011-12-01
The interplay between the geometrical theory of dynamical systems and the trajectory-based description of aperiodically time-dependent fluid flows has led to significant advances in understanding the role of chaotic transport in geophysical flows at scales dominated by advection. Lagrangian transport analysis utilizing either the time-dependent geometry of intersecting stable and unstable manifolds of the so-called Distinguished Hyperbolic Trajectories (DHT), or ridges of finite-time Lyapunov exponent fields (LCS), provide a much needed and complementary insight into ephemeral mechanisms responsible for the existence of `leaky' transport barriers and 'leaky' mesoscale eddies. However, to date most oceanic applications have been confined to 2D analysis of near surface regions in 'perfect' flows not accounting for model or measurement error, and with the tacit assumption of negligible vertical velocities. I will systematically address issues concerning the regimes of applicability of two-dimensional analysis in 3D aperiodically time-dependent flows, as well as outstanding challenges in fully 3D Lagrangian transport analysis. Even for perfect horizontal velocities, little is known about the vertical extent of stable/unstable manifolds associated with DHTs and/or other special structures relevant to stratified 3D flows. In particular, their sensitivity to errors in the vertical velocities and data assimilation methods has been little studied. Rigorous results regarding the above issues will be illustrated by revealing and mathematically tractable toy models, as well as examples from a detailed study in an eddy-rich region from the Gulf of Mexico and the Mediterranean. New ways of quantifying the uncertainty in Lagrangian predictions will also be presented.
Droste, Stephanie; Governale, Michele
2016-04-13
We study the finite-time full counting statistics for subgap transport through a single-level quantum dot tunnel-coupled to one normal and one superconducting lead. In particular, we determine the factorial and the ordinary cumulants both for finite times and in the long-time limit. We find that the factorial cumulants violate the sign criterion, indicating a non-binomial distribution, even in absence of Coulomb repulsion due to the presence of superconducting correlations. At short times the cumulants exhibit oscillations which are a signature of the coherent transfer of Cooper pairs between the dot and the superconductor. PMID:26963047
NASA Astrophysics Data System (ADS)
Droste, Stephanie; Governale, Michele
2016-04-01
We study the finite-time full counting statistics for subgap transport through a single-level quantum dot tunnel-coupled to one normal and one superconducting lead. In particular, we determine the factorial and the ordinary cumulants both for finite times and in the long-time limit. We find that the factorial cumulants violate the sign criterion, indicating a non-binomial distribution, even in absence of Coulomb repulsion due to the presence of superconducting correlations. At short times the cumulants exhibit oscillations which are a signature of the coherent transfer of Cooper pairs between the dot and the superconductor.
Modeling pollutant transport using a meshless-lagrangian particle model
Carrington, D. B.; Pepper, D. W.
2002-01-01
A combined meshless-Lagrangian particle transport model is used to predict pollutant transport over irregular terrain. The numerical model for initializing the velocity field is based on a meshless approach utilizing multiquadrics established by Kansa. The Lagrangian particle transport technique uses a random walk procedure to depict the advection and dispersion of pollutants over any type of surface, including street and city canyons
Landauer’s formula with finite-time relaxation: Kramers’ crossover in electronic transport
NASA Astrophysics Data System (ADS)
Gruss, Daniel; Velizhanin, Kirill A.; Zwolak, Michael
2016-04-01
Landauer’s formula is the standard theoretical tool to examine ballistic transport in nano- and meso-scale junctions, but it necessitates that any variation of the junction with time must be slow compared to characteristic times of the system, e.g., the relaxation time of local excitations. Transport through structurally dynamic junctions is, however, increasingly of interest for sensing, harnessing fluctuations, and real-time control. Here, we calculate the steady-state current when relaxation of electrons in the reservoirs is present and demonstrate that it gives rise to three regimes of behavior: weak relaxation gives a contact-limited current; strong relaxation localizes electrons, distorting their natural dynamics and reducing the current; and in an intermediate regime the Landauer view of the system only is recovered. We also demonstrate that a simple equation of motion emerges, which is suitable for efficiently simulating time-dependent transport.
Landauer's formula with finite-time relaxation: Kramers' crossover in electronic transport
NASA Astrophysics Data System (ADS)
Gruss, Daniel; Velizhanin, Kirill; Zwolak, Michael
Landauer's formula relates the conductance of a region of interest to its transmission probability. It is the standard theoretical tool to examine ballistic transport in nano- and meso-scale junctions and devices. This view of transport as transmission necessitates a simplified view of transmission, one occurring through an essentially fixed structure. Starting from a description of transport that includes relaxation of electrons in the reservoirs, we derive a Landauer-like formula for the steady-state current. We demonstrate that the finite relaxation time gives rise to three regimes of behavior. Weak relaxation within a small region nearby to the junction gives a contact limited current. Strong relaxation also influences the current by localizing electrons, distorting their natural dynamics and reducing the current. In an intermediate regime, the standard Landauer view is recovered. This behavior is analogous to Kramers' turnover in chemical reactions. Supported by UMD/CNST Cooperative Research Agreement, Award 70NANB10H193.
Landauer’s formula with finite-time relaxation: Kramers’ crossover in electronic transport
Gruss, Daniel; Velizhanin, Kirill A.; Zwolak, Michael
2016-04-20
Landauer’s formula is the standard theoretical tool to examine ballistic transport in nano- and meso-scale junctions, but it necessitates that any variation of the junction with time must be slow compared to characteristic times of the system, e.g., the relaxation time of local excitations. Transport through structurally dynamic junctions is, however, increasingly of interest for sensing, harnessing fluctuations, and real-time control. Here, we calculate the steady-state current when relaxation of electrons in the reservoirs is present and demonstrate that it gives rise to three regimes of behavior: weak relaxation gives a contact-limited current; strong relaxation localizes electrons, distorting their naturalmore » dynamics and reducing the current; and in an intermediate regime the Landauer view of the system only is recovered. Lastly, we also demonstrate that a simple equation of motion emerges, which is suitable for efficiently simulating time-dependent transport.« less
Landauer's formula with finite-time relaxation: Kramers' crossover in electronic transport.
Gruss, Daniel; Velizhanin, Kirill A; Zwolak, Michael
2016-01-01
Landauer's formula is the standard theoretical tool to examine ballistic transport in nano- and meso-scale junctions, but it necessitates that any variation of the junction with time must be slow compared to characteristic times of the system, e.g., the relaxation time of local excitations. Transport through structurally dynamic junctions is, however, increasingly of interest for sensing, harnessing fluctuations, and real-time control. Here, we calculate the steady-state current when relaxation of electrons in the reservoirs is present and demonstrate that it gives rise to three regimes of behavior: weak relaxation gives a contact-limited current; strong relaxation localizes electrons, distorting their natural dynamics and reducing the current; and in an intermediate regime the Landauer view of the system only is recovered. We also demonstrate that a simple equation of motion emerges, which is suitable for efficiently simulating time-dependent transport. PMID:27094206
Landauer’s formula with finite-time relaxation: Kramers’ crossover in electronic transport
Gruss, Daniel; Velizhanin, Kirill A.; Zwolak, Michael
2016-01-01
Landauer’s formula is the standard theoretical tool to examine ballistic transport in nano- and meso-scale junctions, but it necessitates that any variation of the junction with time must be slow compared to characteristic times of the system, e.g., the relaxation time of local excitations. Transport through structurally dynamic junctions is, however, increasingly of interest for sensing, harnessing fluctuations, and real-time control. Here, we calculate the steady-state current when relaxation of electrons in the reservoirs is present and demonstrate that it gives rise to three regimes of behavior: weak relaxation gives a contact-limited current; strong relaxation localizes electrons, distorting their natural dynamics and reducing the current; and in an intermediate regime the Landauer view of the system only is recovered. We also demonstrate that a simple equation of motion emerges, which is suitable for efficiently simulating time-dependent transport. PMID:27094206
On tide-induced lagrangian residual current and residual transport: 1. Lagrangian residual current
Feng, Shizuo; Cheng, Ralph T.; Pangen, Xi
1986-01-01
Residual currents in tidal estuaries and coastal embayments have been recognized as fundamental factors which affect the long-term transport processes. It has been pointed out by previous studies that it is more relevant to use a Lagrangian mean velocity than an Eulerian mean velocity to determine the movements of water masses. Under weakly nonlinear approximation, the parameter k, which is the ratio of the net displacement of a labeled water mass in one tidal cycle to the tidal excursion, is assumed to be small. Solutions for tides, tidal current, and residual current have been considered for two-dimensional, barotropic estuaries and coastal seas. Particular attention has been paid to the distinction between the Lagrangian and Eulerian residual currents. When k is small, the first-order Lagrangian residual is shown to be the sum of the Eulerian residual current and the Stokes drift. The Lagrangian residual drift velocity or the second-order Lagrangian residual current has been shown to be dependent on the phase of tidal current. The Lagrangian drift velocity is induced by nonlinear interactions between tides, tidal currents, and the first-order residual currents, and it takes the form of an ellipse on a hodograph plane. Several examples are given to further demonstrate the unique properties of the Lagrangian residual current.
Programmers manual for a one-dimensional Lagrangian transport model
Schoellhamer, D.H.; Jobson, H.E.
1986-01-01
A one-dimensional Lagrangian transport model for simulating water-quality constituents such as temperature, dissolved oxygen , and suspended sediment in rivers is presented in this Programmers Manual. Lagrangian transport modeling techniques, the model 's subroutines, and the user-written decay-coefficient subroutine are discussed in detail. Appendices list the program codes. The Programmers Manual is intended for the model user who needs to modify code either to adapt the model to a particular need or to use reaction kinetics not provided with the model. (Author 's abstract)
On Lagrangian stochastic modelling of material transport in oceanic gyres
NASA Astrophysics Data System (ADS)
Reynolds, A. M.
2002-11-01
The introduction of ‘spin’ into second-order Lagrangian stochastic models (LSM) for stationary turbulence with broken reflectional symmetry is shown to result in the prediction of super-diffusive transport at intermediate times and the occurrence of anomalously large normal diffusion at later times. These characteristic features of material transport in oceanic gyres cannot be reproduced by two-dimensional first-order LSM. A correspondence is established between high-dimensional, low-order LSM and lower-dimensional, higher-order LSM. It is found that time-dependent spin statistics allow for the coexistence of rotating particle trajectories and non-oscillatory Lagrangian velocity autocorrelation functions.
Users manual for a one-dimensional Lagrangian transport model
Schoellhamer, D.H.; Jobson, H.E.
1986-01-01
A Users Manual for the Lagrangian Transport Model (LTM) is presented. The LTM uses Lagrangian calculations that are based on a reference frame moving with the river flow. The Lagrangian reference frame eliminates the need to numerically solve the convective term of the convection-diffusion equation and provides significant numerical advantages over the more commonly used Eulerian reference frame. When properly applied, the LTM can simulate riverine transport and decay processes within the accuracy required by most water quality studies. The LTM is applicable to steady or unsteady one-dimensional unidirectional flows in fixed channels with tributary and lateral inflows. Application of the LTM is relatively simple and optional capabilities improve the model 's convenience. Appendices give file formats and three example LTM applications that include the incorporation of the QUAL II water quality model 's reaction kinetics into the LTM. (Author 's abstract)
Implications of Lagrangian transport for coupled chemistry-climate simulations
NASA Astrophysics Data System (ADS)
Stenke, A.; Dameris, M.; Grewe, V.; Garny, H.
2008-10-01
For the first time a purely Lagrangian transport algorithm is applied in a fully coupled chemistry-climate model (CCM). We use the Lagrangian scheme ATTILA for the transport of water vapour, cloud water and chemical trace species in the ECHAM4.L39(DLR)/CHEM (E39C) CCM. The advantage of the Lagrangian approach is that it is numerically non-diffusive and therefore maintains steeper and more realistic gradients than the operational semi-Lagrangian transport scheme. In case of radiatively active species changes in the simulated distributions feed back to model dynamics which in turn affect the modelled transport. The implications of the Lagrangian transport scheme for stratospheric model dynamics and tracer distributions in the upgraded model version E39C-ATTILA (E39C-A) are evaluated by comparison with observations and results of the E39C model with the operational semi-Lagrangian advection scheme. We find that several deficiencies in stratospheric dynamics in E39C seem to originate from a pronounced modelled wet bias and an associated cold bias in the extra-tropical lowermost stratosphere. The reduction of the simulated moisture and temperature bias in E39C-A leads to a significant advancement of stratospheric dynamics in terms of the mean state as well as annual and interannual variability. As a consequence of the favourable numerical characteristics of the Lagrangian transport scheme and the improved model dynamics, E39C-A generally shows more realistic stratospheric tracer distributions: Compared to E39C high stratospheric chlorine (Cly) concentrations extend further downward and agree now well with analyses derived from observations. Therefore E39C-A realistically covers the altitude of maximum ozone depletion in the stratosphere. The location of the ozonopause, i.e. the transition from low tropospheric to high stratospheric ozone values, is also clearly improved in E39C-A. Furthermore, the simulated temporal evolution of stratospheric Cly in the past is
Lagrangian transport induced by peristaltic pumping in a closed channel
NASA Astrophysics Data System (ADS)
Ng, Chiu-On; Ma, Ye
2009-11-01
Lagrangian transport induced by peristaltic waves traveling on the boundaries of a two-dimensional rectangular closed channel is studied analytically. Based on the Lagrangian description, an asymptotic analysis is performed to generate explicit expressions for the leading-order oscillatory as well as the higher-order time-mean mass transport (or steady streaming) velocities as functions of the wave properties. Two cases are considered. The first case, which is for slow wave frequency or very small wave amplitude such that the steady-streaming Reynolds number (Res) is very small, recovers the one studied previously in the literature, but with all the results fully presented in the Lagrangian sense. The second case, corresponding to high-frequency pumping such as Res is order unity, is where it has been handled analytically. It is found that the overall mixing resulting from the mass transport can depend on the phase shift of the two waves, the wave number, the frequency, as well as the amplitude of the waves.
Lagrangian simulation of multidimensional anomalous transport at the MADE site
NASA Astrophysics Data System (ADS)
Zhang, Yong; Benson, David A.
2008-04-01
Contaminant transport through regional-scale natural geological formations typically exhibits several ``anomalous'' features, including direction-dependent spreading rates, channeling along preferential flow paths, trapping of solute in relatively immobile domains, and/or the local variation of transport speed. Simulating these plume characteristics can be computationally intensive using a traditional advection-dispersion equation (ADE) because anomalous features of transport generally depend on local-scale subsurface properties. Here we develop an alternative simulation approach that solves the full nonlocal, multidimensional, spatiotemporal fractional-order ADE with variable coefficients in a Lagrangian framework using a novel non-Markovian random walk method. This model allows us to simulate anomalous plumes without the need to explicitly define local-scale heterogeneity. The simple model accurately simulates the tritium plume measured at the extensively characterized MADE test site.
Enhancements to the Branched Lagrangian Transport Modeling System
Jobson, Harvey E.
1997-01-01
The Branched Lagrangian Transport Model (BLTM) has received wide use within the U.S. Geological Survey over the past 10 years. This report documents the enhancements and modifications that have been made to this modeling system since it was first introduced. The programs in the modeling system are arranged into five levels?programs to generate time-series of meteorological data (EQULTMP, SOLAR), programs to process time-series data (INTRP, MRG), programs to build input files for transport model (BBLTM, BQUAL2E), the model with defined reaction kinetics (BLTM, QUAL2E), and post processor plotting programs (CTPLT, CXPLT). An example application is presented to illustrate how the modeling system can be used to simulate 10 water-quality constituents in the Chattahoochee River below Atlanta, Georgia.
Lagrangian analysis of fluid transport in empirical vortex ring flows
NASA Astrophysics Data System (ADS)
Shadden, Shawn C.; Dabiri, John O.; Marsden, Jerrold E.
2006-04-01
In this paper we apply dynamical systems analyses and computational tools to fluid transport in empirically measured vortex ring flows. Measurements of quasisteadily propagating vortex rings generated by a mechanical piston-cylinder apparatus reveal lobe dynamics during entrainment and detrainment that are consistent with previous theoretical and numerical studies. In addition, the vortex ring wake of a free-swimming Aurelia aurita jellyfish is measured and analyzed in the framework of dynamical systems to elucidate similar lobe dynamics in a naturally occurring biological flow. For the mechanically generated rings, a comparison of the net entrainment rate based on the present methods with a previous Eulerian analysis shows good correspondence. However, the current Lagrangian framework is more effective than previous analyses in capturing the transport geometry, especially when the flow becomes more unsteady, as in the case of the free-swimming jellyfish. Extensions of these results to more complex flow geometries is suggested.
Stretching and folding in finite time.
Ma, Tian; Ouellette, Nicholas T; Bollt, Erik M
2016-02-01
Complex flows mix efficiently, and this process can be understood by considering the stretching and folding of material volumes. Although many metrics have been devised to characterize stretching, fewer are able to capture folding in a quantitative way in spatiotemporally variable flows. Here, we extend our previous methods based on the finite-time curving of fluid-element trajectories to nonzero scales and show that this finite-scale finite-time curvature contains information about both stretching and folding. We compare this metric to the more commonly used finite-time Lyapunov exponent and illustrate our methods using experimental flow-field data from a quasi-two-dimensional laboratory flow. Our new analysis tools add to the growing set of Lagrangian methods for characterizing mixing in complex, aperiodic fluid flows. PMID:26931593
Stretching and folding in finite time
NASA Astrophysics Data System (ADS)
Ma, Tian; Ouellette, Nicholas T.; Bollt, Erik M.
2016-02-01
Complex flows mix efficiently, and this process can be understood by considering the stretching and folding of material volumes. Although many metrics have been devised to characterize stretching, fewer are able to capture folding in a quantitative way in spatiotemporally variable flows. Here, we extend our previous methods based on the finite-time curving of fluid-element trajectories to nonzero scales and show that this finite-scale finite-time curvature contains information about both stretching and folding. We compare this metric to the more commonly used finite-time Lyapunov exponent and illustrate our methods using experimental flow-field data from a quasi-two-dimensional laboratory flow. Our new analysis tools add to the growing set of Lagrangian methods for characterizing mixing in complex, aperiodic fluid flows.
Coupled Eulerian-Lagrangian transport of large debris by tsunamis
NASA Astrophysics Data System (ADS)
Conde, Daniel A. S.; Ferreira, Rui M. L.; Sousa Oliveira, Carlos
2016-04-01
Tsunamis are notorious for the large disruption they can cause on coastal environments, not only due to the imparted momentum of the incoming wave but also due to its capacity to transport large quantities of solid debris, either from natural or human-made sources, over great distances. A 2DH numerical model under development at CERIS-IST (Ferreira et al., 2009; Conde, 2013) - STAV2D - capable of simulating solid transport in both Eulerian and Lagrangian paradigms will be used to assess the relevance of Lagrangian-Eulerian coupling when modelling the transport of solid debris by tsunamis. The model has been previously validated and applied to tsunami scenarios (Conde, 2013), being well-suited for overland tsunami propagation and capable of handling morphodynamic changes in estuaries and seashores. The discretization scheme is an explicit Finite Volume technique employing flux-vector splitting and a reviewed Roe-Riemann solver. Source term formulations are employed in a semi-implicit way, including the two-way coupling of the Lagrangian and Eulerian solvers by means of conservative mass and momentum transfers between fluid and solid phases. The model was applied to Sines Port, a major commercial port in Portugal, where two tsunamigenic scenarios are considered: an 8.5 Mw scenario, consistent with the Great Lisbon Earthquake and Tsunami of the 1st November 1755 (Baptista, 2009), and an hypothetical 9.5 Mw worst-case scenario based on the same historical event. Open-ocean propagation of these scenarios were simulated with GeoClaw model from ClawPack (Leveque, 2011). Following previous efforts on the modelling of debris transport by tsunamis in seaports (Conde, 2015), this work discusses the sensitivity of the obtained results with respect to the phenomenological detail of the employed Eulerian-Lagrangian formulation and the resolution of the mesh used in the Eulerian solver. The results have shown that the fluid to debris mass ratio is the key parameter regarding the
NASA Astrophysics Data System (ADS)
Mancho, Ana M.; Mendoza, Carolina
2009-11-01
In recent years there has been a lot of progress in the application of dynamical systems concepts to the description of transport in oceanic flows. In these flows the classical dynamical system theory does not apply since they are aperiodic and finite-time defined. Recently, for describing these flows a new definition of distinguished trajectory has been proposed (Madrid & Mancho, Chaos, 2009). Distinguished trajectories act as organizing centres of the geometrical template of aperiodic time-dependent flows, like fixed points and periodic orbits do in time independent or periodic flows. The computation of distinguished trajectories makes use of a function M of which we show contains a lot of Lagrangian information. In this presentation I will discuss how the visualization of this function M, allows identifying relevant Lagrangian features at a glance. In particular we report an application to real altimetry data taken from satellite in the area of the Kuroshio current. The function M also determines the stable and unstable subspaces of the distinguished hyperbolic trajectories which are tangent to the invariant manifolds. From the computation of stable and unstable manifolds we report an accurate description of transport routes in this region.
Lagrangian Calculations of Age Spectra and Implications For Stratospheric Transport
NASA Astrophysics Data System (ADS)
Reithmeier, C.; Sausen, R.
The Lagrangian transport scheme ATTILA, which runs online in the climate model ECHAM4 and calculates about 190000 globally distributed trajectories, is used to compute the mean age and age spectra of stratospheric air in ECHAM4. While most studies assume stationary transport when calculating the age of air, this presentation investigates the temporal evolution of the age spectra. The age spectra exhibit two distinct shapes: At low and midlatitudes the age spectra have a typical asymmetric shape with one peak and a long tail towards higher values, whereas at high and polar latitudes the age spectra have several distinct maxima, which are one year apart. Investigation of the seasonal variation of the polar age spectrum indicates that polar stratospheric air masses are relatively isolated from lower latitudes throughout most of the year, exchange taking place only during a short period (of about two months) in summer. The shape of the polar age spectra (with several distinct maxima) is a combined effect of the seasonal variation of exchange between polar and extra-polar latitudes as described above, and the seasonal variation of the upward mass flux at the tropical tropopause which implies that the period of strongest mass flux is pronounced in the age spectrum.
NASA Astrophysics Data System (ADS)
van den Bremer, Ton S.; Taylor, Paul H.
2014-11-01
Although the literature has examined Stokes drift, the net Lagrangian transport by particles due to of surface gravity waves, in great detail, the motion of fluid particles transported by surface gravity wave groups has received considerably less attention. In practice nevertheless, the wave field on the open sea often has a group-like structure. The motion of particles is different, as particles at sufficient depth are transported backwards by the Eulerian return current that was first described by Longuet-Higgins & Stewart (1962) and forms an inseparable counterpart of Stokes drift for wave groups ensuring the (irrotational) mass balance holds. We use WKB theory to study the variation of the Lagrangian transport by the return current with depth distinguishing two-dimensional seas, three-dimensional seas, infinite depth and finite depth. We then provide dimensional estimates of the net horizontal Lagrangian transport by the Stokes drift on the one hand and the return flow on the other hand for realistic sea states in all four cases. Finally we propose a simple scaling relationship for the transition depth: the depth above which Lagrangian particles are transported forwards by the Stokes drift and below which such particles are transported backwards by the return current.
Transport induced by mean-eddy interaction: I. Theory, and relation to Lagrangian lobe dynamics
NASA Astrophysics Data System (ADS)
Ide, Kayo; Wiggins, Stephen
2015-02-01
In this paper we develop a method for the estimation of Transport Induced by the Mean-Eddy interaction (TIME) in two-dimensional unsteady flows. The method is based on the dynamical systems approach to fluid transport and can be viewed as a hybrid combination of Lagrangian and Eulerian methods. The (Eulerian) boundaries across which we consider (Lagrangian) transport are kinematically defined by appropriately chosen streamlines of the mean flow. By evaluating the impact of the mean-eddy interaction on transport, the TIME method can be used as a diagnostic tool for transport processes that occur during a specified time interval along a specified boundary segment. We introduce two types of TIME functions: one that quantifies the accumulation of flow properties and another that measures the displacement of the transport geometry. The spatial geometry of transport is described by the so-called pseudo-lobes, and temporal evolution of transport by their dynamics. In the case where the TIME functions are evaluated along a separatrix, the pseudo-lobes have a relationship to the lobes of Lagrangian transport theory. In fact, one of the TIME functions is identical to the Melnikov function that is used to measure the distance, at leading order in a small parameter, between the two invariant manifolds that define the Lagrangian lobes. We contrast the similarities and differences between the TIME and Lagrangian lobe dynamics in detail. An application of the TIME method is carried out for inter-gyre transport in the wind-driven oceanic circulation model and a comparison with the Lagrangian transport theory is made.
3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"
NASA Technical Reports Server (NTRS)
Douglass, A.
2005-01-01
The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.
Monitoring the Amazon plume northwestward transport along Lagrangian pathways
NASA Astrophysics Data System (ADS)
Fournier, Severine; Gaultier, Lucile; Vandemark, Douglas; Lee, Tong; Gierach, Michelle
2016-04-01
area. The objective of this study is to investigate the interannual variability in Amazon-Orinoco freshwater transport from the rivers' mouth northwestward over 2010-2014. We use a Lagrangian advection method to track the particles and follow their biophysical properties along their trajectory using measurements from Aquarius, SMOS, and Aqua MODIS. The pathways of the Amazon-Orinoco plume waters can therefore be analyzed and quantified, enabling an investigation of the biophysical processes associated with the Amazon River and Orinoco River freshwaters as they are advected from the river mouth to the open ocean. From one year to another, the amount of Amazon-Orinoco particles reaching the northwestern part of the plume is variable causing different physical and biogeochemical influences in the area. In 2011, a larger amount of particles reaches that area, the mechanisms responsible for this unusual northwestward transport of the shallow plume waters are under investigation, such as river discharge, advection, NBC rings. On the contrary, in 2014, fewer particles reach this northwestern area taking a more coastal pathway. This suggests a higher influence of the Orinoco River that year.
A Lagrangian Approach to Modelling Proppant Transport with Tip Screen-Out in KGD Hydraulic Fractures
NASA Astrophysics Data System (ADS)
Dontsov, E. V.; Peirce, A. P.
2015-11-01
This study introduces a continuum approach to model proppant transport in hydraulic fractures in a Lagrangian frame of reference. The model for the proppant transport is based on the recently obtained slurry flow solution inside a channel, where the latter utilizes a phenomenological constitutive relationship for a slurry. This approach allows us to describe the transition from Poiseuille flow with an effective viscosity to Darcy flow as the particle concentration increases towards the maximum value. The algorithm is presented for the one-dimensional case, for which propagation of a symmetric Kristinovich-Zheltov-Geertsma-De Klerk fracture is considered. To examine the effectiveness of the Lagrangian approach for proppant transport modelling, a set of parameters, for which proppant particles reach the fracture tip and cause the development of a proppant plug is selected. In this situation, the coupling between the hydraulic fracture propagation and proppant transport is the most significant. To estimate the accuracy of the Lagrangian proppant transport model, the results are compared to the predictions of an Eulerian proppant transport model, which utilizes the same algorithm for hydraulic fracture propagation. It is shown that, although both approaches have the same convergence rate, the error of the Lagrangian approach is three to five times smaller, which depends on the number of proppant elements used in the Lagrangian approach. This permits us to use a coarser mesh for hydraulic fracture propagation, and to obtain results with similar accuracy up to a hundred times faster.
Atmospheric rivers moisture transport from a Lagrangian perspective
NASA Astrophysics Data System (ADS)
Ramos, A. M.; Nieto, R.; Tomé, R.; Gimeno, L.; Trigo, R. M.; Liberato, M. L. R.; Lavers, D. A.
2015-12-01
An automated atmospheric rivers (ARs) detection algorithm is used for the North Atlantic Ocean Basin allowing the identification of the major ARs that affected western European coasts between 1979 and 2014 over the winter half-year (October to March). The entire west coast of Europe was divided into five domains, namely, the Iberian Peninsula (9.75° W; 36-43.75° N), France (4.5° W; 43.75-50° N), UK (4.5° W; 50-59° N), southern Scandinavia and the Netherlands (5.25° E; 50-59° N), and northern Scandinavia (5.25° E; 59-70° N). Following the identification of the main ARs that made landfall in western Europe, a Lagrangian analysis was then applied in order to identify the main sources of moisture that reach each domain. The Lagrangian dataset used was obtained from the FLEXPART model global simulation from 1979 to 2012, where the atmosphere was divided into approximately 2.0 million parcels, and it was forced by ERA-Interim reanalysis on a 1° latitude-longitude grid. Results show that, in general, for all regions considered, the major climatological source of moisture extends along the subtropical North Atlantic, from the Florida Peninsula (northward of 20° N), to each sink region, with the nearest coast to each sink region always appearing as a local maximum of evaporation. In addition, during the AR events, the Atlantic subtropical source is reinforced and displaced, with a slight northward movement of the moisture sources is found when the sink region is positioned at higher latitudes. In conclusion, the results confirm the advection of moisture linked to ARs from subtropical ocean areas, but also the existence of a tropical one, and the mid-latitude sources further the analysed longitude along the North Atlantic is located eastward.
Evaluation of wastewater contaminant transport in surface waters using verified Lagrangian sampling.
Antweiler, Ronald C; Writer, Jeffrey H; Murphy, Sheila F
2014-02-01
Contaminants released from wastewater treatment plants can persist in surface waters for substantial distances. Much research has gone into evaluating the fate and transport of these contaminants, but this work has often assumed constant flow from wastewater treatment plants. However, effluent discharge commonly varies widely over a 24-hour period, and this variation controls contaminant loading and can profoundly influence interpretations of environmental data. We show that methodologies relying on the normalization of downstream data to conservative elements can give spurious results, and should not be used unless it can be verified that the same parcel of water was sampled. Lagrangian sampling, which in theory samples the same water parcel as it moves downstream (the Lagrangian parcel), links hydrologic and chemical transformation processes so that the in-stream fate of wastewater contaminants can be quantitatively evaluated. However, precise Lagrangian sampling is difficult, and small deviations - such as missing the Lagrangian parcel by less than 1h - can cause large differences in measured concentrations of all dissolved compounds at downstream sites, leading to erroneous conclusions regarding in-stream processes controlling the fate and transport of wastewater contaminants. Therefore, we have developed a method termed "verified Lagrangian" sampling, which can be used to determine if the Lagrangian parcel was actually sampled, and if it was not, a means for correcting the data to reflect the concentrations which would have been obtained had the Lagrangian parcel been sampled. To apply the method, it is necessary to have concentration data for a number of conservative constituents from the upstream, effluent, and downstream sites, along with upstream and effluent concentrations that are constant over the short-term (typically 2-4h). These corrections can subsequently be applied to all data, including non-conservative constituents. Finally, we show how data
Eulerian-Lagrangian localized adjoint methods for reactive transport in groundwater
Ewing, R.E.; Wang, Hong
1996-12-31
In this paper, we present Eulerian-Lagrangian localized adjoint methods (ELLAM) to solve convection-diffusion-reaction equations governing contaminant transport in groundwater flowing through an adsorbing porous medium. These ELLAM schemes can treat various combinations of boundary conditions and conserve mass. Numerical results are presented to demonstrate the strong potential of ELLAM schemes.
Flow topology, Lagrangian statistics, and transport in resistive drift-wave turbulence
NASA Astrophysics Data System (ADS)
Kadoch, B.; Del-Castillo-Negrete, Diego; Bos, W. J. T.; Schneider, K.
2012-10-01
Transport is strongly influenced by coherent structures. In particular, trapping in vortices tends to arrest transport and zonal flows can induce large Lagrangian displacements. It is thus of interest to characterize coherent structures from a Lagrangian perspective. For 2-D flows, the Eulerian Weiss criterion provides a tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). In Ref.footnotetextB. Kadoch, D. del-Castillo-Negrete, W.J.T Bos, and K. Schneider, Phys. Rev. E 83, 036314 (2011). we proposed the Lagrangian Weiss criterion (i.e. the Weiss field computed along particle orbits) and applied it to 2-D Navier-Stokes turbulence. Here we apply this criterion to resistive drift-wave turbulence. The probability density functions (pdfs) of residence time in the topologically different regions are computed for ensembles of Lagrangian tracers. It is shown that in elliptic and hyperbolic regions the pdfs have algebraically decaying tails. The pdf of residence time in elliptic regions is proposed as a measure of particle trapping, and the relationship with waiting time statistics in continuous time random walk models of anomalous transport is explored.
Implications of Lagrangian transport for simulations with a coupled chemistry-climate model
NASA Astrophysics Data System (ADS)
Stenke, A.; Dameris, M.; Grewe, V.; Garny, H.
2009-08-01
For the first time a purely Lagrangian transport algorithm is applied in a fully coupled chemistry-climate model (CCM). We use the numerically non-diffusive Lagrangian scheme ATTILA instead of the operational semi-Lagrangian scheme for the transport of water vapour, cloud water and chemical trace species in the CCM E39C. The new model version including the Lagrangian scheme is referred to as E39C-A. The implications of the Lagrangian transport scheme for stratospheric model dynamics and tracer distributions in E39C-A are evaluated by comparison with observations and results of the previous model version E39C. We found in a previous paper that several deficiencies in stratospheric dynamics in E39C originate from a pronounced modelled wet bias and an associated cold bias in the extra-tropical lowermost stratosphere. Contrary to the semi-Lagrangian scheme ATTILA shows a largely reduced meridional transport of water vapour from the tropical upper troposphere into the extratropical lowermost stratosphere. The reduction of the moisture and temperature bias in E39C-A leads to a significant advancement of stratospheric dynamics in terms of the mean state as well as annual and interannual variability. In this study we show that as a consequence of both, the favourable numerical characteristics of the Lagrangian transport scheme and the improved model dynamics, E39C-A generally shows more realistic distributions of chemical trace species: Compared to E39C high stratospheric chlorine (Cly) concentrations extend further downward. Therefore E39C-A realistically covers the altitude of maximum ozone depletion in the stratosphere. The location of the ozonopause, i.e. the transition from low tropospheric to high stratospheric ozone values, is also clearly improved in E39C-A. Not only the spatial distribution but also the temporal evolution of stratospheric Cly in the past is realistically reproduced in E39C-A which is an important step towards a more reliable projection of future
NASA Astrophysics Data System (ADS)
Qi, Rui; Huang, Biao
2016-01-01
Transport mechanism is critical for understanding natural phenomena in the solar system and is beneficial to space mission design. In this study, transport mechanism in the bicircular four-body problem is numerically explored by using Lagrangian coherent structure (LCS), a tool widely used for identifying transport barriers in fluid flow. First, equations of motion of the bicircular problem are derived and five topology configurations of forbidden region are presented. Then, definition and computational method of LCS are introduced. Finally, properties of LCS which are useful for revealing transport mechanism in the four-body problem are numerically investigated.
Lagrangian Transport Calculations Using UARS Data. Part I: Passive Tracers
NASA Technical Reports Server (NTRS)
Manney, G. L.; Lahoz, W. A.; Harwood, R. S.; Zurek, R. W.; Kumer, J. B.; Mergenthaler, J. L.; Roche, A. E.; O'Neill, A; Swinbank, R.; Waters, J. W.
1994-01-01
The transport of passive tracers observed by UARS has been simulated using computed trajectories of thousands of air parcels initialized on a three-dimensional stratospheric grid. These trajectories are calculated in isentropic coordinates using horizontal winds provided by the United Kingdom Meteorological Office data assimilation system and vertical (cross-isentropic) velocities computed using a fast radiation code.
Rotation prevents finite-time breakdown
NASA Astrophysics Data System (ADS)
Liu, Hailiang; Tadmor, Eitan
2004-02-01
We consider a two-dimensional (2D) convection model augmented with the rotational Coriolis forcing, Ut+ U·∇ xU=2 kU⊥, with a fixed 2 k being the inverse Rossby number. We ask whether the action of dispersive rotational forcing alone, U⊥, prevents the generic finite-time breakdown of the free nonlinear convection. The answer provided in this work is a conditional yes. Namely, we show that the rotating Euler equations admit global smooth solutions for a subset of generic initial configurations. With other configurations, however, finite-time breakdown of solutions may and actually does occur. Thus, global regularity depends on whether the initial configuration crosses an intrinsic, O(1) critical threshold (CT), which is quantified in terms of the initial vorticity, ω0=∇× U0, and the initial spectral gap associated with the 2×2 initial velocity gradient, η0≔ λ2(0)- λ1(0), λj(0)= λj(∇ U0). Specifically, global regularity of the rotational Euler equation is ensured if and only if 4kω 0(α)+η 20(α)<4k 2,∀α∈ R2. We also prove that the velocity field remains smooth if and only if it is periodic. An equivalent Lagrangian formulation reconfirms the CT and shows a global periodicity of velocity field as well as the associated particle orbits. Moreover, we observe yet another remarkable periodic behavior exhibited by the gradient of the velocity field. The spectral dynamics of the Eulerian formulation [SIAM J. Math. Anal. 33 (2001) 930] reveals that the vorticity and the divergence of the flow evolve with their own path-dependent period. We conclude with a kinetic formulation of the rotating Euler equation.
Transport and Lagrangian Statistics in Rotating Stratified Turbulence
NASA Astrophysics Data System (ADS)
Rosenberg, D. L.
2015-12-01
Transport plays a crucial role in geophysical flows, both in theatmosphere and in the ocean. Transport in such flows is ultimatelycontrolled by small-scale turbulence, although the large scales arein geostrophic balance between pressure gradient, gravity and Coriolisforces. As a result of the seemingly random nature of the flow, singleparticles are dispersed by the flow and on time scales significantlylonger than the eddy turn-over time, they undergo a diffusive motionwhose diffusion coefficient is the integral of the velocity correlationfunction. On intermediate time scales, in homogeneous, isotropic turbuilence(HIT) the separation between particle pairs has been argued to grow withtime according to the Richardson law: <(Δ x)2(t)> ~ t3, with aproportionality constant that depends on the initial particleseparation. The description of the phenomena associated withthe dispersion of single particles, or of particle pairs, ultimatelyrests on relatively simple statistical properties of the flowvelocity transporting the particles, in particular on its temporalcorrelation function. In this work, we investigate particle dispersionin the anisotropic case of rotating stratified turbulence examining whetherthe dependence on initial particle separation differs from HIT,particularly in the presence of an inverse cascade.
NASA Astrophysics Data System (ADS)
Chacon, Luis; Del-Castillo-Negrete, Diego; Hauck, Cory
2012-10-01
Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (χ/χ˜10^10 in fusion plasmas). Recently, a Lagrangian Green's function approach, developed for the purely parallel transport case,footnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011)^,footnotetextD. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, 19, 056112 (2012) has been extended to the anisotropic transport case in the tokamak-ordering limit with constant density.footnotetextL. Chac'on, D. del-Castillo-Negrete, C. Hauck, JCP, submitted (2012) An operator-split algorithm is proposed that allows one to treat Eulerian and Lagrangian components separately. The approach is shown to feature bounded numerical errors for arbitrary χ/χ ratios, which renders it asymptotic-preserving. In this poster, we will present the generalization of the Lagrangian approach to arbitrary magnetic fields. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.
NASA Astrophysics Data System (ADS)
Abalos, M.; Ploeger, F.; Konopka, P.; Randel, W. J.; Serrano, E.
2013-11-01
We aim to reconcile the recently published, apparently contrasting results regarding the relative importance of tropical upwelling versus horizontal transport for the seasonality of ozone above the tropical tropopause. Different analysis methods in the literature (Lagrangian versus Eulerian, and isentropic versus pressure vertical coordinates) yield different perspectives of ozone transport, and the results must be carefully compared in equivalent terms to avoid misinterpretation. By examining the Lagrangian calculations in the Eulerian formulation, we show here that the results are in fact consistent with each other and with a common understanding of the ozone transport processes near and above the tropical tropopause. We further emphasize that the complementary approaches are suited for answering two different scientific questions: (1) what drives the observed seasonal cycle in ozone at a particular level above the tropical tropopause? and (2) how important is horizontal transport from mid-latitudes for ozone concentrations in the tropical lower stratosphere? Regarding the first question, the analysis of the transformed Eulerian mean (TEM) ozone budget shows that the annual cycle in tropical upwelling is the main forcing of the ozone seasonality at altitudes with large vertical gradients in the tropical lower stratosphere. To answer the second question a Lagrangian framework must be used, and the results show that a large fraction (~50%) of the ozone molecules ascending through the tropical lower stratosphere is of extra-tropical origin and has been in-mixed from mid-latitudes.
NASA Astrophysics Data System (ADS)
Abalos, M.; Ploeger, F.; Konopka, P.; Randel, W. J.; Serrano, E.
2013-07-01
We aim to reconcile the recently published, apparently contrasting results regarding the relative importance of tropical upwelling versus horizontal transport for the seasonality of ozone above the tropical tropopause. Different analysis methods in the literature (Lagrangian versus Eulerian, and isentropic versus pressure vertical coordinates) yield different perspectives of ozone transport, and the results must be carefully compared in equivalent terms to avoid misinterpretation. By examining the Lagrangian calculations in the Eulerian formulation, we show here that the results are in fact consistent with each other and with a common understanding of the ozone transport processes near and above the tropical tropopause. We further emphasize that the complementary approaches are suited for answering two different scientific questions: (1) what drives the observed seasonal cycle in ozone at a particular level above the tropical tropopause? and (2) how important is horizontal transport from mid-latitudes for ozone concentrations in the tropical lower stratosphere? Regarding the first question, the analysis of the Transformed Eulerian Mean (TEM) ozone budget shows that the annual cycle in tropical upwelling is the main forcing of the ozone seasonality at altitudes with large vertical gradients in the tropical lower stratosphere. To answer the second question a Lagrangian framework must be used, and the results show that a large fraction (∼50%) of the ozone molecules ascending through the tropical lower stratosphere is of extra-tropical origin and has been in-mixed from mid-latitudes.
Lagrangian Transport Calculations Using UARS Data. Part 2; Ozone
NASA Technical Reports Server (NTRS)
Manney, Gloria L.; Zurek, R. W.; Froidevaux, L.; Waters, J. W.; ONeill, A.; Swinbank, R.
1995-01-01
Trajectory calculations are used to examine ozone transport in the polar winter stratosphere during periods of the Upper Atmosphere Research Satellite (UARS) observations. The value of these calculations for determining mass transport was demonstrated previously using UARS observations of long-lived tracers, In the middle stratosphere, the overall ozone behavior observed by the Microwave Limb Sounder in the polar vortex is reproduced by this purely dynamical model. Calculations show the evolution of ozone in the lower stratosphere during early winter to be dominated by dynamics in December 1992 in the Arctic. Calculations for June 1992 in the Antarctic show evidence of chemical ozone destruction and indicate that approx. 50% of the chemical destruction may be masked by dynamical effects, mainly diabatic descent, which bring higher ozone into the lower-stratospheric vortex. Estimating differences between calculated and observed fields suggests that dynamical changes masked approx. 20% - 35% of chemical ozone loss during late February and early March 1993 in the Arctic. In the Antarctic late winter, in late August and early September 1992, below approx. 520 K, the evolution of vortex-averaged ozone is entirely dominated by chemical effects; above this level, however, chemical ozone depletion can be partially or completely masked by dynamical effects. Our calculations for 1992 showed that chemical loss was nearly completely compensated by increases due to diabatic descent at 655 K.
Applying dispersive changes to Lagrangian particles in groundwater transport models
Konikow, Leonard F.
2010-01-01
Method-of-characteristics groundwater transport models require that changes in concentrations computed within an Eulerian framework to account for dispersion be transferred to moving particles used to simulate advective transport. A new algorithm was developed to accomplish this transfer between nodal values and advecting particles more precisely and realistically compared to currently used methods. The new method scales the changes and adjustments of particle concentrations relative to limiting bounds of concentration values determined from the population of adjacent nodal values. The method precludes unrealistic undershoot or overshoot for concentrations of individual particles. In the new method, if dispersion causes cell concentrations to decrease during a time step, those particles in the cell having the highest concentration will decrease the most, and those with the lowest concentration will decrease the least. The converse is true if dispersion is causing concentrations to increase. Furthermore, if the initial concentration on a particle is outside the range of the adjacent nodal values, it will automatically be adjusted in the direction of the acceptable range of values. The new method is inherently mass conservative.
Applying Dispersive Changes to Lagrangian Particles in Groundwater Transport Models
Konikow, L.F.
2010-01-01
Method-of-characteristics groundwater transport models require that changes in concentrations computed within an Eulerian framework to account for dispersion be transferred to moving particles used to simulate advective transport. A new algorithm was developed to accomplish this transfer between nodal values and advecting particles more precisely and realistically compared to currently used methods. The new method scales the changes and adjustments of particle concentrations relative to limiting bounds of concentration values determined from the population of adjacent nodal values. The method precludes unrealistic undershoot or overshoot for concentrations of individual particles. In the new method, if dispersion causes cell concentrations to decrease during a time step, those particles in the cell having the highest concentration will decrease the most, and those with the lowest concentration will decrease the least. The converse is true if dispersion is causing concentrations to increase. Furthermore, if the initial concentration on a particle is outside the range of the adjacent nodal values, it will automatically be adjusted in the direction of the acceptable range of values. The new method is inherently mass conservative. ?? US Government 2010.
Lagrangian analysis of mixing and transport of water masses in the marine bays
NASA Astrophysics Data System (ADS)
Prants, S. V.; Ponomarev, V. I.; Budyansky, M. V.; Uleysky, M. Yu.; Fayman, P. A.
2013-01-01
The Lagrangian approach to studying the mixing and transport of a passive admixture in marine bays and gulfs based on the methods of a theory of dynamic systems is developed. This approach is employed to investigate the lateral mixing and transport of waters in the Peter the Great Bay, Japan Sea, using a velocity field of the predictive numerical hydrodynamic circulation model of a synoptic scale. It is shown that the Lagrangian characteristics, such as the maximum accumulated Lyapunov exponent, the time of particle stay in the bay, particle relative displacements, and the number of cyclonic and anticyclonic rotations, allow us to describe the movement of water masses, the character of mixing, and chaos in the Bay. In integrating the advection equations forward and backward in time, maps showing a number of particle arrivals to different regions of the Bay make it possible to establish corridors through which particles leave and enter the Bay.
Lagrangian transport of water vapor and CFCs in a coupled Chemistry Climate Model
NASA Astrophysics Data System (ADS)
Hoppe, Charlotte; Müller, Rolf; Hoffmann, Lars; Konopka, Paul; Plöger, Felix; Grooß, Jens-Uwe
2013-04-01
We describe the implementation of a Lagrangian transport core in a chemistry climate model (CCM). Thereby we address the common problem of properly representing trace gas distributions in a classical Eulerian framework with a fixed model grid, particularly in regions with strong trace gas gradients. A prominent example is stratospheric water vapor, which is an important driver of surface climate change on decadal scales. In this case, the transport representation is particularly important in the tropical tropopause layer (TTL), where tropospheric air enters into the stratosphere. We have coupled the Chemical Lagrangian Model of the Stratosphere (CLaMS) with the ECHAM-MESSy Atmospheric Chemistry Model (EMAC). The latter includes the ECHAM5 climate model, and the MESSy interface, which allows for flexible coupling and switching between different submodels. The chemistry transport model CLaMS provides a fully Lagrangian transport representation to calculate constituent transport for an ensemble of air parcels that move along trajectories. To facilitate the calculation of long time-series a simplified chemistry scheme was implemented. Various studies show that the CLaMS model is particularly suited to properly represent dynamics and chemistry in the UT/LS region. The analysis of mean age of stratospheric air gives insight into the different transport characteristics of the Eulerian and the Lagrangian transport schemes. Mean age of air, calculated in both frameworks, is compared regarding the representation of important processes, i.e. descent in the polar vortex, upwelling in the tropical pipe, and isentropic in-mixing in subtropical regions. We also compared the zonal mean distributions and photochemical lifetimes of CFC-11 and CFC-12 with climatologies from different satellite experiments (ACE-FTS, HIRDLS, and MIPAS). CLaMS stratospheric water vapor distributions show remarkable differences compared to the stratospheric water vapor simulated by ECHAM, especially in
Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.
2014-09-01
We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while the second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X_{⊥} /X_{∥} becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L^{2}_{∥}/X1L^{2}_{⊥} → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.
Refining finite-time Lyapunov exponent ridges and the challenges of classifying them
NASA Astrophysics Data System (ADS)
Allshouse, Michael R.; Peacock, Thomas
2015-08-01
While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of a FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by a FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model.
Refining finite-time Lyapunov exponent ridges and the challenges of classifying them.
Allshouse, Michael R; Peacock, Thomas
2015-08-01
While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of a FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by a FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model. PMID:26328581
NASA Astrophysics Data System (ADS)
Rypina, Irina I.
The Lagrangian dynamics of two-dimensional incompressible fluid flows is considered, with emphasis on transport processes in atmospheric and oceanic flows. The dynamical-systems-based approach is adopted; the Lagrangian motion in such systems is studied with the aid of Kolmogorov-Arnold-Moser (KAM) theory, and results relating to stable and unstable manifolds and lobe dynamics. Some nontrivial extensions of well-known results are discussed, and some extensions of the theory are developed. In problems for which the flow field consists of a steady background on which a time-dependent perturbation is superimposed, it is shown that transport barriers arise naturally and play a critical role in transport processes. Theoretical results are applied to the study of transport in measured and simulated oceanographic and atmospheric flows. Two particular problems are considered. First, we study the Lagrangian dynamics of the zonal jet at the perimeter of the Antarctic Stratospheric Polar Vortex during late winter/early spring within which lies the "ozone hole". In this system, a robust transport barrier is found near the core of a zonal jet under typical conditions, which is responsible for trapping of the ozone-depleted air within the ozone hole. The existence of such a barrier is predicted theoretically and tested numerically with use of a dynamically-motivated analytically-prescribed model. The second, oceanographic, application considered is the study of the surface transport in the Adriatic Sea. The surface flow in the Adriatic is characterized by a robust three-gyre background circulation pattern. Motivated by this observation, the Lagrangian dynamics of a perturbed three-gyre system is studied, with emphasis on intergyre transport and the role of transport barriers. It is shown that a qualitative change in transport properties, accompanied by a qualitative change in the structure of stable and unstable manifolds occurs in the perturbed three-gyre system when the
Finite-time braiding exponents
NASA Astrophysics Data System (ADS)
Budišić, Marko; Thiffeault, Jean-Luc
2015-08-01
Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow.
Finite-time braiding exponents.
Budišić, Marko; Thiffeault, Jean-Luc
2015-08-01
Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow. PMID:26328578
Asymptotic-preserving Lagrangian approach for modeling anisotropic transport in magnetized plasmas
NASA Astrophysics Data System (ADS)
Chacon, Luis; Del-Castillo-Negrete, Diego
2012-03-01
Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (the transport-coefficient ratio χ/χ˜10^10 in fusion plasmas). Recently, a novel Lagrangian Green's function method has been proposedfootnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011); D. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, submitted (2011) to solve the local and non-local purely parallel transport equation in general 3D magnetic fields. The approach avoids numerical pollution, is inherently positivity-preserving, and is scalable algorithmically (i.e., work per degree-of-freedom is grid-independent). In this poster, we discuss the extension of the Lagrangian Green's function approach to include perpendicular transport terms and sources. We present an asymptotic-preserving numerical formulation, which ensures a consistent numerical discretization temporally and spatially for arbitrary χ/χ ratios. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.
PTV measurements of Lagrangian particle transport by surface gravity wave groups
NASA Astrophysics Data System (ADS)
van den Bremer, Ton; Whittaker, Colin; Raby, Alison; Taylor, Paul
2015-11-01
We present detailed PTV (particle tracking velocimetry) measurements of the Lagrangian transport and trajectories of neutrally buoyant particles underneath two-dimensional surface gravity wave groups in a laboratory flume. By focussing our attention on wave groups of moderate steepness, we confirm the predictions of standard second-order multi-chromatic wave theory, in which the body of fluid satisfies the potential flow equations. Particles near the surface are transported forwards and their motion is dominated by Stokes drift. Particles at sufficient depth are transported backwards by the Eulerian return current that was first described by Longuet-Higgins & Stewart (1962) and forms an inseparable counterpart of Stokes drift for surface wave groups ensuring the (irrotational) mass balance holds. Finally, we provide experimental validation of a simple scaling relationship, derived based under the assumption of separation of scales, for the transition depth: the depth above which Lagrangian particles are transported forwards by the Stokes drift and below which such particles are transported backwards by the return current. We present results for a range of effective water depths.
Implications of Lagrangian Tracer Transport for Coupled Chemistry-Climate Simulations
NASA Astrophysics Data System (ADS)
Stenke, A.
2009-05-01
Today's coupled chemistry-climate models (CCM) consider a large number of trace species and feedback processes. Due to the radiative effect of some species, errors in simulated tracer distributions can feed back to model dynamics. Thus, shortcomings of the applied transport schemes can have severe implications for the overall model performance. Traditional Eulerian approaches show a satisfactory performance in case of homogeneously distributed trace species, but they can lead to severe problems when applied to highly inhomogeneous tracer distributions. In case of sharp gradients many schemes show a considerable numerical diffusion. Lagrangian approaches, on the other hand, combine a number of favourable numerical properties: They are strictly mass-conserving and do not suffer from numerical diffusion. Therefore they are able to maintain steeper gradients. A further advantage is that they allow the transport of a large number of tracers without being prohibitively expensive. A variety of benefits for stratospheric dynamics and chemistry resulting from a Lagrangian transport algorithm are demonstrated by the example of the CCM E39C. In an updated version of E39C, called E39C-A, the operational semi-Lagrangian advection scheme has been replaced with the purely Lagrangian scheme ATTILA. It will be shown that several model deficiencies can be cured by the choice of an appropriate transport algorithm. The most important advancement concerns the reduction of a pronounced wet bias in the extra- tropical lowermost stratosphere. In turn, the associated temperature error ("cold bias") is significantly reduced. Stratospheric wind variations are now in better agreement with observations, e.g. E39C-A is able to reproduce the stratospheric wind reversal in the Southern Hemisphere in summer which was not captured by the previous model version. Resulting changes in wave propagation and dissipation lead to a weakening of the simulated mean meridional circulation and therefore a more
NASA Astrophysics Data System (ADS)
Gotovac, Hrvoje; Srzic, Veljko
2014-05-01
Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different Eulerian, Lagrangian and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present Eulerian Lagrangian Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large
Lagrangian transport in a microtidal coastal area: the Bay of Palma, island of Mallorca, Spain
NASA Astrophysics Data System (ADS)
Hernández-Carrasco, I.; López, C.; Orfila, A.; Hernández-García, E.
2013-10-01
Coastal transport in the Bay of Palma, a small region in the island of Mallorca, Spain, is characterized in terms of Lagrangian descriptors. The data sets used for this study are the output for two months (one in autumn and one in summer) of a high resolution numerical model, ROMS (Regional Ocean Model System), forced atmospherically and with a spatial resolution of 300 m. The two months were selected because of their different wind regime, which is the main driver of the sea dynamics in this area. Finite-size Lyapunov exponents (FSLEs) were used to locate semi-persistent Lagrangian coherent structures (LCS) and to understand the different flow regimes in the bay. The different wind directions and regularity in the two months have a clear impact on the surface bay dynamics, whereas only topographic features appear clearly in the bottom structures. The fluid interchange between the bay and the open ocean was studied by computing particle trajectories and residence time (RT) maps. The escape rate of particles out of the bay is qualitatively different, with a 32% greater escape rate of particles to the ocean in October than in July, owing to the different geometric characteristics of the flow. We show that LCSs separate regions with different transport properties by displaying spatial distributions of residence times on synoptic Lagrangian maps together with the location of the LCSs. Correlations between the time-dependent behavior of FSLE and RT are also investigated, showing a negative dependence when the stirring characterized by FSLE values moves particles in the direction of escape.
A set oriented definition of finite-time Lyapunov exponents and coherent sets
NASA Astrophysics Data System (ADS)
Tallapragada, Phanindra; Ross, Shane D.
2013-05-01
The problem of phase space transport, which is of interest from both the theoretical and practical point of view, has been investigated extensively using geometric and probabilistic methods. Two important tools to study this problem that have emerged in recent years are finite-time Lyapunov exponents (FTLE) and the Perron-Frobenius operator. The FTLE measures the averaged local stretching around reference trajectories. Regions with high stretching are used to identify phase space transport barriers. One probabilistic method is to consider the spectrum of the Perron-Frobenius operator of the flow to identify almost-invariant densities. These almost-invariant densities are used to identify almost invariant sets. In this paper, a set-oriented definition of the FTLE is proposed which is applicable to phase space sets of finite size and reduces to the usual definition of FTLE in the limit of infinitesimal phase space elements. This definition offers a straightforward connection between the evolution of probability densities and finite-time stretching experienced by phase space curves. This definition also addresses some concerns with the standard computation of the FTLE. For the case of autonomous and periodic vector fields we provide a simplified method to calculate the set-oriented FTLE using the Perron-Frobenius operator. Based on the new definition of the FTLE we propose a simple definition of finite-time coherent sets applicable to vector fields of general time-dependence, which are the analogues of almost-invariant sets in autonomous and time-periodic vector fields. The coherent sets we identify will necessarily be separated from one another by ridges of high FTLE, providing a link between the framework of coherent sets and that of codimension one Lagrangian coherent structures. Our identification of coherent sets is applied to three examples.
Quantum finite time availability for parametric oscillators
NASA Astrophysics Data System (ADS)
Hoffmann, Karl Heinz; Schmidt, Kim; Salamon, Peter
2015-06-01
The availability of a thermodynamic system out of equilibrium with its environment describes its ability to perform work in a reversible process which brings it to equilibrium with this environment. Processes in finite time can usually not be performed reversibly thus leading to unavoidable losses. In order to account for these losses the concept of finite time availability was introduced. We here add a new feature through the introduction of quantum finite time availability for an ensemble of parametric oscillators. For such systems there exists a certain critical time, the FEAT time. Quantum finite time availability quantifies the available work from processes which are shorter than the FEAT time of the oscillator ensemble.
Birkholzer, J.; Karasaki, K.
1996-09-01
Fracture network simulators have been extensively used in the past for obtaining a better understanding of flow and transport processes in fractured rock. However, most of these models do not account for fluid or solute exchange between the fractures and the porous matrix, although diffusion into the matrix pores can have a major impact on the spreading of contaminants. In the present paper a new finite element code TRIPOLY is introduced which combines a powerful Lagrangian-Eulerian approach for solving flow and transport in networks of discrete fractures with an efficient method to account for the diffusive interaction between the fractures and the adjacent matrix blocks. The code is capable of handling large-scale fracture-matrix systems comprising individual fractures and matrix blocks of arbitrary size, shape, and dimension.
Temperature and solute-transport simulation in streamflow using a Lagrangian reference frame
Jobson, Harvey E.
1980-01-01
A computer program for simulating one-dimensional, unsteady temperature and solute transport in a river has been developed and documented for general use. The solution approach to the convective-diffusion equation uses a moving reference frame (Lagrangian) which greatly simplifies the mathematics of the solution procedure and dramatically reduces errors caused by numerical dispersion. The model documentation is presented as a series of four programs of increasing complexity. The conservative transport model can be used to route a single conservative substance. The simplified temperature model is used to predict water temperature in rivers when only temperature and windspeed data are available. The complete temperature model is highly accurate but requires rather complete meteorological data. Finally, the 10-parameter model can be used to route as many as 10 interacting constituents through a river reach. (USGS)
NASA Astrophysics Data System (ADS)
Hoffmann, L.; Rößler, T.; Griessbach, S.; Heng, Y.; Stein, O.
2016-05-01
Sulfur dioxide (SO2) emissions from strong volcanic eruptions are an important natural cause for climate variations. We applied our new Lagrangian transport model Massive-Parallel Trajectory Calculations to perform simulations for three case studies of volcanic eruption events. The case studies cover the eruptions of Grímsvötn, Iceland, Puyehue-Cordón Caulle, Chile, and Nabro, Eritrea, in May and June 2011. We used SO2 observations of the Atmospheric Infrared Sounder (AIRS/Aqua) and a backward trajectory approach to initialize the simulations. Besides validation of the new model, the main goal of our study was a comparison of simulations with different meteorological data products. We considered three reanalyses, i.e., ERA-Interim, Modern-Era Retrospective Analysis for Research and Applications (MERRA), and National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) Reanalysis Project as well as the European Centre for Medium-Range Weather Forecasts (ECMWF) operational analysis. Qualitatively, the SO2 distributions from the simulations compare well not only with the AIRS data but also with Cloud-Aerosol Lidar with Orthogonal Polarization and Michelson Interferometer for Passive Atmospheric Sounding aerosol observations. Transport deviations and the critical success index (CSI) are analyzed to evaluate the simulations quantitatively. During the first 5 or 10 days after the eruptions we found the best performance for the ECMWF analysis (CSI range of 0.25-0.31), followed by ERA-Interim (0.25-0.29), MERRA (0.23-0.27), and NCAR/NCEP (0.21-0.23). High temporal and spatial resolution of the meteorological data does lead to improved performance of Lagrangian transport simulations of volcanic emissions in the upper troposphere and lower stratosphere.
NASA Astrophysics Data System (ADS)
Weinzierl, B.; Sauer, D. N.; Walser, A.; Dollner, M.; Reitebuch, O.; Gross, S.; Chouza, F.; Ansmann, A.; Toledano, C.; Freudenthaler, V.; Kandler, K.; Schäfler, A.; Baumann, R.; Tegen, I.; Heinold, B.
2014-12-01
Aerosol particles are regularly transported over long distances impacting air quality, health, weather and climate thousands of kilometers downwind of the source. During transport, particle properties are modified thereby changing the associated impact on the radiation budget. Although mineral dust is of key importance for the climate system many questions such as the change of the dust size distribution during long-range transport, the role of wet and dry removal mechanisms, and the complex interaction between mineral dust and clouds remain open. In June/July 2013, the Saharan Aerosol Long-range Transport and Aerosol-Cloud-Interaction Experiment (SALTRACE: http://www.pa.op.dlr.de/saltrace) was conducted to study the transport and transformation of Saharan mineral dust. Besides ground-based lidar and in-situ instruments deployed on Cape Verde, Barbados and Puerto Rico, the DLR research aircraft Falcon was equipped with an extended aerosol in-situ instrumentation, a nadir-looking 2-μm wind lidar and instruments for standard meteorological parameters. During SALTRACE, five large dust outbreaks were studied by ground-based, airborne and satellite measurements between Senegal, Cape Verde, the Caribbean, and Florida. Highlights included the Lagrangian sampling of a dust plume in the Cape Verde area on 17 June which was again measured with the same instrumentation on 21 and 22 June 2013 near Barbados. Between Cape Verde and Barbados, the aerosol optical thickness (500 nm) decreased from 0.54 to 0.26 and the stratification of the dust layers changed significantly from a rather homogenous structure near Africa to a 3-layer structure with embedded cumulus clouds in the Caribbean. In the upper part of the dust layers in the Caribbean, the aerosol properties were similar to the observations near Africa. In contrast, much more variability in the dust properties was observed between 0.7 and 2.5 km altitude probably due to interaction of the mineral dust with clouds. In our
NASA Astrophysics Data System (ADS)
Pisso, Ignacio; Patra, Prabir; Breivik, Knut
2015-04-01
Lagrangian transport models based on times series of Eulerian fields provide a computationally affordable way of achieving very high resolution for limited areas and time periods. This makes them especially suitable for the analysis of point-wise measurements of atmospheric tracers. We present an application illustrated with examples of greenhouse gases from anthropogenic emissions in urban areas and biogenic emissions in Japan and of pollutants in the Arctic. We asses the algorithmic complexity of the numerical implementation as well as the use of non-procedural techniques such as Object-Oriented programming. We discuss aspects related to the quantification of uncertainty from prior information in the presence of model error and limited number of observations. The case of non-linear constraints is explored using direct numerical optimisation methods.
Local finite-time Lyapunov exponent, local sampling and probabilistic source and destination regions
NASA Astrophysics Data System (ADS)
BozorgMagham, A. E.; Ross, S. D.; Schmale, D. G., III
2015-11-01
The finite-time Lyapunov exponent (FTLE) is a powerful Lagrangian concept widely used for describing large-scale flow patterns and transport phenomena. However, field experiments usually have modest scales. Therefore, it is necessary to bridge the gap between the concept of FTLE and field experiments. In this paper, two independent observations are discussed: (i) approximation of the local FTLE time series at a fixed location as a function of known distances between the destination (or source) points of released (or collected) particles and local velocity, and (ii) estimation of the distances between the destination (or source) points of the released (or collected) particles when consecutive release (or sampling) events are performed at a fixed location. These two observations lay the groundwork for an ansatz methodology that can practically assist in field experiments where consecutive samples are collected at a fixed location, and it is desirable to attribute source locations to the collected particles, and also in planning of optimal local sampling of passive particles for maximal diversity monitoring of atmospheric assemblages of microorganisms. In addition to deterministic flows, the more realistic case of unresolved turbulence and low-resolution flow data that yield probabilistic source (or destination) regions are studied. It is shown that, similar to deterministic flows, Lagrangian coherent structures (LCS) and local FTLE can describe the separation of probabilistic source (or destination) regions corresponding to consecutively collected (or released) particles.
Long-range pollution transport: Trans-Atlantic mechanisms and Lagrangian modeling methods
NASA Astrophysics Data System (ADS)
Owen, Robert Christopher
Over the past several decades, it has become apparent that anthropogenic activities have resulted in the large-scale enhancement of the levels of many trace gases throughout the troposphere. More recently, attention has been given to the transport pathway taken by these emissions as they are dispersed throughout the atmosphere. The transport pathway determines the physical characteristics of emissions plumes and therefore plays an important role in the chemical transformations that can occur downwind of source regions. For example, the production of ozone (O3) is strongly dependent upon the transport its precursors undergo. O3 can initially be formed within air masses while still over polluted source regions. These polluted air masses can experience continued O3 production or O3 destruction downwind, depending on the air mass's chemical and transport characteristics. At present, however, there are a number of uncertainties in the relationships between transport and O3 production in the North Atlantic lower free troposphere. The first phase of the study presented here used measurements made at the Pico Mountain observatory and model simulations to determine transport pathways for US emissions to the observatory. The Pico Mountain observatory was established in the summer of 2001 in order to address the need to understand the relationships between transport and O3 production. Measurements from the observatory were analyzed in conjunction with model simulations from the Lagrangian particle dispersion model (LPDM), FLEX-PART, in order to determine the transport pathway for events observed at the Pico Mountain observatory during July 2003. A total of 16 events were observed, 4 of which were analyzed in detail. The transport time for these 16 events varied from 4.5 to 7 days, while the transport altitudes over the ocean ranged from 2-8 km, but were typically less than 3 km. In three of the case studies, eastward advection and transport in a weak warm conveyor belt (WCB
NASA Astrophysics Data System (ADS)
Piñones, Andrea; Hofmann, Eileen E.; Dinniman, Michael S.; Klinck, John M.
2011-07-01
The relative contribution of ocean circulation in producing areas where marine mammals and other predators concentrate to produce biological hot spots along the continental shelf of the western Antarctic Peninsula (wAP) was investigated with numerical Lagrangian particle tracking simulations. Circulation distributions used in the Lagrangian simulations were obtained from the Regional Ocean Modeling System (ROMS) configured for the wAP region, with a horizontal resolution of 4 km and a vertical resolution of 24 sigma-layers. To determine release points for the floats, the simulated circulation fields were first analyzed to estimate scales of temporal variability. The temporal decorrelation scales of the simulated surface flow over most of the wAP shelf were 2-3 days. However, decorrelation scales of about 40 days were found for the surface flow in the southern part of Marguerite Bay. Temporal decorrelation scales for the flow below the permanent pycnocline at the depth of Circumpolar Deep Water (CDW) intrusions (below 250 m) were between 40 and 70 days along the northern flank of Marguerite Trough and extending into Marguerite Bay. Near Adelaide Island, Anvers Island and the offshore side of Alexander Island, the velocity decorrelation scales varied between 40 and 60 days. Floats were released in the wAP simulated circulation fields along the outer and mid-shelf at a range of depths in different seasons. The simulated particle trajectories showed preferred sites for across-shelf transport, with Marguerite Trough being a primary pathway for movement of floats into Marguerite Bay, Crystal Sound and the inner shelf region. The three primary biological hot spots, Crystal Sound, Laubeuf Fjord, and off Alexander Island, were sites with the longest particle residence times, being 18-27 days for Alexander Island and Crystal Sound to almost 35 days for Laubeuf Fjord. However, the source regions and circulation processes that provided the input of particles differed for each
On fast computation of finite-time coherent sets using radial basis functions
NASA Astrophysics Data System (ADS)
Froyland, Gary; Junge, Oliver
2015-08-01
Finite-time coherent sets inhibit mixing over finite times. The most expensive part of the transfer operator approach to detecting coherent sets is the construction of the operator itself. We present a numerical method based on radial basis function collocation and apply it to a recent transfer operator construction [G. Froyland, "Dynamic isoperimetry and the geometry of Lagrangian coherent structures," Nonlinearity (unpublished); preprint arXiv:1411.7186] that has been designed specifically for purely advective dynamics. The construction [G. Froyland, "Dynamic isoperimetry and the geometry of Lagrangian coherent structures," Nonlinearity (unpublished); preprint arXiv:1411.7186] is based on a "dynamic" Laplace operator and minimises the boundary size of the coherent sets relative to their volume. The main advantage of our new approach is a substantial reduction in the number of Lagrangian trajectories that need to be computed, leading to large speedups in the transfer operator analysis when this computation is costly.
On fast computation of finite-time coherent sets using radial basis functions.
Froyland, Gary; Junge, Oliver
2015-08-01
Finite-time coherent sets inhibit mixing over finite times. The most expensive part of the transfer operator approach to detecting coherent sets is the construction of the operator itself. We present a numerical method based on radial basis function collocation and apply it to a recent transfer operator construction [G. Froyland, "Dynamic isoperimetry and the geometry of Lagrangian coherent structures," Nonlinearity (unpublished); preprint arXiv:1411.7186] that has been designed specifically for purely advective dynamics. The construction [G. Froyland, "Dynamic isoperimetry and the geometry of Lagrangian coherent structures," Nonlinearity (unpublished); preprint arXiv:1411.7186] is based on a "dynamic" Laplace operator and minimises the boundary size of the coherent sets relative to their volume. The main advantage of our new approach is a substantial reduction in the number of Lagrangian trajectories that need to be computed, leading to large speedups in the transfer operator analysis when this computation is costly. PMID:26328580
The application of flux-form semi-Lagrangian transport scheme in a spectral atmosphere model
NASA Astrophysics Data System (ADS)
Wang, Xiaocong; Liu, Yimin; Wu, Guoxiong; Lin, Shian-Jiann; Bao, Qing
2013-01-01
A flux-form semi-Lagrangian transport scheme (FFSL) was implemented in a spectral atmospheric GCM developed and used at IAP/LASG. Idealized numerical experiments show that the scheme is good at shape preserving with less dissipation and dispersion, in comparison with other conventional schemes. Importantly, FFSL can automatically maintain the positive definition of the transported tracers, which was an underlying problem in the previous spectral composite method (SCM). To comprehensively investigate the impact of FFSL on GCM results, we conducted sensitive experiments. Three main improvements resulted: first, rainfall simulation in both distribution and intensity was notably improved, which led to an improvement in precipitation frequency. Second, the dry bias in the lower troposphere was significantly reduced compared with SCM simulations. Third, according to the Taylor diagram, the FFSL scheme yields simulations that are superior to those using the SCM: a higher correlation between model output and observation data was achieved with the FFSL scheme, especially for humidity in lower troposphere. However, the moist bias in the middle and upper troposphere was more pronounced with the FFSL scheme. This bias led to an over-simulation of precipitable water in comparison with reanalysis data. Possible explanations, as well as solutions, are discussed herein.
Adaptive time stepping algorithm for Lagrangian transport models: Theory and idealised test cases
NASA Astrophysics Data System (ADS)
Shah, Syed Hyder Ali Muttaqi; Heemink, Arnold Willem; Gräwe, Ulf; Deleersnijder, Eric
2013-08-01
Random walk simulations have an excellent potential in marine and oceanic modelling. This is essentially due to their relative simplicity and their ability to represent advective transport without being plagued by the deficiencies of the Eulerian methods. The physical and mathematical foundations of random walk modelling of turbulent diffusion have become solid over the years. Random walk models rest on the theory of stochastic differential equations. Unfortunately, the latter and the related numerical aspects have not attracted much attention in the oceanic modelling community. The main goal of this paper is to help bridge the gap by developing an efficient adaptive time stepping algorithm for random walk models. Its performance is examined on two idealised test cases of turbulent dispersion; (i) pycnocline crossing and (ii) non-flat isopycnal diffusion, which are inspired by shallow-sea dynamics and large-scale ocean transport processes, respectively. The numerical results of the adaptive time stepping algorithm are compared with the fixed-time increment Milstein scheme, showing that the adaptive time stepping algorithm for Lagrangian random walk models is more efficient than its fixed step-size counterpart without any loss in accuracy.
NASA Astrophysics Data System (ADS)
Moharana, N. R.; Speetjens, M. F. M.; Trieling, R. R.; Clercx, H. J. H.
2013-09-01
Magnetic actuation of microscopic beads is a promising technique for enhancement and manipulation of scalar transport in micro-fluidic systems. This implies laminar and essentially three-dimensional (3D) unsteady flow conditions. The present study addresses fundamental transport phenomena in such configurations in terms of 3D coherent structures formed by the Lagrangian fluid trajectories in a 3D time-periodic flow driven by a rotating sphere. The flow field is represented by an exact Stokes solution superimposed by a nonlinear closed-form perturbation. This facilitates systematic "activation" and exploration of two fundamental states: (i) invariant spheroidal surfaces accommodating essentially 2D Hamiltonian dynamics; (ii) formation of intricate 3D coherent structures (spheroidal shells interconnected by tubes) and onset to 3D dynamics upon weak perturbation of the former state. Key to the latter state is emergence of isolated periodic points and the particular foliation and interaction of the associated manifolds, which relates intimately to coherent structures of the unperturbed state. The occurrence of such fundamental states and corresponding dynamics is (qualitative) similar to findings on a realistic 3D lid-driven flow subject to weak fluid inertia. This implies, first, a universal response scenario to weak perturbations and, second, an adequate representation of physical effects by the in essence artificial perturbation. The study thus offers important new insights into a class of flow configurations with great practical potential.
CFD Lagrangian Modeling of Water Droplet Transport for ISS Hygiene Activity Application
NASA Technical Reports Server (NTRS)
Son, Chang H.
2013-01-01
The goal of this study was to assess the impacts of free water propagation in the Waste and Hygiene Compartment (WHC) installed in Node 3. Free water can be generated inside the WHC in small quantities due to crew hygiene activity. To mitigate potential impact of free water in Node 3 cabin the WHC doorway is enclosed by a waterproof bump-out, Kabin, with openings at the top and bottom. At the overhead side of the rack, there is a screen that prevents large drops of water from exiting. However, as the avionics fan in the WHC causes airflow toward the deck side of the rack, small quantities of free water may exit at the bottom of the Kabin. A Computational Fluid Dynamics (CFD) analysis of Node 3 cabin airflow enable identifying the paths of water transport. To simulate the droplet transport the Lagrangian discrete phase approach was used. Various initial droplet distributions were considered in the study. The droplet diameter was varied in the range of 5-20 mm. The results of the computations showed that most of the drops fall to the rack surface not far from the WHC curtain.
Modeling coupled nanoparticle aggregation and transport in porous media: A Lagrangian approach
NASA Astrophysics Data System (ADS)
Taghavy, Amir; Pennell, Kurt D.; Abriola, Linda M.
2015-01-01
Changes in nanoparticle size and shape due to particle-particle interactions (i.e., aggregation or agglomeration) may significantly alter particle mobility and retention in porous media. To date, however, few modeling studies have considered the coupling of transport and particle aggregation processes. The majority of particle transport models employ an Eulerian modeling framework and are, consequently, limited in the types of collisions and aggregate sizes that can be considered. In this work, a more general Lagrangian modeling framework is developed and implemented to explore coupled nanoparticle aggregation and transport processes. The model was verified through comparison of model simulations to published results of an experimental and Eulerian modeling study (Raychoudhury et al., 2012) of carboxymethyl cellulose (CMC)-modified nano-sized zero-valent iron particle (nZVI) transport and retention in water-saturated sand columns. A model sensitivity analysis reveals the influence of influent particle concentration (ca. 70 to 700 mg/L), primary particle size (10-100 nm) and pore water velocity (ca. 1-6 m/day) on particle-particle, and, consequently, particle-collector interactions. Model simulations demonstrate that, when environmental conditions promote particle-particle interactions, neglecting aggregation effects can lead to under- or over-estimation of nanoparticle mobility. Results also suggest that the extent to which higher order particle-particle collisions influence aggregation kinetics will increase with the fraction of primary particles. This work demonstrates the potential importance of time-dependent aggregation processes on nanoparticle mobility and provides a numerical model capable of capturing/describing these interactions in water-saturated porous media.
NASA Astrophysics Data System (ADS)
McIlhany, Kevin L.; Guth, Stephen; Wiggins, Stephen
2015-06-01
In this paper, we extend the notion of Eulerian indicators (EIs), previously developed for two dimensional time dependent flows, to three dimensional time dependent flows, where the time dependence can be arbitrary. These are applied to a study of transport and mixing in the Hill's spherical vortex subject to a linear strain rate field. We consider the axisymmetric case and the fully three dimensional case with different types of time dependence. We develop a Lagrangian characterization of transport and mixing appropriate for open three dimensional flows and we show that the EIs provide a detailed description of the flow structure that can be correlated with the Lagrangian transport and mixing results. The EIs yield results consistent with the dynamics of the Hill's vortex flow characteristics, correlation with transverse shear, and anti-correlation with transversality.
Finite-time barriers to reaction front propagation
NASA Astrophysics Data System (ADS)
Locke, Rory; Mahoney, John; Mitchell, Kevin
2015-11-01
Front propagation in advection-reaction-diffusion systems gives rise to rich geometric patterns. It has been shown for time-independent and time-periodic fluid flows that invariant manifolds, termed burning invariant manifolds (BIMs), serve as one-sided dynamical barriers to the propagation of reaction front. More recently, theoretical work has suggested that one-sided barriers, termed burning Lagrangian Coherent structures (bLCSs), exist for fluid velocity data prescribed over a finite time interval, with no assumption on the time-dependence of the flow. In this presentation, we use a time-varying fluid ``wind'' in a double-vortex channel flow to demonstrate that bLCSs form the (locally) most attracting or repelling fronts.
GPU and APU computations of Finite Time Lyapunov Exponent fields
NASA Astrophysics Data System (ADS)
Conti, Christian; Rossinelli, Diego; Koumoutsakos, Petros
2012-03-01
We present GPU and APU accelerated computations of Finite-Time Lyapunov Exponent (FTLE) fields. The calculation of FTLEs is a computationally intensive process, as in order to obtain the sharp ridges associated with the Lagrangian Coherent Structures an extensive resampling of the flow field is required. The computational performance of this resampling is limited by the memory bandwidth of the underlying computer architecture. The present technique harnesses data-parallel execution of many-core architectures and relies on fast and accurate evaluations of moment conserving functions for the mesh to particle interpolations. We demonstrate how the computation of FTLEs can be efficiently performed on a GPU and on an APU through OpenCL and we report over one order of magnitude improvements over multi-threaded executions in FTLE computations of bluff body flows.
Finite time stabilization of delayed neural networks.
Wang, Leimin; Shen, Yi; Ding, Zhixia
2015-10-01
In this paper, the problem of finite time stabilization for a class of delayed neural networks (DNNs) is investigated. The general conditions on the feedback control law are provided to ensure the finite time stabilization of DNNs. Then some specific conditions are derived by designing two different controllers which include the delay-dependent and delay-independent ones. In addition, the upper bound of the settling time for stabilization is estimated. Under fixed control strength, discussions of the extremum of settling time functional are made and a switched controller is designed to optimize the settling time. Finally, numerical simulations are carried out to demonstrate the effectiveness of the obtained results. PMID:26264170
Parameterizing Urban Canopy Layer transport in an Lagrangian Particle Dispersion Model
NASA Astrophysics Data System (ADS)
Stöckl, Stefan; Rotach, Mathias W.
2016-04-01
The percentage of people living in urban areas is rising worldwide, crossed 50% in 2007 and is even higher in developed countries. High population density and numerous sources of air pollution in close proximity can lead to health issues. Therefore it is important to understand the nature of urban pollutant dispersion. In the last decades this field has experienced considerable progress, however the influence of large roughness elements is complex and has as of yet not been completely described. Hence, this work studied urban particle dispersion close to source and ground. It used an existing, steady state, three-dimensional Lagrangian particle dispersion model, which includes Roughness Sublayer parameterizations of turbulence and flow. The model is valid for convective and neutral to stable conditions and uses the kernel method for concentration calculation. As most Lagrangian models, its lower boundary is the zero-plane displacement, which means that roughly the lower two-thirds of the mean building height are not included in the model. This missing layer roughly coincides with the Urban Canopy Layer. An earlier work "traps" particles hitting the lower model boundary for a recirculation period, which is calculated under the assumption of a vortex in skimming flow, before "releasing" them again. The authors hypothesize that improving the lower boundary condition by including Urban Canopy Layer transport could improve model predictions. This was tested herein by not only trapping the particles, but also advecting them with a mean, parameterized flow in the Urban Canopy Layer. Now the model calculates the trapping period based on either recirculation due to vortex motion in skimming flow regimes or vertical velocity if no vortex forms, depending on incidence angle of the wind on a randomly chosen street canyon. The influence of this modification, as well as the model's sensitivity to parameterization constants, was investigated. To reach this goal, the model was
Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean.
Beron-Vera, Francisco J; Olascoaga, María J; Haller, George; Farazmand, Mohammad; Triñanes, Joaquín; Wang, Yan
2015-08-01
Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions. PMID:26328583
Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean
NASA Astrophysics Data System (ADS)
Beron-Vera, Francisco J.; Olascoaga, María J.; Haller, George; Farazmand, Mohammad; Triñanes, Joaquín; Wang, Yan
2015-08-01
Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.
Lagrangian model simulation of the turbulent transport of evaporating jet droplets
NASA Astrophysics Data System (ADS)
Edson, James Bearer
The HEXOS (Humidity EXchange Over the Sea) subprograms HEXIST (HEXOS EXperiment in Simulation Tunnel) and CLUSE (Couche Limite Unidimensionnelle Stationaire d'Embruns) were designed to investigate the generation, turbulent transport, and evaporation of droplets ejected by bursting bubbles within the air-sea simulation tunnel at Institute de Mecanique Statistique de la Turbulence. Droplet concentration size spectra and turbulence characteristics were measured under various conditions to study the effects of wind speed and humidity on the above processes. The bubbles were produced by aeration devices to insure repeatability when necessary. The Lagrangian model developed as part of this investigation simulates the generation and advection of evaporating jet drops. The technique used to advect the droplets is similar to Langevin simulations of vertical dispersion. However, the approach differs significantly in that the particles (i.e., jet drops) are not constrained to follow the turbulent motion of the wind field exactly. This was accomplished by deriving an expression for the particle's vertical velocity which includes a mean fall velocity, reduced velocity variance, and a particle integral time scale which includes parameters to account for inertial effects and nonzero fall velocity. The source function is derived from an assumed bubble spectrum of the form dN/dr=Cr(-beta), where C and beta are chosen to best fit the measured data. Once chosen, these parameters are fixed so that true comparisons can be between modeled and measured data. The droplets are released at their ejection heights so that droplet production is treated as an elevated source. Profiles of droplet size spectra are then calculated downwind of the source by keeping track of the particle's size and position. These profiles show excellent agreement with those measured during HEXIST and CLUSE.
NASA Astrophysics Data System (ADS)
Oger, G.; Marrone, S.; Le Touzé, D.; de Leffe, M.
2016-05-01
This paper addresses the accuracy of the weakly-compressible SPH method. Interpolation defects due to the presence of anisotropic particle structures inherent to the Lagrangian character of the Smoothed Particle Hydrodynamics (SPH) method are highlighted. To avoid the appearance of these structures which are detrimental to the quality of the simulations, a specific transport velocity is introduced and its inclusion within an Arbitrary Lagrangian Eulerian (ALE) formalism is described. Unlike most of existing particle disordering/shifting methods, this formalism avoids the formation of these anisotropic structures while a full consistency with the original Euler or Navier-Stokes equations is maintained. The gain in accuracy, convergence and numerical diffusion of this formalism is shown and discussed through its application to various challenging test cases.
NASA Astrophysics Data System (ADS)
Stenke, A.; Grewe, V.; Ponater, M.
2008-10-01
The Lagrangian advection scheme ATTILA has been applied for the transport of water vapor and cloud water in the general circulation model (GCM) ECHAM4.L39(DLR) (E39) instead of the operational semi-Lagrangian transport scheme (SLT). ATTILA is a purely Lagrangian scheme that is numerically non-diffusive, while the operational semi-Lagrangian scheme exhibits a considerable numerical diffusion in the presence of sharp gradients. The model version E39/SLT significantly overestimates the water vapor mixing ratio in the extratropical lowermost stratosphere (wet bias) by a factor of 3-5 compared to HALOE observations. Compared to E39/SLT, E39/ATTILA shows substantially reduced water vapor mixing ratios in the extratropical lowermost stratosphere up to 70%, and a steeper meridional water vapor gradient in the subtropics which is in better agreement with observations. Furthermore, the temperature distribution as simulated with E39/SLT is characterized by a pronounced cold temperature bias in the extratropical lowermost stratosphere (cold bias) and in the polar stratosphere above 50 hPa in winter (cold pole). The improvements concerning the water vapor distribution in E39/ATTILA lead to a substantial reduction of the simulated cold bias by approximately 5-7 K which also results in a better representation of the modeled tropopause, especially in the extratropics. Sensitivity studies indicate that the warming of the extratropical lowermost stratosphere in E39/ATTILA is directly related to the reduced wet bias resulting in a less infrared radiative cooling. Additionally, the cold pole problem is also slightly reduced in E39/ATTILA by approximately 2-5 K.
NASA Astrophysics Data System (ADS)
Lee, H.-J.; Kim, S.-W.; Brioude, J.; Cooper, O. R.; Frost, G. J.; Kim, C.-H.; Park, R. J.; Trainer, M.; Woo, J.-H.
2014-03-01
Nitrogen dioxide (NO2) columns observed from space have been useful in detecting the increase of nitrogen oxides (NOx) emissions in East Asia, particularly China, coinciding with rapid economic growth during the past several decades. NO2 columns retrieved above a particular location reflect a combination of local NOx emissions and transported NOx from upwind sources. In this study, we demonstrate the transport of NOx emitted in East Asia using satellite and surface in situ measurements and Lagrangian particle dispersion model simulations. Enhanced satellite NO2 columns in the Yellow Sea (between China and South Korea) and the East Sea (between South Korea and Japan), and different seasonal variations of NO2 in China, North and South Korea, and Japan, suggest the importance of NOx transport in understanding the local NOx budget. Lagrangian transport model simulations with tracers of different chemical lifetimes identify source-receptor relationships that explain high NO2 over the oceans and springtime peaks in Korea and Japan, with China being the most likely source region. Our results have important implications for studies using satellite NO2 retrievals to derive NOx emissions at local scales in regions adjacent to large sources, such as in East Asia, Europe, and the Eastern U.S.
Speetjens, M. F. M.; Demissie, E. A.; Metcalfe, G.; Clercx, H. J. H.
2014-11-15
Laminar mixing by the inline-mixing principle is a key to many industrial fluids-engineering systems of size extending from micrometers to meters. However, insight into fundamental transport phenomena particularly under the realistic conditions of three-dimensionality (3D) and fluid inertia remains limited. This study addresses these issues for inline mixers with cylindrical geometries and adopts the Rotated Arc Mixer (RAM) as a representative system. Transport is investigated from a Lagrangian perspective by identifying and examining coherent structures that form in the 3D streamline portrait. 3D effects and fluid inertia introduce three key features that are not found in simplified configurations: transition zones between consecutive mixing cells of the inline-mixing flow; local upstream flow (in certain parameter regimes); transition/inertia-induced breaking of symmetries in the Lagrangian equations of motion (causing topological changes in coherent structures). Topological considerations strongly suggest that there nonetheless always exists a net throughflow region between inlet and outlet of the inline-mixing flow that is strictly separated from possible internal regions. The Lagrangian dynamics in this region admits representation by a 2D time-periodic Hamiltonian system. This establishes one fundamental kinematic structure for the present class of inline-mixing flows and implies universal behavior in that all states follow from the Hamiltonian breakdown of one common integrable state. A so-called period-doubling bifurcation is the only way to eliminate transport barriers originating from this state and thus is a necessary (yet not sufficient) condition for global chaos. Important in a practical context is that a common simplification in literature, i.e., cell-wise fully-developed Stokes flow (“2.5D approach”), retains these fundamental kinematic properties and deviates from the generic 3D inertial case only in a quantitative sense. This substantiates its
NASA Astrophysics Data System (ADS)
Reithmeier, Christian; Sausen, Robert; Grewe, Volker
2008-02-01
The Lagrangian scheme ATTILA is used to calculate age spectra and the mean age of air in the general circulation model ECHAM4. The advantage of the Lagrangian method is that temporal variation in transport is taken into account and that beyond transport times the actual transport pathways can be investigated. We found a strong seasonal cycle in mean age and age spectra, especially at high latitudes. When plotting polar age spectra against time, it can clearly be seen that the edge of the polar vortex acts as an efficient transport barrier and that exchange with extra-polar air takes place only for a short period of approximately two months after the polar vortex has broken down. Compared to observations the mean age is reproduced satisfactorily below approximately 20 km. Above that level however, the mean age is underestimated, especially at high latitudes. Furthermore, the observed sharp meridional gradient is located too far polewards in the model, which indicates that the subtropical transport barrier is too weak. There is a distinct variation in the shape of the age spectra with latitude. At low latitudes the age spectra consist of one single peak, whereas at higher latitudes secondary peaks appear, which are one year apart and whose positions in the spectrum are independent of the location. At polar latitudes there are even several peaks of approximately equal size. We explain these peaks with two superposing processes. First, the seasonal cycle of the upward mass flux at the tropical tropopause produces a single peak age distribution. And second, at polar latitudes, the temporal evolution of the polar vortex allows mixing of polar and subtropical air only once a year, which results in a superposition of these single peak age distributions. A final investigation of the transport pathways gave indications for predominant routes from the tropics to high latitudes resulting in altitude dependent meridional transport, however, more detailed studies of 3D
Lagrangian coherent structures in the Gulf Stream
NASA Astrophysics Data System (ADS)
Liu, Yi; Wilson, Chris; Green, Melissa
2015-11-01
Finite-time Lyapunov exponent (FTLE) is calculated to identify Lagrangian coherent structures in the Gulf Stream region. The velocity fields are determined using the geostrophic velocities derived from satellite altimetry data. The coherent structures in and around the Gulf Stream are delineated by the both positive and negative FTLE ridges, and represent boundaries between dynamically distinct regions that are important to investigate transport and mixing processes in the ocean. Alternating positive and negative FTLE ridge patterns are found to line the meandering jet, which indicate the regions of entrainment and detrainment along the jet. Results compare well with the Bower kinematic model of a meandering jet, although it is clear that the kinematic model is an over-simplification of the jet dynamics, and studying the dynamics of vortex interaction with the jet is important for understanding fluid transfer in the Gulf Stream region.
A particle number conserving Lagrangian method for mixing-driven reactive transport
NASA Astrophysics Data System (ADS)
Bolster, Diogo; Paster, Amir; Benson, David A.
2016-02-01
The purely Lagrangian algorithm for chemical reactions introduced by Benson and Meerschaert (2008) suffers from a low-concentration resolution problem. We alleviate the problem by redefining the probabilistic collision/reaction (birth/death) stochastic process as a mass-reduction operation. Theoretically, this corresponds to replacing an on/off particle with a large number of "subparticles" and tracking the number fraction. The new particle reaction process maintains the original particle numbers but adjusts each particle's mass upon reaction. Several simulations show the veracity as well as the gains in low-concentration resolution offered by the algorithm. We also compare the results to those obtained by a traditional finite difference model with suitably defined initial condition, demonstrating that the Lagrangian models match these.
NASA Astrophysics Data System (ADS)
Sato, Tatsuhiro; Tomiyama, Tomoe; Morita, Toyohisa; Murata, Tomohiro
We propose a method for solving the crew rescheduling problem (CRP) and the vehicle rescheduling problem (VRP) based on the Lagrangian relaxation method. The CRP/VRP is formulated as an integer programming problem on the basis of a network flow modeling approach from which a Lagrangian relaxation problem is constructed by relaxing the constraint that links multiple resources. Using two procedures that generate the upper and lower bounds of the primal problem, both of which utilize an efficient shortest path algorithm for the directed acyclic graph (DAG), the proposed method gradually improves the gap between the upper and lower bounds while updating Lagrangian multipliers. Experimental results of real-world vehicle rescheduling data from Japanese railway lines indicated that the proposed method generated feasible solutions that were confirmed to be fairly close to the optimal solutions according to the gap between the upper and lower bounds, and also clarified the quality of the other method's solution by using the gap, which could lead to streamlining and sophisticating real-world rescheduling related activities.
Input-output finite-time stabilization of linear systems with finite-time boundedness.
Guo, Yang; Yao, Yu; Wang, Shicheng; Ma, Kemao; Liu, Kai; Guo, Jian
2014-07-01
The paper presents linear system Input-Output Finite-Time Stabilization (IO-FTS) method under Finite-Time Boundedness (FTB) constraint. A state feedback controller is designed, via Linear Matrix Inequalities (LMIs), to guarantee the system both IO-FTS and FTB. The proposed methods are applied to the guidance design of a class of terminal guidance systems to suppress disturbances with IO-FTS method and FTB constraints simultaneously satisfied. The simulation results illustrate the effectiveness of the proposed methods. PMID:24947432
An Eulerian approach for computing the finite time Lyapunov exponent
NASA Astrophysics Data System (ADS)
Leung, Shingyu
2011-05-01
We propose efficient Eulerian methods for approximating the finite-time Lyapunov exponent (FTLE). The idea is to compute the related flow map using the Level Set Method and the Liouville equation. There are several advantages of the proposed approach. Unlike the usual Lagrangian-type computations, the resulting method requires the velocity field defined only at discrete locations. No interpolation of the velocity field is needed. Also, the method automatically stops a particle trajectory in the case when the ray hits the boundary of the computational domain. The computational complexity of the algorithm is O(Δ x-( d+1) ) with d the dimension of the physical space. Since there are the same number of mesh points in the x- t space, the computational complexity of the proposed Eulerian approach is optimal in the sense that each grid point is visited for only O(1) time. We also extend the algorithm to compute the FTLE on a co-dimension one manifold. The resulting algorithm does not require computation on any local coordinate system and is simple to implement even for an evolving manifold.
NASA Astrophysics Data System (ADS)
Cimorelli, L.; Cozzolino, L.; D'Aniello, A.; Morlando, F.; Pianese, D.; Singh, V. P.
2016-07-01
In this paper, a new numerical model for the simulation of constituent transport in both steady and unsteady flow conditions is presented. The transport model is a routing procedure in which the advection process is solved by means of the Lagrangian coordinate transformation, while the dispersion process is approximated within each time step by means of the convolution principle, exploiting a multilinear procedure. In order to facilitate the application of the Lagrangian coordinate transformation during unsteady flow conditions, the unsteady velocity field corresponding to the linearized parabolic approximation of the Saint Venant Equations is provided, taking into account appropriate boundary conditions. Finally, classic BOD-DO relationships are embedded into the routing procedure in order to perform water quality applications with reactive constituents. The model is first demonstrated with respect to a numerical water quality model in both steady and unsteady hydraulic conditions, and is then applied to two real-world cases. Because of its characteristics, the proposed model seems suitable for real time forecast of pollutant concentrations when an emergency event occurs, or for water quality management in real rivers.
Feng, Shizuo; Cheng, Ralph T.; Pangen, Xi
1986-01-01
The transports of solutes and other tracers are fundamental to estuarine processes. The apparent transport mechanisms are convection by tidal current and current-induced shear effect dispersion for processes which take place in a time period of the order of a tidal cycle. However, as emphasis is shifted toward the effects of intertidal processes, the net transport is mainly determined by tide-induced residual circulation and by residual circulation due to other processes. The commonly used intertidal conservation equation takes the form of a convection-dispersion equation in which the convective velocity is the Eulerian residual current, and the dispersion terms are often referred to as the phase effect dispersion or, sometimes, as the “tidal dispersion.” The presence of these dispersion terms is merely the result of a Fickian type hypothesis. Since the actual processes are not Fickian, thus a Fickian hypothesis obscures the physical significance of this equation. Recent research results on residual circulation have suggested that long-term transport phenomena are closely related to the Lagrangian residual current or the Lagrangian residual transport. In this paper a new formulation of an intertidal conservation equation is presented and examined in detail. In a weakly nonlinear tidal estuary the resultant intertidal transport equation also takes the form of a convection-dispersion equation without the ad hoc introduction of phase effect dispersion in a form of dispersion tensor. The convective velocity in the resultant equation is the first-order Lagrangian residual current (the sum of the Eulerian residual current and the Stokes drift). The remaining dispersion terms are important only in higher-order solutions; they are due to shear effect dispersion and turbulent mixing. There exists a dispersion boundary layer adjacent to shoreline boundaries. An order of magnitude estimate of the properties in the dispersion boundary layer is given. The present treatment
Universality of finite-time disentanglement
NASA Astrophysics Data System (ADS)
Drumond, Raphael C.; Duarte, Cristhiano; Terra Cunha, Marcelo; Nemes, M. C.
2016-02-01
In this paper we investigate how common the phenomenon of finite time disentanglement (FTD) is with respect to the set of quantum dynamics of bipartite quantum states with finite-dimensional Hilbert spaces. Considering a quantum dynamics from a general sense as just a continuous family of completely positive trace preserving maps (CPTP) (parametrized by the time variable) acting on the space of the bipartite systems, we conjecture that FTD happens for all dynamics but those when all maps of the family are induced by local unitary operations. We prove that this conjecture is valid for two important cases: (i) when all maps are induced by unitaries and (ii) for pairs of qubits, when all maps are unital. Moreover, we prove some general results about unitaries that preserve product states and about CPTP maps preserving pure states.
Finite time singularity in a glass
NASA Astrophysics Data System (ADS)
Gallaire, Francois; Viola, Francesco; Dollet, Benjamin; Brun, Pierre-Thomas
2015-11-01
Using a simple liquid-foam sloshing system as prototype, we demonstrate that nonlinear friction effects, resulting from the multiscale nature of moving contact lines, become predominant at low amplitude and result in a finite-time arrest of the oscillations. This result is in strong contrast with the classical exponential relaxation induced by linear damping. We proceed to derive a model for the oscillation of foam in a cylinder accounting for capillary effects near the container walls, which we solve using multiple scales analysis. These results help rationalize our experimental observations and reveal the importance of sublinear effects in perturbation theory. F.G. aknowledges funding from ERC SimCoMiCs 280117.
Soltanian, Mohamad Reza; Ritzi, Robert W; Dai, Zhenxue; Huang, Chao Cheng
2015-03-01
Physical and chemical heterogeneities have a large impact on reactive transport in porous media. Examples of heterogeneous attributes affecting reactive mass transport are the hydraulic conductivity (K), and the equilibrium sorption distribution coefficient (Kd). This paper uses the Deng et al. (2013) conceptual model for multimodal reactive mineral facies and a Lagrangian-based stochastic theory in order to analyze the reactive solute dispersion in three-dimensional anisotropic heterogeneous porous media with hierarchical organization of reactive minerals. An example based on real field data is used to illustrate the time evolution trends of reactive solute dispersion. The results show that the correlation between the hydraulic conductivity and the equilibrium sorption distribution coefficient does have a significant effect on reactive solute dispersion. The anisotropy ratio does not have a significant effect on reactive solute dispersion. Furthermore, through a sensitivity analysis we investigate the impact of changing the mean, variance, and integral scale of K and Kd on reactive solute dispersion. PMID:25532767
Lagrangian transport near perturbed periodic lines in three-dimensional unsteady flows
NASA Astrophysics Data System (ADS)
Speetjens, Michel
2015-11-01
Periodic lines formed by continuous strings of periodic points are key organizing entities in the Lagrangian flow topology of certain three-dimensional (3D) time-periodic flows. Such lines generically consist of elliptic and/or hyperbolic points and thus give rise to 3D flow topologies made up of families of concentric closed trajectories embedded in chaotic regions. Weak perturbation destroys the periodic lines and causes said trajectories to coalesce into families of concentric tubes. However, emergence of isolated periodic points near the disintegrating periodic lines and/or partitioning of the original lines into elliptic and hyperbolic segments interrupt the tube formation. This yields incomplete tubes that interact with the (chaotic) environment through their open ends, resulting in intricate and essentially 3D flow topologies These phenomena have been observed in various realistic flows yet the underlying mechanisms are to date only partially understood. This study deepens insight into the (perturbed) Lagrangian dynamics of these flows by way of a linearized representation of the equations of motion near the periodic lines. Predictions on the basis of this investigation are in full (qualitative) agreement with observed behavior in the actual flows
A random field approach to the Lagrangian modeling of turbulent transport in vegetated canopies
NASA Astrophysics Data System (ADS)
Cesari, Rita; Paradisi, Paolo
2015-09-01
We present an application of a Lagrangian Stochastic Model (LSM) to turbulent dispersion over complex terrain, where turbulent coherent structures are known to play a crucial role. We investigate the case of a vegetated canopy by using semi-empirical parameterizations of turbulence profiles in the region inside and above a canopy layer. The LSM is based on a 4-dimensional Fokker-Planck (4DFP) equation, which extends the standard Thomson87 Lagrangian approach. The 4DFP model is derived by means of a Random Field description of the turbulent velocity field. The main advantage of this approach is that not only the experimental Eulerian one-point statistics, but also the Eulerian two-point two-time covariance structure can be included explicitly in the LSM. At variance with the standard Thomson87 approach, the 4DFP model allows to consider explicit parameterizations of the turbulent coherent structures as it explicitly includes both spatial and temporal correlation functions. In order to investigate the effect of the turbulent geometrical structure on a scalar concentration profile, we performed numerical simulations with two different covariance parameterizations, the first one isotropic and the second anisotropic. We show that the accumulation of scalars near the ground is due to the anisotropic geometrical properties of the turbulent boundary layer.
Heberton, C.I.; Russell, T.F.; Konikow, L.F.; Hornberger, G.Z.
2000-01-01
This report documents the U.S. Geological Survey Eulerian-Lagrangian Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.
Finite-time singularity signature of hyperinflation
NASA Astrophysics Data System (ADS)
Sornette, D.; Takayasu, H.; Zhou, W.-X.
2003-07-01
We present a novel analysis extending the recent work of Mizuno et al. (Physica A 308 (2002) 411) on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a generalization of Cagan's model of inflation based on the mechanism of “inflationary expectation” of positive feedbacks between realized growth rate and people's expected growth rate, we find that hyperinflations can be characterized by a power law singularity culminating at a critical time tc. Mizuno et al.'s double-exponential function can be seen as a discrete time-step approximation of our more general non-linear ODE formulation of the price dynamics which exhibits a finite-time singular behavior. This extension of Cagan's model, which makes natural the appearance of a critical time tc, has the advantage of providing a well-defined end of the clearly unsustainable hyperinflation regime. We find an excellent and reliable agreement between theory and data for Germany, Hungary, Peru and Bolivia. For Brazil, Israel and Nicaragua, the super-exponential growth seems to be already contaminated significantly by the existence of a cross-over to a stationary regime.
A lagrangian-eulerian description of debris transport by a tsunami in the Lisbon waterfront
NASA Astrophysics Data System (ADS)
Conde, Daniel; Canelas, Ricardo; Baptista, Maria Ana; João Telhado, Maria; Ferreira, Rui M. L.
2013-04-01
Several major tsunamis are known to have struck the Portuguese coast over the past millennia (Baptista and Miranda, 2009). The Tagus estuary has great exposure to tsunami occurrences and, being bordered by the largest metropolitan area in the country, is a particularly worrisome location in what concerns safety of populations and economic losses due to disruption of built infrastructures. The last major earthquake and tsunami combination known to have critically affected the Tagus estuary dates back to November 1st 1755. This catastrophe critically damaged Lisbon's infrastructures, led to numerous casualties and priceless heritage losses. The urban tissue of the present city still bears visible the effects of the catastrophe and of the ensuing protection measures. The objective of this work is to simulate the propagation of debris carried by a 1755-like tsunami along the present-day bathimetric and altimetric conditions of Lisbon waterfront. Particular emphasis was directed to the modeling of vehicles since the tsunami is likely to affect areas that are major traffic nodes such as Alcântara, with more than 1500 vehicles in road network of about 3 km. The simulation tool employed is based on a 2DH spatial (eulerian) shallow-flow approach suited to complex and dynamic bottom boundaries. The discretization technique relies on a finite-volume scheme, based on a flux-splitting technique incorporating a reviewed version of the Roe Riemann solver (Canelas et al. 2013). Two formulations were employed to model the advection of debris: a fully coupled continuum approach, where solid bodies are described by the concentration only and an uncoupled material (lagrangian) formulation where solid bodies are tracked between two time-steps once the flow field is determined by the eulerian solver. In the latter case, concentrations are updated after tracking the solid bodies thus correcting the mass and momentum balance to be used for the next time-step. The urban tissue was
The Lagrangian method provides estimates of the chemical and physical evolution of air arriving in the daytime boundary layer at Baltimore. Study results indicate a dominant role for regional transport contributions of those days when sulfate air pollution is highest in Baltimor...
NASA Astrophysics Data System (ADS)
Ng, C. S.; Bhattacharjee, A.
1996-08-01
A sufficient condition is obtained for the development of a finite-time singularity in a highly symmetric Euler flow, first proposed by Kida [J. Phys. Soc. Jpn. 54, 2132 (1995)] and recently simulated by Boratav and Pelz [Phys. Fluids 6, 2757 (1994)]. It is shown that if the second-order spatial derivative of the pressure (pxx) is positive following a Lagrangian element (on the x axis), then a finite-time singularity must occur. Under some assumptions, this Lagrangian sufficient condition can be reduced to an Eulerian sufficient condition which requires that the fourth-order spatial derivative of the pressure (pxxxx) at the origin be positive for all times leading up to the singularity. Analytical as well as direct numerical evaluation over a large ensemble of initial conditions demonstrate that for fixed total energy, pxxxx is predominantly positive with the average value growing with the numbers of modes.
Lagrangian Flow networks: a new way to characterize transport and connectivity in geophysical flows
NASA Astrophysics Data System (ADS)
Ser-Giacomi, Enrico; Hernandez-Garcia, Emilio; Lopez, Cristobal; Rossi, Vincent; Vasile, Ruggero
2015-04-01
Water and air transport are among the basic processes shaping the climate of our planet. Heat and salinity fluxes change sea water density, and thus drive the global thermohaline circulation. Atmospheric winds force the ocean motion, and also transport moisture, heat or chemicals, impacting the regional climate. We describe transport among different regions of the ocean or the atmosphere by flow networks, giving a discrete and robust representation of the fluid advection dynamics. We use network-theory tools to gain insights into transport problem. Local and global features of the networks are extracted from many numerical experiments to give a time averaged description of the system. Classical concepts like dispersion, mixing and connectivity are finally related to a set of network-like objects contributing to build a "dictionary" between network measures and physical quantities in geophysical flows.
NASA Astrophysics Data System (ADS)
Owen, R. C.; Honrath, R. E.; Val Martin, M.; Lapina, K.
2006-12-01
The Lagrangian transport model FLEXPART has been proven to be a useful tool for the analysis of atmospheric trace gas measurements. In particular, backward simulations, which produce a retroplume product analogous to backward trajectories, have proven to be particularly flexible. While trajectories account for advection, retroplumes can also account for turbulence, convection and deformation of an air parcel. Furthermore, when considering tracers or species with only first-order removal processes, retroplumes can be used to calculate source-receptor relationships. In this work, we present techniques for using retroplumes in conjunction with forward model results to determine transport characteristics for specific species and sources. When these two standard products are combined, information about the distribution, dilution, mixing, and removal of a modeled species en route to a receptor can be determined. We apply these methods in conjunction with measurements of CO, ozone, and nitrogen oxides from the PICO-NARE station, a mountain top observatory in the free troposphere, located in the Azores Islands in the central North Atlantic Ocean.
A massively parallel semi-Lagrangian algorithm for solving the transport equation
Manson, Russell; Wang, Dali
2010-01-01
The scalar transport equation underpins many models employed in science, engineering, technology and business. Application areas include, but are not restricted to, pollution transport, weather forecasting, video analysis and encoding (the optical flow equation), options and stock pricing (the Black-Scholes equation) and spatially explicit ecological models. Unfortunately finding numerical solutions to this equation which are fast and accurate is not trivial. Moreover, finding such numerical algorithms that can be implemented on high performance computer architectures efficiently is challenging. In this paper the authors describe a massively parallel algorithm for solving the advection portion of the transport equation. We present an approach here which is different to that used in most transport models and which we have tried and tested for various scenarios. The approach employs an intelligent domain decomposition based on the vector field of the system equations and thus automatically partitions the computational domain into algorithmically autonomous regions. The solution of a classic pure advection transport problem is shown to be conservative, monotonic and highly accurate at large time steps. Additionally we demonstrate that the algorithm is highly efficient for high performance computer architectures and thus offers a route towards massively parallel application.
Cross-frontal transport along the Keweenaw coast in Lake Superior: a Lagrangian model study
NASA Astrophysics Data System (ADS)
Chen, Changsheng; Zhu, Jianrong; Kang, KiRyong; Liu, Hedong; Ralph, Elise; Green, Sarah A.; Budd, Judith Wells
2002-11-01
Offshore transport across the thermal front along the Keweenaw coast in Lake Superior was examined by tracking the trajectories of water particles in the model-simulated three-dimensional (3D) flow field of July 1973. Particles were released at different depths and horizontal locations within the Keweenaw Current during various wind events and were tracked until the end of the month. The trajectories of water particles showed a remarkable offshore cross-frontal water transport at the topographic-splitting point on the eastern side of the Keweenaw Waterway and near Eagle Harbor. This transport was driven dominantly by wind-induced Ekman flow near the surface but was controlled by local bottom topography in the deep region. A northeastward wind prevailed over the lake during July 1973. This wind tended to produce onshore water transports near the surface and hence caused downwelling against the coast. An offshore current was expected in the deep region based on the conservation of water mass. The vortex shedding off coastal bathymetry abutments plus baroclinic instability of the thermal front also led to offshore meandering of the temperature field in the deep region over local varying bottom topography. This meandering tended to produce a cyclonic vorticity and drove particles offshore across the thermal front along the northern coast of the Keweenaw Peninsula.
Birkholzer, J.; Karasaki, K.
1996-07-01
Fracture network simulators have extensively been used in the past for obtaining a better understanding of flow and transport processes in fractured rock. However, most of these models do not account for fluid or solute exchange between the fractures and the porous matrix, although diffusion into the matrix pores can have a major impact on the spreading of contaminants. In the present paper a new finite element code TRIPOLY is introduced which combines a powerful fracture network simulator with an efficient method to account for the diffusive interaction between the fractures and the adjacent matrix blocks. The fracture network simulator used in TRIPOLY features a mixed Lagrangian-Eulerian solution scheme for the transport in fractures, combined with an adaptive gridding technique to account for sharp concentration fronts. The fracture-matrix interaction is calculated with an efficient method which has been successfully used in the past for dual-porosity models. Discrete fractures and matrix blocks are treated as two different systems, and the interaction is modeled by introducing sink/source terms in both systems. It is assumed that diffusive transport in the matrix can be approximated as a one-dimensional process, perpendicular to the adjacent fracture surfaces. A direct solution scheme is employed to solve the coupled fracture and matrix equations. The newly developed combination of the fracture network simulator and the fracture-matrix interaction module allows for detailed studies of spreading processes in fractured porous rock. The authors present a sample application which demonstrate the codes ability of handling large-scale fracture-matrix systems comprising individual fractures and matrix blocks of arbitrary size and shape.
Numerical modeling of pollutant transport using a Lagrangian marker particle technique
NASA Technical Reports Server (NTRS)
Spaulding, M.
1976-01-01
A derivation and code were developed for the three-dimensional mass transport equation, using a particle-in-cell solution technique, to solve coastal zone waste discharge problems where particles are a major component of the waste. Improvements in the particle movement techniques are suggested and typical examples illustrated. Preliminary model comparisons with analytic solutions for an instantaneous point release in a uniform flow show good results in resolving the waste motion. The findings to date indicate that this computational model will provide a useful technique to study the motion of sediment, dredged spoils, and other particulate waste commonly deposited in coastal waters.
Finite-time barriers to front propagation in two-dimensional fluid flows.
Mahoney, John R; Mitchell, Kevin A
2015-08-01
Recent theoretical and experimental investigations have demonstrated the role of certain invariant manifolds, termed burning invariant manifolds (BIMs), as one-way dynamical barriers to reaction fronts propagating within a flowing fluid. These barriers form one-dimensional curves in a two-dimensional fluid flow. In prior studies, the fluid velocity field was required to be either time-independent or time-periodic. In the present study, we develop an approach to identify prominent one-way barriers based only on fluid velocity data over a finite time interval, which may have arbitrary time-dependence. We call such a barrier a burning Lagrangian coherent structure (bLCS) in analogy to Lagrangian coherent structures (LCSs) commonly used in passive advection. Our approach is based on the variational formulation of LCSs using curves of stationary "Lagrangian shear," introduced by Farazmand et al. [Physica D 278-279, 44 (2014)] in the context of passive advection. We numerically validate our technique by demonstrating that the bLCS closely tracks the BIM for a time-independent, double-vortex channel flow with an opposing "wind." PMID:26328575
Finite-time barriers to front propagation in two-dimensional fluid flows
NASA Astrophysics Data System (ADS)
Mahoney, John R.; Mitchell, Kevin A.
2015-08-01
Recent theoretical and experimental investigations have demonstrated the role of certain invariant manifolds, termed burning invariant manifolds (BIMs), as one-way dynamical barriers to reaction fronts propagating within a flowing fluid. These barriers form one-dimensional curves in a two-dimensional fluid flow. In prior studies, the fluid velocity field was required to be either time-independent or time-periodic. In the present study, we develop an approach to identify prominent one-way barriers based only on fluid velocity data over a finite time interval, which may have arbitrary time-dependence. We call such a barrier a burning Lagrangian coherent structure (bLCS) in analogy to Lagrangian coherent structures (LCSs) commonly used in passive advection. Our approach is based on the variational formulation of LCSs using curves of stationary "Lagrangian shear," introduced by Farazmand et al. [Physica D 278-279, 44 (2014)] in the context of passive advection. We numerically validate our technique by demonstrating that the bLCS closely tracks the BIM for a time-independent, double-vortex channel flow with an opposing "wind."
Lagrangian coherent structures in n-dimensional systems
NASA Astrophysics Data System (ADS)
Lekien, Francois; Shadden, Shawn C.; Marsden, Jerrold E.
2007-06-01
Numerical simulations and experimental observations reveal that unsteady fluid systems can be divided into regions of qualitatively different dynamics. The key to understanding transport and stirring is to identify the dynamic boundaries between these almost-invariant regions. Recently, ridges in finite-time Lyapunov exponent fields have been used to define such hyperbolic, almost material, Lagrangian coherent structures in two-dimensional systems. The objective of this paper is to develop and apply a similar theory in higher dimensional spaces. While the separatrix nature of these structures is their most important property, a necessary condition is their almost material nature. This property is addressed in this paper. These results are applied to a model of Rayleigh-Bénard convection based on a three-dimensional extension of the model of Solomon and Gollub.
NASA Astrophysics Data System (ADS)
Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander
2016-02-01
We present the development of the Adjoint of the Global Eulerian-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated
NASA Astrophysics Data System (ADS)
Santoni, G. W.; Xiang, B.; Kort, E. A.; Daube, B.; Andrews, A. E.; Sweeney, C.; Wecht, K.; Peischl, J.; Ryerson, T. B.; Angevine, W. M.; Trainer, M.; Nehrkorn, T.; Eluszkiewicz, J.; Wofsy, S. C.
2012-12-01
We present constraints on California emission inventories of methane (CH4) using atmospheric observations from nine NOAA P-3 flights during the California Nexus (CalNex) campaign in May and June of 2010. Measurements were made using a quantum cascade laser spectrometer (QCLS) and a cavity ring-down spectrometer (CRDS) and calibrated to NOAA standards in-flight. Five flights sampled above the northern and southern central valley and an additional four flights probed the south coast air basin, quantifying emissions from the Los Angeles basin. The data show large (>100 ppb) CH4 enhancements associated with point and area sources such as cattle and manure management, landfills, wastewater treatment, gas production and distribution infrastructure, and rice agriculture. We compare aircraft observations to modeled CH4 distributions by accounting for a) transport using the Stochastic Time-Inverted Lagrangian Transport (STILT) model driven by Weather Research and Forecasting (WRF) meteorology, b) emissions from inventories such as EDGAR and ones constructed from California-specific state and county databases, each gridded to 0.1° x 0.1° resolution, and c) spatially and temporally evolving boundary conditions such as GEOS-Chem and a NOAA aircraft profile measurement derived curtain imposed at the edge of the WRF domain. After accounting for errors associated with transport, planetary boundary layer height, lateral boundary conditions, seasonality of emissions, and the spatial resolution of surface emission prior estimates, we find that the California Air Resources Board (CARB) CH4 budget is a factor of 1.64 too low. Using a Bayesian inversion to the flight data, we estimate California's CH4 budget to be 2.5 TgCH4/yr, with emissions from cattle and manure management, landfills, rice, and natural gas infrastructure, representing roughly 82%, 26%, 9% and 32% (sum = 149% with other sources accounting for the additional 15%) of the current CARB CH4 budget estimate of 1.52 TgCH4
NASA Astrophysics Data System (ADS)
Smith, M.; McDonald, A. J.
2012-04-01
Finite-time Lyapunov exponents are often used to measure mixing in the stratosphere and have been used to investigate the horizontal transport of trace gases near the polar vortices. A better understanding of the dynamics of the polar vortices should provide insight into the circumstances under which odd nitrogen and hydrogen produced by energetic particle precipitation (EPP) in the mesosphere and lower thermosphere (MLT) can be transported to lower levels of the atmosphere. A climatology of finite-time Lyapunov exponents for isentropic surfaces in the stratosphere ranging from 550-2300K for both the northern and southern hemispheres has been created for the observational period of the EOS-MLS instrument.The Lyapunov exponents are derived by using output from a Lagrangian trajectory model forced by data from the MERRA reanalysis. They are calculated at each point on a 2° x 4° global grid by running trajectories for two neighbouring parcels which are initially 1km apart and measuring their separation after a period of time. In order to ensure that the parcel trajectories remain close enough to each other for the exponents to be a good measure of local mixing, the distance between the parcels is periodically reset to 1km. In order to provide a consistency check Lyapunov exponents and trajectories have also been calculated at 550K using NCEP/NCAR reanalysis data. Initial comparisons suggest that the qualitative agreement is quite good between the results using the two different reanalyses. Comparison of the variations in the Lyapunov exponents and trace gas distributions using EOS-MLS data during periods where the stratospheric polar vortices are undisturbed and periods which are disturbed by stratospheric sudden warmings are also discussed. Studying how stratospheric sudden warmings (SSWs) affect the atmospheric dynamics in polar regions is particularly worthwhile since recent studies have shown that they have a significant modulating influence upon the EPP
NASA Technical Reports Server (NTRS)
Considine, David B.; Natarajan, Murali; Fairlie, T. D.; Lingenfelser, Gretchen S.; Bernath, Peter
2007-01-01
We use the LaRC Lagrangian Chemistry and Transport Model (LCTM) [Considine et al., 2007; Pierce et al., 2003] to intercompare ACE, Aura, and HALOE observations of long-lived trace species. The LCTM calculates the transport, mixing, and photochemical evolution of an ensemble of parcels that have been initialized from ACE-FTS measurements. Here we focus on late November, 2004 comparisons, due to the previous 3-week period of continuous HALOE observations and MLS v2.2 data on November 29, 2004.
NASA Astrophysics Data System (ADS)
Sodemann, H.; Lai, T. M.; Marenco, F.; Ryder, C. L.; Flamant, C.; Knippertz, P.; Rosenberg, P.; Bart, M.; McQuaid, J. B.
2015-06-01
Due to the harshness and inaccessibility of desert regions, the uncertainties concerning the processes of dust mobilization at the surface, airborne transport, and sedimentation are still considerable, limiting the ability to perform model simulations. In June 2011, a comprehensive data set of ground-based and airborne in situ measurements and remote sensing observations was acquired within the Fennec/Lagrangian Dust Source Inversion Experiment (LADUNEX) field campaign in the western Sahara region. Here we evaluate the ability of the state-of-the-art Lagrangian particle dispersion model FLEXPART, newly fitted with a dust mobilization capability, to simulate dust transport in this region. We investigate a case where a large mesoscale convective system (MCS) triggered dust emissions in central Mali, which subsequently moved as a large cold pool dust front toward northern Mauritania. Specifying dust mobilization for this case is shown to be an important obstacle to simulating dust transport during this event, since neither the MCS nor the associated cold pool-causing dust emission is represented in the meteorological analysis. Obtaining a realistic dust transport simulation for this case therefore requires an inversion approach using a manual specification of the dust sources supported by satellite imagery. When compared to in situ and remote sensing data from two aircraft, the Lagrangian dust transport simulations represent the overall shape and evolution of the dust plume well. While accumulation and coarse mode dust are well represented in the simulation, giant mode particles are considerably underestimated. Our results re-emphasize that dust emission associated with deep moist convection remains a key issue for reliable dust model simulations in northern Africa.
Attracting Lagrangian coherent structures on Riemannian manifolds.
Karrasch, Daniel
2015-08-01
It is a wide-spread convention to identify repelling Lagrangian Coherent Structures (LCSs) with ridges of the forward finite-time Lyapunov exponent (FTLE) field and to identify attracting LCSs with ridges of the backward FTLE. However, we show that, in two-dimensional incompressible flows, also attracting LCSs appear as ridges of the forward FTLE field. This raises the issue of the characterization of attracting LCSs using a forward finite-time Lyapunov analysis. To this end, we extend recent results regarding the relationship between forward and backward maximal and minimal FTLEs, to both the whole finite-time Lyapunov spectrum and to stretch directions. This is accomplished by considering the singular value decomposition (SVD) of the linearized flow map. By virtue of geometrical insights from the SVD, we provide characterizations of attracting LCSs in forward time for two geometric approaches to hyperbolic LCSs. We apply these results to the attracting FTLE ridge of the incompressible saddle flow. PMID:26328582
Attracting Lagrangian coherent structures on Riemannian manifolds
NASA Astrophysics Data System (ADS)
Karrasch, Daniel
2015-08-01
It is a wide-spread convention to identify repelling Lagrangian Coherent Structures (LCSs) with ridges of the forward finite-time Lyapunov exponent (FTLE) field and to identify attracting LCSs with ridges of the backward FTLE. However, we show that, in two-dimensional incompressible flows, also attracting LCSs appear as ridges of the forward FTLE field. This raises the issue of the characterization of attracting LCSs using a forward finite-time Lyapunov analysis. To this end, we extend recent results regarding the relationship between forward and backward maximal and minimal FTLEs, to both the whole finite-time Lyapunov spectrum and to stretch directions. This is accomplished by considering the singular value decomposition (SVD) of the linearized flow map. By virtue of geometrical insights from the SVD, we provide characterizations of attracting LCSs in forward time for two geometric approaches to hyperbolic LCSs. We apply these results to the attracting FTLE ridge of the incompressible saddle flow.
Dynamic isoperimetry and the geometry of Lagrangian coherent structures
NASA Astrophysics Data System (ADS)
Froyland, Gary
2015-10-01
The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. We propose a novel, direct geometric method to identify subsets of phase space that remain strongly coherent over a finite time duration. This new method is based on a dynamic extension of classical (static) isoperimetric problems; the latter are concerned with identifying submanifolds with the smallest boundary size relative to their volume. The present work introduces dynamic isoperimetric problems; the study of sets with small boundary size relative to volume as they are evolved by a general dynamical system. We formulate and prove dynamic versions of the fundamental (static) isoperimetric (in)equalities; a dynamic Federer-Fleming theorem and a dynamic Cheeger inequality. We introduce a new dynamic Laplace operator and describe a computational method to identify coherent sets based on eigenfunctions of the dynamic Laplacian. Our results include formal mathematical statements concerning geometric properties of finite-time coherent sets, whose boundaries can be regarded as Lagrangian coherent structures. The computational advantages of our new approach are a well-separated spectrum for the dynamic Laplacian, and flexibility in appropriate numerical approximation methods. Finally, we demonstrate that the dynamic Laplace operator can be realised as a zero-diffusion limit of a newly advanced probabilistic transfer operator method [9] for finding coherent sets, which is based on small diffusion. Thus, the present approach sits naturally alongside the probabilistic approach [9], and adds a formal geometric interpretation.
Yeh, Gour-Tsyh; Carpenter, S.L.; Hopkins, P.L.; Siegel, M.D.
1995-11-01
The computer program LEHGC is a Hybrid Lagrangian-Eulerian Finite-Element Model of HydroGeo-Chemical (LEHGC) Transport Through Saturated-Unsaturated Media. LEHGC iteratively solves two-dimensional transport and geochemical equilibrium equations and is a descendant of HYDROGEOCHEM, a strictly Eulerian finite-element reactive transport code. The hybrid Lagrangian-Eulerian scheme improves on the Eulerian scheme by allowing larger time steps to be used in the advection-dominant transport calculations. This causes less numerical dispersion and alleviates the problem of calculated negative concentrations at sharp concentration fronts. The code also is more computationally efficient than the strictly Eulerian version. LEHGC is designed for generic application to reactive transport problems associated with contaminant transport in subsurface media. Input to the program includes the geometry of the system, the spatial distribution of finite elements and nodes, the properties of the media, the potential chemical reactions, and the initial and boundary conditions. Output includes the spatial distribution of chemical element concentrations as a function of time and space and the chemical speciation at user-specified nodes. LEHGC Version 1.1 is a modification of LEHGC Version 1.0. The modification includes: (1) devising a tracking algorithm with the computational effort proportional to N where N is the number of computational grid nodes rather than N{sup 2} as in LEHGC Version 1.0, (2) including multiple adsorbing sites and multiple ion-exchange sites, (3) using four preconditioned conjugate gradient methods for the solution of matrix equations, and (4) providing a model for some features of solute transport by colloids.
NASA Technical Reports Server (NTRS)
Pavish, D. L.; Spaulding, M. L.
1977-01-01
A computer coded Lagrangian marker particle in Eulerian finite difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow.
Lagrangian analysis of hemodynamics data from FSI simulation
Duvernois, Vincent; Marsden, Alison L.; Shadden, Shawn C.
2013-01-01
We present the computation of Lagrangian-based flow characterization measures for time-dependent, deformable-wall, finite-element blood flow simulations. Applicability of the algorithm is demonstrated in a fluid–structure interaction simulation of blood flow through a total cavopulmonary connection (Fontan procedure), and results are compared with a rigid-vessel simulation. Specifically, we report on several important Lagrangian-based measures including flow distributions, finite-time Lyapunov exponent fields, particle residence time, and exposure time calculations. Overall, strong similarity in Lagrangian measures of the flow between deformable and rigid-vessel models was observed. PMID:23559551
NASA Astrophysics Data System (ADS)
Hendabadi, Sahar; Del Alamo, Juan Carlos; Benito, Yolanda; Yotti, Raquel; Bermejo, Javier; Shadden, Shawn
2012-11-01
We discuss work towards understanding human left ventricle (LV) transport and mixing characteristics in normal subjects and patients with dilated cardiomyopathy. Prior studies have shown that the fluid dynamics in the left ventricle (LV) play a major role in dictating overall cardiac health. This study utilizes a noninvasive method to obtain planar velocity data over the apical long-axis view of the LV from color Doppler and B-mode ultrasound measurements. We use a Lagrangian measure to study unsteady behavior of blood transport inside the LV. We compute finite-time Lyapunov exponent (FTLE) fields to extract Lagrangian coherent structures (LCS) from the empirical data. This application presents a particular challenge to Lagrangian computations due to the presence of moving flux, and no-flux, boundaries. We describe a method for unstructured grid generation from the LV motion, and LCS computation on the deforming unstructured grid. Results demonstrate that LCS reveal the moving boundaries confining the blood volume injected to the LV in diastole and ejected into the aorta in systole. We discuss findings related to the quantification of the LV vortex, whose geometry and motion is thought to be an important indicator of cardiac health.
A definition of spectrum for differential equations on finite time
NASA Astrophysics Data System (ADS)
Berger, A.; Doan, T. S.; Siegmund, S.
Hyperbolicity of an autonomous rest point is characterised by its linearization not having eigenvalues on the imaginary axis. More generally, hyperbolicity of any solution which exists for all times can be defined by means of Lyapunov exponents or exponential dichotomies. We go one step further and introduce a meaningful notion of hyperbolicity for linear systems which are defined for finite time only, i.e. on a compact time interval. Hyperbolicity now describes the transient dynamics on that interval. In this framework, we provide a definition of finite-time spectrum, study its relations with classical concepts, and prove an analogue of the Sacker-Sell spectral theorem: For a d-dimensional system the spectrum is non-empty and consists of at most d disjoint (and often compact) intervals. An example illustrates that the corresponding spectral manifolds may not be unique, which in turn leads to several challenging questions.
Kibble-Zurek mechanism and finite-time scaling
NASA Astrophysics Data System (ADS)
Huang, Yingyi; Yin, Shuai; Feng, Baoquan; Zhong, Fan
2014-10-01
The Kibble-Zurek (KZ) mechanism has been applied to a variety of systems ranging from low-temperature Bose-Einstein condensations to grand unification scales in particle physics and cosmology and from classical phase transitions to quantum phase transitions. Here, we show that finite-time scaling (FTS) provides a detailed improved understanding of the mechanism. In particular, the finite time scale, which is introduced by the external driving (or quenching) and results in FTS, is the origin of the division of the adiabatic regimes from the impulse regime in the KZ mechanism. The origin of the KZ scaling for the defect density, generated during the driving through a critical point, is not that the correlation length ceases growing in the nonadiabatic impulse regime, but rather, is that it is taken over by the effective finite length scale corresponding to the finite time scale. We also show that FTS accounts well for and improves the scaling ansatz proposed recently by Liu, Polkovnikov, and Sandvik, [Phys. Rev. B 89, 054307 (2014), 10.1103/PhysRevB.89.054307]. Further, we show that their universal power-law scaling form applies only to some observables in cooling but not to heating. Even in cooling, it is invalid either when an appropriate external field is present. However, this finite-time-finite-size scaling calls for caution in application of FTS. Detailed scaling behaviors of the FTS and finite-size scaling, along with their crossover, are explicitly demonstrated, with the dynamic critical exponent z being estimated for two- and three-dimensional Ising models under the usual Metropolis dynamics. These values of z are found to give rise to better data collapses than the extant values do in most cases but take on different values in heating and cooling in both two- and three-dimensional spaces.
A finite-time exponent for random Ehrenfest gas
Moudgalya, Sanjay; Chandra, Sarthak; Jain, Sudhir R.
2015-10-15
We consider the motion of a system of free particles moving on a plane with regular hard polygonal scatterers arranged in a random manner. Calling this the Ehrenfest gas, which is known to have a zero Lyapunov exponent, we propose a finite-time exponent to characterize its dynamics. As the number of sides of the polygon goes to infinity, when polygon tends to a circle, we recover the usual Lyapunov exponent for the Lorentz gas from the exponent proposed here. To obtain this result, we generalize the reflection law of a beam of rays incident on a polygonal scatterer in a way that the formula for the circular scatterer is recovered in the limit of infinite number of vertices. Thus, chaos emerges from pseudochaos in an appropriate limit. - Highlights: • We present a finite-time exponent for particles moving in a plane containing polygonal scatterers. • The exponent found recovers the Lyapunov exponent in the limit of the polygon becoming a circle. • Our findings unify pseudointegrable and chaotic scattering via a generalized collision rule. • Stretch and fold:shuffle and cut :: Lyapunov:finite-time exponent :: fluid:granular mixing.
NASA Astrophysics Data System (ADS)
Shashkin, Vladimir; Fadeev, Rostislav; Tolstykh, Mikhail
2016-01-01
The article presents conservative cascade scheme using reduced grid (CCS-RG) - a finite volume semi-Lagrangian (FVSL) algorithm for numerical solution of 3D advection equation on the sphere. The CCS-RG is based on the cascade approach that allows to split 3D advected quantity mass remapping between the Lagrangian and Eulerian grids onto 3 1D remappings. Another feature is using a quasi-uniform spaced reduced latitude-longitude grid on the sphere. The scheme is inherently mass-conservative, monotonic and stable with large time-steps. The CCS-RG performance is tested with the advection cases from the Dynamical Core Model Intercomparison Project test suite. The impact of the reduced grids and two different monotonic filters on the solution is investigated. The comparison with the results obtained by other schemes proves competitive accuracy of CCS-RG. In most cases, the numerical solution obtained with various reduced grids is as accurate as the regular grid solution.
NASA Astrophysics Data System (ADS)
Soltanian, Mohamad Reza; Ritzi, Robert W.; Huang, Chao Cheng; Dai, Zhenxue
2015-03-01
This series of papers addresses the transport of sorbing solutes in groundwater. In part 2, plume dispersion, as quantified by the particle displacement variance, X11R>(t>), is linked to hierarchical sedimentary architecture using a Lagrangian-based transport model. This allows for a fundamental understanding of how dispersion arises from the hierarchical architecture of sedimentary facies, and allows for a quantitative decomposition of dispersion into facies-related contributions at different scales within the hierarchy. As in part 1, the plume behavior is assumed to be controlled by linear-equilibrium sorption and the heterogeneity in both the log permeability, Y=ln>(k>), and the log distribution coefficient, Ξ=ln>(Kd>). Heterogeneity in Y and Ξ arises from sedimentary processes and is structured by the consequent sedimentary architecture. Our goal is to understand the basic science of the dispersion process at this very fundamental level. The spatial auto and cross covariances for the relevant attributes are linear sums of terms corresponding to the probability of transitioning across stratal facies types defined at different scales. Unlike previous studies that used empirical relationships for the spatial covariances, here the model parameters are developed from independent measurements of physically quantifiable attributes of the stratal architecture (i.e., proportions and lengths of facies types, and univariate statistics for Y and Ξ). Nothing is assumed about Y-Ξ point correlation; it is allowed to differ by facies type. However, it is assumed that Y and Ξ variance is small but meaningful, and that pore-scale dispersion is negligible. The time-dependent spreading rate is a function of the effective ranges of the cross-transition probability structures (i.e., the ranges of indicator correlation structures) for each relevant scale of stratal hierarchy. As in part 1, the well-documented perchloroethene (PCE) tracer test at the Borden research site is
Theory of Self-Similar Oscillatory Finite-Time Singularities
NASA Astrophysics Data System (ADS)
Sornette, D.; Ide, K.
A simple two-dimensional system is introduced which suggests a qualitative dynamical relationship between (1) stock market prices in the presence of nonlinear trend-followers and nonlinear value investors, (2) the world human population with a competition between a population-dependent growth rate and a nonlinear dependence on a finite carrying capacity and (3) the failure of materials subjected to a time-varying stress with a competition between positive geometrical feedback on the damage variable and nonlinear healing. Our model keeps three key ingredients (inertia, nonlinear positive and negative feedbacks) that compete to give rise to singularities in finite time decorated by accelerating oscillations.
Finite-time thermodynamic analysis of the Stirling engine
Ibrahim, O.M.; Ladas, H.G.
1995-12-31
This paper presents a finite-time thermodynamic analysis of the Stirling engine cycle. A lumped-parameter thermodynamic model is used to describe the dynamic behavior of the Stirling engine. The mathematical formulation of this model is based on mass and energy balances with associated heat transfer rate equations. These governing equations are formulated into a set of ordinary differential equations, which are then solved numerically to obtain the dynamic behavior of the Stirling engine. Close inspection of the governing equations reveals that the time to complete on cycle, {tau} and the engine time constant, {tau}{sub c} always appear together in a dimensionless ratio. This ratio, {tau}/{tau}{sub c}, is defined here as the Finite-Time Parameter, FTP. The effects of FTP upon power output and efficiency, are studied. The results show that there exists an optimum power output for a given engine design, based on engine speed and heat-transfer contact time. The results also provide an engineering evaluation procedure to improve the efficiency and power output of Stirling engines.
NASA Astrophysics Data System (ADS)
Carlson, Daniel F.; Griffa, Annalisa; Zambianchi, Enrico; Suaria, Giuseppe; Corgnati, Lorenzo; Magaldi, Marcello G.; Poulain, Pierre-Marie; Russo, Aniello; Bellomo, Lucio; Mantovani, Carlo; Celentano, Paolo; Molcard, Anne; Borghini, Mireno
2016-04-01
Surface drifters and virtual particles are used to investigate transport between seven coastal regions in the central and southern Adriatic Sea to estimate the degree to which these regions function as a network. Alongshore coastal currents and cyclonic gyres are the primary circulation features that connected regions in the Adriatic Sea. The historical drifter observations span 25 years and, thus, provide estimates of transport between regions realized by the mean surface circulation. The virtual particle trajectories and a dedicated drifter experiment show that southeasterly Sirocco winds can drive eastward cross-Adriatic transport from the Italian coast near the Gargano Promontory to the Dalmatian Islands in Croatia. Southeasterly winds disrupt alongshore transport on the west coast. Northwesterly Mistral winds enhanced east-to-west transport and resulted in stronger southeastward coastal currents in the western Adriatic current (WAC) and export to the northern Ionian Sea. The central Italian regions showed strong connections from north to south, likely realized by alongshore transport in the WAC. Alongshore, downstream transport was weaker on the east coast, likely due to the more complex topography introduced by the Dalmatian Islands of Croatia. Cross-Adriatic connection percentages were higher for east-to-west transport. Cross-Adriatic transport, in general, occurred via the cyclonic sub-gyres, with westward (eastward) transport observed in the northern (southern) arms of the central and southern gyres.
Lagrangian fronts in the ocean
NASA Astrophysics Data System (ADS)
Prants, S. V.; Budyansky, M. V.; Uleysky, M. Yu.
2014-05-01
We introduce the concept of Lagrangian fronts (LFs) in the ocean and describe their importance for analyzing water mixing and transport and the specific features and differences from hydrological fronts. A method of calculating LFs in a given velocity field is proposed. Based on altimeter velocity fields from AVISO data in the northwestern Pacific, we calculate the Lagrangian synoptic maps and identify LFs of different spatial and temporal scales. Using statistical analysis of saury catches in different years according to the Goskomrybolovstvo (State Fisheries Committee of the Russian Federation), we show that LFs can serve as good indicators of places that are favorable for fishing.
NASA Astrophysics Data System (ADS)
Park, Young-Gyu; Son, Young Baek; Choi, Byoung-Ju; Kim, Yong Hoon
2014-05-01
Lagrangian particle tracking experiments were conducted to understand the pathway of the floating green algae patches observed in the Yellow Sea (YS) and East China Sea (ECS) in summer 2011. The numerical simulation results indicated that dominant southerly winds during June and July 2011 were related to offshore movement of the floating green algae, especially their eastward extension in the YS/ECS. An infrequent and unusual event occurred in June 2011: a severe Tropical Strom MEARI, caused the green algae to detach from the coast and initiated movement to the east. After the typhoon event, sea surface temperature recovered rapidly enough to grow the floating green algae, and wind and local current controlled the movement of the massive floating algae patches (coastal accumulation or offshore advection in the area). Analysis of the floating green algae movement using satellite images during passage of Typhoon MAON in July 2011 revealed that the floating green algae patches were significantly controlled by both ocean currents and enhanced winds. These findings suggest that the floating green algae bloom off Qingdao, China and in the middle of the YS and ECS in the summer of 2011 occurred due to the combined effects of recent rapid expansion of seaweed aquaculture, strong winds, and the wind patterns in blooming regions. Our combined approach, using satellite data and numerical simulations, provides a robust estimate for tracing and monitoring changes in green algae blooms on a regional scale.
The Finite Time Lyapunov Exponent Field of N Interacting Vortices in the Zero Viscosity Limit
NASA Astrophysics Data System (ADS)
Galvez, Richard; Green, Melissa
2015-11-01
We present an analysis of the Finite Time Lyapunov Exponent (FTLE) field of interacting vortices in the potential flow limit. This work is based on an inviscid approximation, but develops a useful tool that will aid in the effort of understanding the interactions of vortices and turbulence in viscous fluids. The FTLE field of N interacting vortices is computed numerically in two dimensions in different physical scenarios: i) orbiting one another with no initial velocities, ii) approaching each other given an initial velocity and iii) as periodically produced behind a circular cylinder. For situation ii) we expand on the cases where the approach velocities of the vortices are less than or greater than a critical capture velocity, that is, the velocity necessary to escape a captured orbit between co-rotating vortices. We focus on the evolution and interaction of the Lagrangian coherent structures (LCS) in these scenarios to determine if there is a way to anticipate the character of vortex interaction by the initial structure of the LCS. Additional remarks will be made on the extrapolation of observations to a large number of interacting vortices (large N). This work was supported by the Air Force Office of Scientific Research under AFOSR Award No. FA9550-14-1-0210.
Modeling Finite-Time Failure Probabilities in Risk Analysis Applications.
Dimitrova, Dimitrina S; Kaishev, Vladimir K; Zhao, Shouqi
2015-10-01
In this article, we introduce a framework for analyzing the risk of systems failure based on estimating the failure probability. The latter is defined as the probability that a certain risk process, characterizing the operations of a system, reaches a possibly time-dependent critical risk level within a finite-time interval. Under general assumptions, we define two dually connected models for the risk process and derive explicit expressions for the failure probability and also the joint probability of the time of the occurrence of failure and the excess of the risk process over the risk level. We illustrate how these probabilistic models and results can be successfully applied in several important areas of risk analysis, among which are systems reliability, inventory management, flood control via dam management, infectious disease spread, and financial insolvency. Numerical illustrations are also presented. PMID:26010201
Parisian ruin over a finite-time horizon
NASA Astrophysics Data System (ADS)
Dębicki, Krzysztof; Hashorva, Enkelejd; Ji, LanPeng
2016-03-01
For a risk process $R_u(t)=u+ct-X(t), t\\ge 0$, where $u\\ge 0$ is the initial capital, $c>0$ is the premium rate and $X(t),t\\ge 0$ is an aggregate claim process, we investigate the probability of the Parisian ruin \\[ \\mathcal{P}_S(u,T_u)=\\mathbb{P}\\{\\inf_{t\\in[0,S]} \\sup_{s\\in[t,t+T_u]} R_u(s)<0\\}, \\] with a given positive constant $S$ and a positive measurable function $T_u$. We derive asymptotic expansion of $\\mathcal{P}_S(u,T_u)$, as $u\\to\\infty$, for the aggregate claim process $X$ modeled by Gaussian processes. As a by-product, we derive the exact tail asymptotics of the infimum of a standard Brownian motion with drift over a finite-time interval.
Sliding mode control method having terminal convergence in finite time
NASA Technical Reports Server (NTRS)
Venkataraman, Subramanian T. (Inventor); Gulati, Sandeep (Inventor)
1994-01-01
An object of this invention is to provide robust nonlinear controllers for robotic operations in unstructured environments based upon a new class of closed loop sliding control methods, sometimes denoted terminal sliders, where the new class will enforce closed-loop control convergence to equilibrium in finite time. Improved performance results from the elimination of high frequency control switching previously employed for robustness to parametric uncertainties. Improved performance also results from the dependence of terminal slider stability upon the rate of change of uncertainties over the sliding surface rather than the magnitude of the uncertainty itself for robust control. Terminal sliding mode control also yields improved convergence where convergence time is finite and is to be controlled. A further object is to apply terminal sliders to robot manipulator control and benchmark performance with the traditional computed torque control method and provide for design of control parameters.
Onsager coefficients of a finite-time Carnot cycle
NASA Astrophysics Data System (ADS)
Izumida, Yuki; Okuda, Koji
2009-08-01
We study a finite-time Carnot cycle of a weakly interacting gas which we can regard as a nearly ideal gas in the limit of Th-Tc→0 where Th and Tc are the temperatures of the hot and cold heat reservoirs, respectively. In this limit, we can assume that the cycle is working in the linear-response regime and can calculate the Onsager coefficients of this cycle analytically using the elementary molecular kinetic theory. We reveal that these Onsager coefficients satisfy the so-called tight-coupling condition and this fact explains why the efficiency at the maximal power ηmax of this cycle can attain the Curzon-Ahlborn efficiency from the viewpoint of the linear-response theory.
Onsager coefficients of a finite-time Carnot cycle.
Izumida, Yuki; Okuda, Koji
2009-08-01
We study a finite-time Carnot cycle of a weakly interacting gas which we can regard as a nearly ideal gas in the limit of T(h)-T(c) --> 0 where T(h) and T(c) are the temperatures of the hot and cold heat reservoirs, respectively. In this limit, we can assume that the cycle is working in the linear-response regime and can calculate the Onsager coefficients of this cycle analytically using the elementary molecular kinetic theory. We reveal that these Onsager coefficients satisfy the so-called tight-coupling condition and this fact explains why the efficiency at the maximal power eta(max) of this cycle can attain the Curzon-Ahlborn efficiency from the viewpoint of the linear-response theory. PMID:19792091
Lagrangian coherent structures are associated with fluctuations in airborne microbial populations
NASA Astrophysics Data System (ADS)
Tallapragada, P.; Ross, S. D.; Schmale, D. G.
2011-09-01
Many microorganisms are advected in the lower atmosphere from one habitat to another with scales of motion being hundreds to thousands of kilometers. The concentration of these microbes in the lower atmosphere at a single geographic location can show rapid temporal changes. We used autonomous unmanned aerial vehicles equipped with microbe-sampling devices to collect fungi in the genus Fusarium 100 m above ground level at a single sampling location in Blacksburg, Virginia, USA. Some Fusarium species are important plant and animal pathogens, others saprophytes, and still others are producers of dangerous toxins. We correlated punctuated changes in the concentration of Fusarium to the movement of atmospheric transport barriers identified as finite-time Lyapunov exponent-based Lagrangian coherent structures (LCSs). An analysis of the finite-time Lyapunov exponent field for periods surrounding 73 individual flight collections of Fusarium showed a relationship between punctuated changes in concentrations of Fusarium and the passage times of LCSs, particularly repelling LCSs. This work has implications for understanding the atmospheric transport of invasive microbial species into previously unexposed regions and may contribute to information systems for pest management and disease control in the future.
NASA Technical Reports Server (NTRS)
Cram, Thomas A.; Persing, John; Montgomery, Michael T.; Braun, Scott A.
2006-01-01
The transport and mixing characteristics of a large sample of air parcels within a mature and vertically sheared hurricane vortex is examined. Data from a high-resolution (2 km grid spacing) numerical simulation of "real-case" Hurricane Bonnie (1998) is used to calculate Lagrangian trajectories of air parcels in various subdomains of the hurricane (namely, the eye, eyewall, and near-environment) to study the degree of interaction (transport and mixing) between these subdomains. It is found that 1) there is transport and mixing from the low-level eye to the eyewall that carries high- Be air which can enhance the efficiency of the hurricane heat engine; 2) a portion of the low-level inflow of the hurricane bypasses the eyewall to enter the eye, that both replaces the mass of the low-level eye and lingers for a sufficient time (order 1 hour) to acquire enhanced entropy characteristics through interaction with the ocean beneath the eye; 3) air in the mid- to upper-level eye is exchanged with the eyewall such that more than half the air of the eye is exchanged in five hours in this case of a sheared hurricane; and 4) that one-fifth of the mass in the eyewall at a height of 5 km has an origin in the mid- to upper-level environment where thet(sub e) is much less than in the eyewall, which ventilates the ensemble average eyewall theta(sub e) by about 1 K. Implications of these findings to the problem of hurricane intensity forecasting are discussed.
NASA Technical Reports Server (NTRS)
Taylor, John A.; Brasseur, G. P.; Zimmerman, P. R.; Cicerone, R. J.
1991-01-01
Sources and sinks of methane and methyl chloroform are investigated using a global three-dimensional Lagrangian tropospheric tracer transport model with parameterized hydroxyl and temperature fields. Using the hydroxyl radical field calibrated to the methyl chloroform observations, the globally averaged release of methane and its spatial and temporal distribution were investigated. Two source function models of the spatial and temporal distribution of the flux of methane to the atmosphere were developed. The first model was based on the assumption that methane is emitted as a proportion of net primary productivity (NPP). The second model identified source regions for methane from rice paddies, wetlands, enteric fermentation, termites, and biomass burning based on high-resolution land use data. The most significant difference between the two models were predictions of methane fluxes over China and South East Asia, the location of most of the world's rice paddies, indicating that either the assumption that a uniform fraction of NPP is converted to methane is not valid for rice paddies, or that NPP is underestimated for rice paddies, or that present methane emission estimates from rice paddies are too high.
Lagrangian coherent structures in hurricanes
NASA Astrophysics Data System (ADS)
Lipinski, Doug; Mohseni, Kamran
2011-11-01
We present the results of a ``surface tracking'' algorithm for efficiently computing Lagrangian coherent structure (LCS) surfaces in three dimensions. The algorithm is applied to data from a Weather Research and Forecasting simulation of hurricane Rita. The highly complicated LCS surfaces reveal complex dynamics and transport in the hurricane, particularly in the lower atmosphere boundary layer and the upper level outflow. The lower level transport in the hurricane is of particular importance for accurate intensity prediction in hurricane forecasts due to the uncertainty in the ocean-atmosphere interaction. Understanding the lower level transport and mixing behavior in hurricanes could lead to significant advances in hurricane intensity prediction.
Volkmar, E.C.; Dahlgren, R.A.; Stringfellow, W.T.; Henson, S.S.; Borglin, S.E.; Kendall, C.; Van Nieuwenhuyse, E. E.
2011-01-01
To investigate the mechanism for diel (24h) changes commonly observed at fixed sampling locations and how these diel changes relate to downstream transport in hypereutrophic surface waters, we studied a parcel of agricultural drainage water as it traveled for 84h in a concrete-lined channel having no additional water inputs or outputs. Algal fluorescence, dissolved oxygen, temperature, pH, conductivity, and turbidity were measured every 30min. Grab samples were collected every 2h for water quality analyses, including nutrients, suspended sediment, and chlorophyll/pheophytin. Strong diel patterns were observed for dissolved oxygen, pH, and temperature within the parcel of water. In contrast, algal pigments and nitrate did not exhibit diel patterns within the parcel of water, but did exhibit strong diel patterns for samples collected at a fixed sampling location. The diel patterns observed at fixed sampling locations for these constituents can be attributed to algal growth during the day and downstream transport (washout) of algae at night. Algal pigments showed a rapid daytime increase during the first 48h followed by a general decrease for the remainder of the study, possibly due to sedimentation and photobleaching. Algal growth (primarily diatoms) was apparent each day during the study, as measured by increasing dissolved oxygen concentrations, despite low phosphate concentrations (<0.01mgL-1). ?? 2011 Elsevier B.V.
NASA Astrophysics Data System (ADS)
Dubey, Sarvesh; Mittal, Rashmi; Lauritzen, Peter H.
2014-06-01
A high-order incremental "remap-type" transport scheme is presented (FF-CSLAM). The scheme utilizes bi-quadratic polynomial subgrid-cell reconstruction functions based on the weighted least squares method. The integration of the reconstruction functions over flux areas, which is inherent in remap schemes, makes use of CSLAM approach of line integration. Though the formal order of the scheme is second order, yet quadratic subgrid scale polynomial reconstruction does lead to improvement in the overall accuracy of the scheme. Since the rigorous search for overlap areas between flux areas and grid cells is cumbersome, two simplifications have been suggested in the literature. The main objectives of this paper are (a) to formulate flux-form CSLAM for the icosahedral-hexagonal grid and (b) to assess the accuracy of two flux-integral simplifications.
A method to calculate finite-time Lyapunov exponents for inertial particles in incompressible flows
NASA Astrophysics Data System (ADS)
Garaboa-Paz, D.; Pérez-Muñuzuri, V.
2015-10-01
The present study aims to improve the calculus of finite-time Lyapunov exponents (FTLEs) applied to describe the transport of inertial particles in a fluid flow. To this aim, the deformation tensor is modified to take into account that the stretching rate between particles separated by a certain distance is influenced by the initial velocity of the particles. Thus, the inertial FTLEs (iFTLEs) are defined in terms of the maximum stretching between infinitesimally close trajectories that have different initial velocities. The advantages of this improvement, if compared to the standard method (Shadden et al., 2005), are discussed for the double-gyre flow and the meandering jet flow. The new method allows one to identify the initial velocity that inertial particles must have in order to maximize their dispersion.
NASA Astrophysics Data System (ADS)
Curcoll Masanes, Roger; Rodó, Xavier; Anton, Jordi; Ballester, Joan; Jornet, Albert; Nofuentes, Manel; Sanchez-Manubens, Judith; Morguí, Josep-Anton
2015-04-01
Kawasaki disease (KD) is an acute, coronary artery vasculitis of young children, and still a medical mystery after more than 40 years. A former study [Rodó et al. 2011] demonstrated that certain patterns of winds in the troposphere above the earth's surface flowing from Asia were associated with the times of the annual peak in KD cases and with days having anomalously high numbers of KD patients. In a later study [Rodó et al. 2014], we used residence times from an Air Transport Model to pinpoint the source region for KD. Simulations were generated from locations spanning Japan from days with either high or low KD incidence. In order to cope with stationarity of synoptic situations, only trajectories for the winter months, when there is the maximum in KD cases, were considered. Trajectories traced back in time 10 days for each dataset and location were generated using the flexible particle Lagrangian dispersion model (FLEXPART Version 8.23 [Stohl et al. 2005]) run in backward mode. The particles modeled were air tracers, with 10,000 particles used on each model run. The model output used was residence time, with an output grid of 0.5° latitude × longitude and a time resolution of 3 h. The data input used for the FLEXPART model was gridded atmospheric wind velocity from the European Center for Medium-Range Weather Forecasts Re-Analysis (ERA-Interim at 1°). Aggregates of winter period back-trajectories were calculated for three different regions of Japan. A common source of wind air masses was located for periods with High Kawasaki disease. Knowing the trajectories of winds from the air transport models, a sampling methodology was developed in order to capture the possible etiological agent or other tracers that could have been released together. This methodology is based on the sterilized filtering of high volumes of the transported air at medium tropospheric levels by aircraft sampling and a later analyze these filters with adequate techniques. High purity
A note on finite-time and fixed-time stability.
Lu, Wenlian; Liu, Xiwei; Chen, Tianping
2016-09-01
In this letter, by discussing ṫ(V)=μ(-1)(V), we provide a general approach to reveal the essence of finite-time stability and fixed-time convergence for the system V̇(t)=μ(V(t)). Thus, we derive some conditions for finite-time and fixed-time convergence. As applications, we propose schemes to achieve finite-time and fixed-time synchronization in complex networked systems. PMID:27239892
Finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems
NASA Astrophysics Data System (ADS)
Xie, Xue-Jun; Zhang, Xing-Hui; Zhang, Kemei
2016-07-01
This paper studies the finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems. Based on the stochastic Lyapunov theorem on finite-time stability, by using the homogeneous domination method, the adding one power integrator and sign function method, constructing a ? Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system finite-time stable in probability.
Finite-time synchronization of complex dynamical networks with multi-links via intermittent controls
NASA Astrophysics Data System (ADS)
Zheng, Mingwen; Li, Lixiang; Peng, Haipeng; Xiao, Jinghua; Yang, Yixian; Zhao, Hui; Ren, Jingfeng
2016-02-01
This paper considers finite-time synchronization of complex multi-links dynamical networks with or without internal time delays via intermittent controls. Two simple intermittent feedback controllers are designed to achieve finite-time synchronization between the drive and response system. Some novel and effective finite-time synchronization criteria are derived based on finite-time stability analysis techniques. By constructing suitable Lyapunov functions, we theoretically prove its correctness. Finally, two numerical simulation examples are given to show the effectiveness of proposed method in this paper.
Lagrangian coherent structures and turbulence characteristics downstream of prosthetic aortic valves
NASA Astrophysics Data System (ADS)
de Tullio, Marco D.
2015-11-01
The flowfield through prosthetic heart valves is investigated by means of direct numerical simulations, considering the fully coupled fluid-structure interaction problem. Two different aortic valve models are modeled: a bileaflet mechanical and a biological one. In order to reveal fluid flow structures and to better understand the transport mechanics, Lagrangian coherent structures (LCS) are used. LCS are distinguished material surfaces that can be identified as boundaries to regions with dynamically distinct behavior, and are revealed as hypersurfaces that locally maximize the finite-time Lyapunov exponent (FTLE) fields. Post-processing the flow simulation data, first FTLE fields are calculated integrating dense meshes of Lagrangian particles backward in time, and then attracting LCS are extracted. A three-jet configuration is distinctive of bi-leaflet mechanical valves, with higher turbulent shear stresses immediately distal to the valve leaflets, while a jet-like flow emerges from the central orifice of bio-prosthetic valves, with high turbulent shear stresses occurring at the edge of the jet. Details of the numerical methodology along with a thorough analysis of the different flow structures developing during the cardiac cycle for the two configurations will be provided.
NASA Astrophysics Data System (ADS)
Hasebe, Fumio; Noguchi, Taisuke
2016-04-01
The sudden decrease in stratospheric water vapor at around the year 2000 to 2001 is relatively well accepted in spite of the difficulty to quantify the long-term variations. This stepwise change is studied by examining the entry value of water to the stratosphere ([H2O]e) and some Lagrangian diagnostics of dehydration taking place in the tropical tropopause layer (TTL). The analysis is made using the backward kinematic trajectories initialized every ˜ 10 days from January 1997 to December 2002 at 400 K potential temperature surface in the tropics. The [H2O]e is estimated by the ensemble mean value of the water saturation mixing ratio (SMR) at the Lagrangian cold point (LCP) where SMR becomes minimum (SMR
NASA Astrophysics Data System (ADS)
Lee, Liming; Kou, Kit Ian; Zhang, Wentao; Liang, Jinling; Liu, Yang
2016-07-01
In this paper, we consider finite-time control problems for linear multi-agent systems subject to exogenous constant disturbances and impulses. Some sufficient conditions are obtained to ensure the finite-time boundedness of the multi-agent systems, which could be then reduced to a feasibility problem involving linear matrix inequalities. Numerical examples are given to illustrate the results.
Continuous composite finite-time convergent guidance laws with autopilot dynamics compensation.
He, Shaoming; Lin, Defu
2015-09-01
This paper has proposed two continuous composite finite-time convergent guidance laws to intercept maneuvering targets in the presence of autopilot lag: one is for hit-to-kill and the other is for zeroing the line-of-sight (LOS) angular rate. More specifically, the nonlinear disturbance observer (NDOB) is used to estimate the lumped uncertainty online while the finite-time control technique is used to fulfill the design goal in finite time. The key feature in derivation of the proposed guidance law is that two integral-type Lyapunov functions are used to avoid analytic differentiation of virtual control law encountered with traditional backstepping. The finite-time stability of the closed-loop nonlinear observer-controller system is established using finite-time bounded (FTB) function and Lyapunov function methods. Numerical simulations with some comparisons are carried out to demonstrate the superiority of the proposed method. PMID:26210638
Finite-time master-slave synchronization and parameter identification for uncertain Lurie systems.
Wang, Tianbo; Zhao, Shouwei; Zhou, Wuneng; Yu, Weiqin
2014-07-01
This paper investigates the finite-time master-slave synchronization and parameter identification problem for uncertain Lurie systems based on the finite-time stability theory and the adaptive control method. The finite-time master-slave synchronization means that the state of a slave system follows with that of a master system in finite time, which is more reasonable than the asymptotical synchronization in applications. The uncertainties include the unknown parameters and noise disturbances. An adaptive controller and update laws which ensures the synchronization and parameter identification to be realized in finite time are constructed. Finally, two numerical examples are given to show the effectiveness of the proposed method. PMID:24785822
Lagrangian Simulation of Combustion
Ahmed F. Ghoniem
2008-05-01
A Lagrangian approach for the simulation of reactive flows has been developed during the course of this project, and has been applied to a number of significant and challenging problems including the transverse jet simulations. An efficient strategy for parallel domain decomposition has also been developed to enable the implementation of the approach on massively parallel architecture. Since 2005, we focused our efforts on the development of a semi-Lagrangian treatment of diffusion, and fast and accurate Lagrangian simulation tools for multiphysics problems including combustion.
NASA Astrophysics Data System (ADS)
Mancho, Ana M.; Wiggins, Stephen; Curbelo, Jezabel; Mendoza, Carolina
2013-11-01
Lagrangian descriptors are a recent technique which reveals geometrical structures in phase space and which are valid for aperiodically time dependent dynamical systems. We discuss a general methodology for constructing them and we discuss a ``heuristic argument'' that explains why this method is successful. We support this argument by explicit calculations on a benchmark problem. Several other benchmark examples are considered that allow us to assess the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (``time averages''). In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We thank CESGA for computing facilities. This research was supported by MINECO grants: MTM2011-26696, I-Math C3-0104, ICMAT Severo Ochoa project SEV-2011-0087, and CSIC grant OCEANTECH. SW acknowledges the support of the ONR (Grant No. N00014-01-1-0769).
Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence
NASA Astrophysics Data System (ADS)
Johnson, Perry L.; Meneveau, Charles
2015-08-01
One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ1 : λ2 : λ3 is shown to be about 4:1:-5, compared to about 8:3:-11 when using only the strain-rate tensor for calculating fluid volume deformations. The results
Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence
Johnson, Perry L. Meneveau, Charles
2015-08-15
One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ{sub 1} : λ{sub 2} : λ{sub 3} is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume
Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets
NASA Astrophysics Data System (ADS)
Froyland, Gary; Horenkamp, Christian; Rossi, Vincent; van Sebille, Erik
2015-08-01
Coherent sets in dynamical systems are regions in phase space that optimally "carry mass" with them under the system's evolution, so that these regions experience minimal leakage. The dominant tool for determining coherent sets is the transfer operator, which provides a complete description of Lagrangian mass transport. In this work, we combine existing transfer operator methods with a windowing scheme to study the spatial and temporal evolution of a so-called Agulhas ring: a large anticyclonic mesoscale eddy playing a key role in inter-ocean exchange of climate-relevant properties. Our focus is on ring decay over time and the windowing scheme enables us to study how the most coherent region (our estimate of the ring) varies in position and size over a period of more than two years. We compare the eddy-like structure and its spatio-temporal changes as revealed by our method and by a classical Eulerian approach.
Wang, Leimin; Shen, Yi
2015-11-01
This paper is concerned about the finite-time stabilizability and instabilizability for a class of delayed memristive neural networks (DMNNs). Through the design of a new nonlinear controller, algebraic criteria based on M -matrix are established for the finite-time stabilizability of DMNNs, and the upper bound of the settling time for stabilization is estimated. In addition, finite-time instabilizability algebraic criteria are also established by choosing different parameters of the same nonlinear controller. The effectiveness and the superiority of the obtained results are supported by numerical simulations. PMID:26277003
Wu, Yuanyuan; Cao, Jinde; Alofi, Abdulaziz; Al-Mazrooei, Abdullah; Elaiw, Ahmed
2015-09-01
This paper deals with the finite-time boundedness and stabilization problem for a class of switched neural networks with time-varying delay and parametric uncertainties. Based on Lyapunov-like function method and average dwell time technique, some sufficient conditions are derived to guarantee the finite-time boundedness of considered uncertain switched neural networks. Furthermore, the state feedback controller is designed to solve the finite-time stabilization problem. Moreover, the proposed sufficient conditions can be simplified into the form of linear matrix equalities for conveniently using Matlab LMI toolbox. Finally, two numerical examples are given to show the effectiveness of the main results. PMID:26103615
Global variational approach to elliptic transport barriers in three dimensions
NASA Astrophysics Data System (ADS)
Oettinger, David; Blazevski, Daniel; Haller, George
2016-03-01
We introduce an approach to identify elliptic transport barriers in three-dimensional, time-aperiodic flows. Obtained as Lagrangian Coherent Structures (LCSs), the barriers are tubular non-filamenting surfaces that form and bound coherent material vortices. This extends a previous theory of elliptic LCSs as uniformly stretching material surfaces from two-dimensional to three-dimensional flows. Specifically, we obtain explicit expressions for the normals of pointwise (near-) uniformly stretching material surfaces over a finite time interval. We use this approach to visualize elliptic LCSs in steady and time-aperiodic ABC-type flows.
Global variational approach to elliptic transport barriers in three dimensions.
Oettinger, David; Blazevski, Daniel; Haller, George
2016-03-01
We introduce an approach to identify elliptic transport barriers in three-dimensional, time-aperiodic flows. Obtained as Lagrangian Coherent Structures (LCSs), the barriers are tubular non-filamenting surfaces that form and bound coherent material vortices. This extends a previous theory of elliptic LCSs as uniformly stretching material surfaces from two-dimensional to three-dimensional flows. Specifically, we obtain explicit expressions for the normals of pointwise (near-) uniformly stretching material surfaces over a finite time interval. We use this approach to visualize elliptic LCSs in steady and time-aperiodic ABC-type flows. PMID:27036192
Kannan, Ravishekar; Guo, Peng; Przekwas, Andrzej
2016-06-01
This paper is the first in a series wherein efficient computational methods are developed and implemented to accurately quantify the transport, deposition, and clearance of the microsized particles (range of interest: 2 to 10 µm) in the human respiratory tract. In particular, this paper (part I) deals with (i) development of a detailed 3D computational finite volume mesh comprising of the NOPL (nasal, oral, pharyngeal and larynx), trachea and several airway generations; (ii) use of CFD Research Corporation's finite volume Computational Biology (CoBi) flow solver to obtain the flow physics for an oral inhalation simulation; (iii) implement a novel and accurate nodal inverse distance weighted Eulerian-Lagrangian formulation to accurately obtain the deposition, and (iv) development of Wind-Kessel boundary condition algorithm. This new Wind-Kessel boundary condition algorithm allows the 'escaped' particles to reenter the airway through the outlets, thereby to an extent accounting for the drawbacks of having a finite number of lung generations in the computational mesh. The deposition rates in the NOPL, trachea, the first and second bifurcation were computed, and they were in reasonable accord with the Typical Path Length model. The quantitatively validated results indicate that these developments will be useful for (i) obtaining depositions in diseased lungs (because of asthma and COPD), for which there are no empirical models, and (ii) obtaining the secondary clearance (mucociliary clearance) of the deposited particles. Copyright © 2015 John Wiley & Sons, Ltd. PMID:26317686
Finite time control for MIMO nonlinear system based on higher-order sliding mode.
Liu, Xiangjie; Han, Yaozhen
2014-11-01
Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm. PMID:25277626
Finite time blowup of solutions to the nonlinear Schrödinger equation without gauge invariance
NASA Astrophysics Data System (ADS)
Fujiwara, Kazumasa; Ozawa, Tohru
2016-08-01
A lifespan estimate and a condition of the initial data for finite time blowup for the nonlinear Schrödinger equation are presented from a view point of ordinary differential equation (ODE) mechanism.
Finite-time stabilization control for discontinuous time-delayed networks: New switching design.
Zhang, Ling-Ling; Huang, Li-Hong; Cai, Zuo-Wei
2016-03-01
This paper discusses the finite-time stabilization problem for time-varying delayed neural networks (DNNs) with discontinuous activation functions. By using fixed point theory and set-valued analysis, we establish the existence theorem of equilibrium point. In order to stabilize the states of this class of discontinuous DNNs in finite time, we design two different kinds of switching controllers which are described by discontinuous functions. Under the framework of Filippov solutions, several new and effective criteria are derived to realize finite-time stabilization of discontinuous DNNs based on the famous finite-time stability theory. Besides, the upper bounds of the settling time of stabilization are estimated. Numerical examples are finally provided to illustrate the correctness of the proposed design method and theoretical results. PMID:26752437
Finite-Time Consensus for Multiagent Systems With Cooperative and Antagonistic Interactions.
Meng, Deyuan; Jia, Yingmin; Du, Junping
2016-04-01
This paper deals with finite-time consensus problems for multiagent systems that are subject to hybrid cooperative and antagonistic interactions. Two consensus protocols are constructed by employing the nearest neighbor rule. It is shown that under the presented protocols, the states of all agents can be guaranteed to reach an agreement in a finite time regarding consensus values that are the same in modulus but may not be the same in sign. In particular, the second protocol can enable all agents to reach a finite-time consensus with a settling time that is not dependent upon the initial states of agents. Simulation results are given to demonstrate the effectiveness and finite-time convergence of the proposed consensus protocols. PMID:25955996
On the Impossibility of Finite-Time Splash Singularities for Vortex Sheets
NASA Astrophysics Data System (ADS)
Coutand, Daniel; Shkoller, Steve
2016-08-01
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface self-intersects in finite time. By means of elementary arguments, we prove that such a singularity cannot occur in finite time for vortex sheet evolution, that is for the two-phase incompressible Euler equations. We prove this by contradiction; we assume that a splash singularity does indeed occur in finite time. Based on this assumption, we find precise blow-up rates for the components of the velocity gradient which, in turn, allow us to characterize the geometry of the evolving interface just prior to self-intersection. The constraints on the geometry then lead to an impossible outcome, showing that our assumption of a finite-time splash singularity was false.
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Sathishkumar, M.; Kaviarasan, B.; Anthoni, S. Marshal
2016-04-01
This article addresses the issue of robust finite-time passivity for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time-varying delays and Markovian jumping parameters. By constructing a proper Lyapunov-Krasovskii functional involving the lower and upper bounds of time delays, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantees the finite-time boundedness and finite-time passivity of the addressed GRNs for all admissible uncertainties and satisfies the given passive performance index. More precisely, the conditions are obtained with respect to the finite-time interval, while the exogenous disturbances are unknown but energy bounded. Furthermore, the Schur complement together with reciprocally convex optimisation approach is used to simplify the derivation in the main results. Finally, three numerical examples are provided to illustrate the validity of the obtained results.
Robust finite-time chaos synchronization of uncertain permanent magnet synchronous motors.
Chen, Qiang; Ren, Xuemei; Na, Jing
2015-09-01
In this paper, a robust finite-time chaos synchronization scheme is proposed for two uncertain third-order permanent magnet synchronous motors (PMSMs). The whole synchronization error system is divided into two cascaded subsystems: a first-order subsystem and a second-order subsystem. For the first subsystem, we design a finite-time controller based on the finite-time Lyapunov stability theory. Then, according to the backstepping idea and the adding a power integrator technique, a second finite-time controller is constructed recursively for the second subsystem. No exogenous forces are required in the controllers design but only the direct-axis (d-axis) and the quadrature-axis (q-axis) stator voltages are used as manipulated variables. Comparative simulations are provided to show the effectiveness and superior performance of the proposed method. PMID:26250587
Decision Making and Finite-Time Motion Control for a Group of Robots.
Lu, Qiang; Liu, Shirong; Xie, Xiaogao; Wang, Jian
2013-04-01
This paper deals with the problem of odor source localization by designing and analyzing a decision-control system (DCS) for a group of robots. In the decision level, concentration magnitude information and wind information detected by robots are used to predict a probable position of the odor source. Specifically, the idea of particle swarm optimization is introduced to give a probable position of the odor source in terms of concentration magnitude information. Moreover, an observation model of the position of the odor source is built according to wind information, and a Kalman filter is used to estimate the position of the odor source, which is combined with the position obtained by using concentration magnitude information in order to make a decision on the position of the odor source. In the control level, two types of the finite-time motion control algorithms are designed; one is a finite-time parallel motion control algorithm, while the other is a finite-time circular motion control algorithm. Precisely, a nonlinear finite-time consensus algorithm is first proposed, and a Lyapunov approach is used to analyze the finite-time convergence of the proposed consensus algorithm. Then, on the basis of the proposed finite-time consensus algorithm, a finite-time parallel motion control algorithm, which can control the group of robots to trace the plume and move toward the probable position of odor source, is derived. Next, a finite-time circular motion control algorithm, which can enable the robot group to circle the probable position of the odor source in order to search for odor clues, is also developed. Finally, the performance capabilities of the proposed DCS are illustrated through the problem of odor source localization. PMID:23033435
On the Finite-Time Splash and Splat Singularities for the 3-D Free-Surface Euler Equations
NASA Astrophysics Data System (ADS)
Coutand, Daniel; Shkoller, Steve
2014-01-01
We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in Castro et al. (Splash singularity for water waves, http://arxiv.org/abs/1106.2120v2, 2011), wherein the evolving 2-D hypersurface, the moving boundary of the fluid domain, self-intersects at a point (or on surface). Such singularities can occur when the crest of a breaking wave falls unto its trough, or in the study of drop impact upon liquid surfaces. Our approach is founded upon the Lagrangian description of the free-boundary problem, combined with a novel approximation scheme of a finite collection of local coordinate charts; as such we are able to analyze a rather general set of geometries for the evolving 2-D free-surface of the fluid. We do not assume the fluid is irrotational, and as such, our method can be used for a number of other fluid interface problems, including compressible flows, plasmas, as well as the inclusion of surface tension effects.
Finite-time stabilisation of simple mechanical systems using continuous feedback
NASA Astrophysics Data System (ADS)
Sanyal, Amit K.; Bohn, Jan
2015-04-01
Stabilisation of simple mechanical systems in finite time with continuous state feedback is considered here. The dynamics are represented by generalised (local) coordinates. A general methodology to construct control Lyapunov functions that are Hölder continuous and that can be used to show finite-time stability of the feedback controlled system, is presented. This construction also gives the feedback control law, and results in the feedback system being Hölder continuous as well. Unlike Lipschitz continuous feedback control systems, the feedback control scheme given here converges to the desired equilibrium in finite time. Moreover, unlike discontinuous and hybrid control schemes, the feedback control law does not lead to chattering in the presence of measurement noise, does not excite unmodelled high-frequency dynamics, and can be implemented with actuators that can only deliver continuous control inputs. The advantages of continuous finite-time stabilisation over continuous asymptotic stabilisation of mechanical systems, has been described in some prior research on finite-time stabilisation of the double integrator. The finite-time stabilisation scheme given here generalises this prior research to multiple degree-of-freedom mechanical systems. A numerical comparison is carried out through numerical simulations on two example systems that are representative of a broad class of simple mechanical systems.
EULER-LAGRANGIAN COMPUTATIONS IN ESTUARINE HYDRODYNAMICS.
Cheng, Ralph T.
1983-01-01
The transport of conservative and suspended matter in fluid flows is a phenomenon of Lagrangian nature because the process is usually convection dominant. Nearly all numerical investigations of such problems use an Eulerian formulation for the convenience that the computational grids are fixed in space and because the vast majority of field data are collected in an Eulerian reference frame. Several examples are given in this paper to illustrate a modeling approach which combines the advantages of both the Eulerian and Lagrangian computational techniques.
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1992-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. Unlike the Lagrangian method previously imposed which is valid only for supersonic flows, the present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.
Identification of lagrangian coherent structures in the turbulent boundary layer
NASA Astrophysics Data System (ADS)
Pan, Chong; Wang, Jinjun; Zhang, Cao
2009-02-01
Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved 2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized as legs of quasi-streamwise vortices extending deep into the near wall region with an inclination angle θ to the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic shape of typical LCS reveals that the probability density distribution of θ accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is implemented to get the ensemble-averaged inclination angle θ R of typical LCS. θ R first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of θ saturates at y +=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to the head is located around y +=100. The ensemble- averaged convection velocity U c of typical LCS is finally calculated from temporal-spatial correlation analysis of FTLE field. It is found that the wall-normal profile of the convection velocity U c( y) accords well with the local mean velocity profile U( y) beyond the buffer layer, evidencing that the downstream convection of hairpins determines the transportation properties of the turbulent boundary layer in the log-region and beyond.
NASA Astrophysics Data System (ADS)
Christov, Ivan C.; Ottino, Julio M.; Lueptow, Richard M.
2011-10-01
Through a combined computational-experimental study of flow in a slowly rotating quasi-two-dimensional container, we show several new aspects related to the kinematics of granular mixing. In the Lagrangian frame, for small numbers of revolutions, the mixing pattern is captured by a model termed "streamline jumping." This minimal model, arising at the limit of a vanishingly thin surface flowing layer, possesses no intrinsic stretching or streamline crossing in the usual sense, yet it can lead to complex particle trajectories. Meanwhile, for intermediate numbers of revolutions, we show the presence of naturally persistent granular mixing patterns, i.e., "strange" eigenmodes of the advection-diffusion operator governing the mixing process in Eulerian frame. Through a comparative analysis of the structure of eigenmodes and the corresponding Poincaré section and finite-time Lyapunov exponent field of the flow, the relationship between the Eulerian and Lagrangian descriptions of mixing is highlighted. Finally, we show how the mapping method for scalar transport can be modified to include diffusion. This allows us to examine (for the first time in a granular flow) the change in shape, lifespan, and eventual decay of eigenmodes due to diffusive effects at larger numbers of revolutions.
Lagrangian analysis of a convective mixed layer
NASA Astrophysics Data System (ADS)
D'Asaro, Eric A.; Winters, Kraig B.; Lien, Ren-Chieh
2002-05-01
We characterize and quantify the transport of heat (Boussinesq density) in a highly idealized entraining convective mixed layer based on simulations of Lagrangian measurements in a two-dimensional model. The primary objectives are to assess and explore the merits and difficulties in estimating the heat budget from perfect and imperfect Lagrangian floats. A significant advantage of Lagrangian measurements is that the time derivative of temperature along these trajectories gives a direct measure of the diffusive heat flux. Using simulated perfect Lagrangian floats, estimates of the surface buoyancy flux, the depth of the mixed layer, vertical profiles of advective and diffusive heat flux, and the overall rate of cooling are shown to agree accurately with the known results extracted from the Eulerian simulations. The Lagrangian nature of the data is exploited to reveal the structure of the flow within the convective layer and to quantify the heat fluxes associated with the different types of eddies. Phase plots of Lagrangian trajectories in density-depth space reveal three distinct classes of motions: (1) plumes, which develop in the cold, heavy near-surface thermal boundary layer and plunge into the mixed layer interior carrying heavy water downward; (2) interior turbulence, comprising random motions between the base of the thermal boundary layer and the base of the surface mixed layer; and (3) entrainment of interior water into plumes below the thermal boundary layer, i.e., a transition from class 2 to class 1. Plumes dominate the heat transport. Simulations were also made using slightly buoyant floats; these are not perfectly Lagrangian. Buoyancy concentrates the floats near the surface resulting in an oversampling of the stronger plumes. Making the same heat budget calculations as with the perfect floats results in a nonzero estimated Lagrangian heating rate in the interior and a curved profile of vertical heat flux that is up to 3 times too large. The local time
Lagrangian description of warm plasmas
NASA Technical Reports Server (NTRS)
Kim, H.
1970-01-01
Efforts are described to extend the averaged Lagrangian method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic Lagrangian is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic Lagrangian. In the first of these, the Lagrangian is obtained by velocity integration of the exact microscopic Lagrangian. In the second, the expanded hydrodynamic Lagrangian is obtained directly from the expanded microscopic Lagrangian. As applications of the microscopic Lagrangian, the small-signal dispersion relations and the coupled mode equations are derived for all possible waves in a warm infinite, weakly inhomogeneous magnetoplasma, and their interactions are examined.
Two-dimensional Lagrangian simulation of suspended sediment
Schoellhamer, David H.
1988-01-01
A two-dimensional laterally averaged model for suspended sediment transport in steady gradually varied flow that is based on the Lagrangian reference frame is presented. The layered Lagrangian transport model (LLTM) for suspended sediment performs laterally averaged concentration. The elevations of nearly horizontal streamlines and the simulation time step are selected to optimize model stability and efficiency. The computational elements are parcels of water that are moved along the streamlines in the Lagrangian sense and are mixed with neighboring parcels. Three applications show that the LLTM can accurately simulate theoretical and empirical nonequilibrium suspended sediment distributions and slug injections of suspended sediment in a laboratory flume.
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…
Finite-time synchronization for memristor-based neural networks with time-varying delays.
Abdurahman, Abdujelil; Jiang, Haijun; Teng, Zhidong
2015-09-01
Memristive network exhibits state-dependent switching behaviors due to the physical properties of memristor, which is an ideal tool to mimic the functionalities of the human brain. In this paper, finite-time synchronization is considered for a class of memristor-based neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, several new sufficient conditions ensuring the finite-time synchronization of memristor-based chaotic neural networks are obtained by using analysis technique, finite time stability theorem and adding a suitable feedback controller. Besides, the upper bounds of the settling time of synchronization are estimated. Finally, a numerical example is given to show the effectiveness and feasibility of the obtained results. PMID:26024807
Robust finite-time tracking control of nonholonomic mobile robots without velocity measurements
NASA Astrophysics Data System (ADS)
Shi, Shang; Yu, Xin; Khoo, Suiyang
2016-02-01
The problem of robust finite-time trajectory tracking of nonholonomic mobile robots with unmeasurable velocities is studied. The contributions of the paper are that: first, in the case that the angular velocity of the mobile robot is unmeasurable, a composite controller including the observer-based partial state feedback control and the disturbance feed-forward compensation is designed, which guarantees that the tracking errors converge to zero in finite time. Second, if the linear velocity as well as the angular velocity of mobile robot is unmeasurable, with a stronger constraint, the finite-time trajectory tracking control of nonholonomic mobile robot is also addressed. Finally, the effectiveness of the proposed control laws is demonstrated by simulation.
Finite-Time Consensus of Multiagent Systems With a Switching Protocol.
Liu, Xiaoyang; Lam, James; Yu, Wenwu; Chen, Guanrong
2016-04-01
In this paper, we study the problem of finite-time consensus of multiagent systems on a fixed directed interaction graph with a new protocol. Existing finite-time consensus protocols can be divided into two types: 1) continuous and 2) discontinuous, which were studied separately in the past. In this paper, we deal with both continuous and discontinuous protocols simultaneously, and design a centralized switching consensus protocol such that the finite-time consensus can be realized in a fast speed. The switching protocol depends on the range of the initial disagreement of the agents, for which we derive an exact bound to indicate at what time a continuous or a discontinuous protocol should be selected to use. Finally, we provide two numerical examples to illustrate the superiority of the proposed protocol and design method. PMID:25974952
Cheng, Jun; Xiang, Huili; Wang, Hailing; Liu, Zhijun; Hou, Liyuan
2016-01-01
This paper studies the finite-time stochastic contractive boundedness problem for a class of Markovian jump linear systems subject to input constraints. First of all, by employing exogenous disturbance, two novel concepts, namely finite-time stochastic contractive stability (FTSCS) and finite-time stochastic contractive boundedness (FTSCB) are introduced. Secondly, a relaxation scheme for incomplete (i.e., partly known, unknown, and uncertain) transition probability descriptions is introduced. Then, two kinds of design methodology of observer-based controllers are proposed. All the design conditions are established by employing a set of linear matrix inequalities (LMIs). At last, numerical examples are given to demonstrate the effectiveness of the proposed approach. PMID:26596242
Finite-time consensus of time-varying nonlinear multi-agent systems
NASA Astrophysics Data System (ADS)
Liu, Qingrong; Liang, Zhishan
2016-08-01
This paper investigates the problem of leader-follower finite-time consensus for a class of time-varying nonlinear multi-agent systems. The dynamics of each agent is assumed to be represented by a strict feedback nonlinear system, where nonlinearities satisfy Lipschitz growth conditions with time-varying gains. The main design procedure is outlined as follows. First, it is shown that the leader-follower consensus problem is equivalent to a conventional control problem of multi-variable high-dimension systems. Second, by introducing a state transformation, the control problem is converted into the construction problem of two dynamic equations. Third, based on the Lyapunov stability theorem, the global finite-time stability of the closed-loop control system is proved, and the finite-time consensus of the concerned multi-agent systems is thus guaranteed. An example is given to verify the effectiveness of the proposed consensus protocol algorithm.
A new protocol for finite-time consensus of detail-balanced multi-agent networks.
Yang, Shaofu; Cao, Jinde; Lu, Jianquan
2012-12-01
In this paper, a finite-time consensus protocol for multi-agent networks is discussed from a new perspective. The order β of the nonlinear function in the protocol is shown to be a crucial parameter in analyzing the finite-time consensus property of multi-agent networks with a detail-balanced communication topology. When β>0, the corresponding protocol can guarantee the consensus of the multi-agent networks. In particular, if β∈(0,1), the consensus can be realized within finite time. A leader-follow model is also investigated in this paper. Finally, several concrete protocols are proposed based on our theoretical analysis, and numerical examples are given to make a comparison among different protocols from the aspect of convergence speed. PMID:23278069
NASA Astrophysics Data System (ADS)
Doan, T. S.; Palmer, K.; Siegmund, S.
2011-06-01
Dynamical behaviour on a compact (finite-time) interval is called monotone-hyperbolic or M-hyperbolic if there exists an invariant splitting consisting of solutions with monotonically decreasing and increasing norms, respectively. This finite-time hyperbolicity notion depends on the norm. For arbitrary norms we prove a spectral theorem based on M-hyperbolicity and extend Gershgorin's circle theorem to this type of finite-time spectrum. Similarly to stable and unstable manifolds, we characterize M-hyperbolicity by means of existence of stable and unstable cones. These cones can be explicitly computed for D-hyperbolic systems with norms induced by symmetric positive definite matrices and also for row diagonally dominant systems with the sup-norm, thus providing sufficient and computable conditions for M-hyperbolicity.
Lagrangian coherent structures and the dynamics of inertial particles
NASA Astrophysics Data System (ADS)
Madhavan, Sudharsan
Dynamics of inertial particles in two-dimensional planar flow have been investigated by evaluating finite-time Lyapunov exponents (FTLE). The first part of our work deals with inertial particle dynamics. The Maxey-Riley equations have been employed to track particles. Patterns formed by inertial particles are reported along with their dependance on Strokes number and density of particles relative to the carrier-fluid density. Our results distinguish patterns formed by particles denser than the fluid (aerosols) from those formed by particles lighter than the fluid (bubbles). Preferential concentration of these particles at specific regions of the flow have been observed. The attenuating, low-pass filter effect of Stokes drag on bubbles are reported for the first time. The results from this part of the work motivated further investigations into the underlying organizing structures of the flow, namely the Lagrangian coherent structures (LCS). LCS is traditionally evaluated using FTLE. In the next part of the work, our objective was to interpret the dynamics of inertial particles by evaluating finite-time Lyapunov exponents on their trajectories. A main result is that aerosols were found to be attracted and preferentially concentrated along ridges of negative finite-time Lyapunov exponents (nFTLE) of the underlying flow. On the other hand bubbles were found to be repelled from these structures and were therefore observed preferentially concentrating away from these zones. These results, being reported for the first time, supplement the existing literature on preferential concentration of inertial particles. Despite having an effect on particle trajectories, increasing the Stokes number had very little effect on inertial finite-time Lyapunov exponents (iFTLE). Furthermore, increasing Stokes number resulted in an increase in the ridges of iFTLE contours for aerosols, whereas for bubbles the opposite was observed. These findings indicate that optimum mixing occurs at
Finite-time synchronization control of a class of memristor-based recurrent neural networks.
Jiang, Minghui; Wang, Shuangtao; Mei, Jun; Shen, Yanjun
2015-03-01
This paper presents a global and local finite-time synchronization control law for memristor neural networks. By utilizing the drive-response concept, differential inclusions theory, and Lyapunov functional method, we establish several sufficient conditions for finite-time synchronization between the master and corresponding slave memristor-based neural network with the designed controller. In comparison with the existing results, the proposed stability conditions are new, and the obtained results extend some previous works on conventional recurrent neural networks. Two numerical examples are provided to illustrate the effective of the design method. PMID:25536233
An integral equation representation approach for valuing Russian options with a finite time horizon
NASA Astrophysics Data System (ADS)
Jeon, Junkee; Han, Heejae; Kim, Hyeonuk; Kang, Myungjoo
2016-07-01
In this paper, we first describe a general solution for the inhomogeneous Black-Scholes partial differential equation with mixed boundary conditions using Mellin transform techniques. Since Russian options with a finite time horizon are usually formulated into the inhomogeneous free-boundary Black-Scholes partial differential equation with a mixed boundary condition, we apply our method to Russian options and derive an integral equation satisfied by Russian options with a finite time horizon. Furthermore, we present some numerical solutions and plots of the integral equation using recursive integration methods and demonstrate the computational accuracy and efficiency of our method compared to other competing approaches.
Global generalised exponential/finite-time control for course-keeping of ships
NASA Astrophysics Data System (ADS)
Sun, Xifang; Chen, Weisheng
2016-06-01
This paper addresses the global generalised exponential/finite-time control of the nonlinear ship course system with an unknown control coefficient. Different from the well-known Nussbaum-gain adaptive rule, a new Lyapunov-based adaptive logic switching rule is proposed to seek the correct control direction of the ship course system. The main advantage of the proposed controller is that it guarantees the global generalised exponential/finite-time control of closed-loop systems. Theoretical analysis and simulation results show the effectiveness of the developed control method.
NASA Astrophysics Data System (ADS)
Guo, Yong; Song, Shen-Min; Li, Xue-Hui
2016-05-01
In this paper, two finite-time attitude coordinated controllers for formation flying spacecraft are investigated based on rotation matrix. Because rotation matrix can represent the set of attitudes both globally and uniquely, the two controllers can deal with unwinding that can result in extra fuel consumption. To address the lack of angular velocity measurement, the second attitude coordinated controller is given by using a novel filter. Through homogeneous method and Lyapunov theories, it is shown that the proposed controllers can achieve the finite-time stability. Numerical simulations also demonstrate that the proposed control schemes are effective.
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1993-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. The present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multidimensional discontinuities with a high level of accuracy, similar to that found in 1D problems.
Gravity, Time, and Lagrangians
ERIC Educational Resources Information Center
Huggins, Elisha
2010-01-01
Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…
Compressible Lagrangian hydrodynamics without Lagrangian cells
NASA Astrophysics Data System (ADS)
Clark, Robert A.
The partial differential Eqs [2.1, 2.2, and 2.3], along with the equation of state 2.4, which describe the time evolution of compressible fluid flow can be solved without the use of a Lagrangian mesh. The method follows embedded fluid points and uses finite difference approximations to ěc nablaP and ěc nabla · ěc u to update p, ěc u and e. We have demonstrated that the method can accurately calculate highly distorted flows without difficulty. The finite difference approximations are not unique, improvements may be found in the near future. The neighbor selection is not unique, but the one being used at present appears to do an excellent job. The method could be directly extended to three dimensions. One drawback to the method is the failure toexplicitly conserve mass, momentum and energy. In fact, at any given time, the mass is not defined. We must perform an auxiliary calculation by integrating the density field over space to obtain mass, energy and momentum. However, in all cases where we have done this, we have found the drift in these quantities to be no more than a few percent.
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1995-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.
Lagrangian-based investigation of the transient flow structures around a pitching hydrofoil
NASA Astrophysics Data System (ADS)
Wu, Qin; Huang, Biao; Wang, Guoyu
2016-02-01
The objective of this paper is to address the transient flow structures around a pitching hydrofoil by combining physical and numerical studies. In order to predict the dynamic behavior of the flow structure effectively, the Lagrangian coherent structures (LCS) defined by the ridges of the finite-time Lyapunov exponent (FTLE) are utilized under the framework of Navier-Stokes flow computations. In the numerical simulations, the k-ω shear stress transport (SST) turbulence model, coupled with a two-equation γ {-Re}_θ transition model, is used for the turbulence closure. Results are presented for a NACA66 hydrofoil undergoing slowly and rapidly pitching motions from 0° to 15° then back to 0° at a moderate Reynolds number Re=7.5× 105. The results reveal that the transient flow structures can be observed by the LCS method. For the slowly pitching case, it consists of five stages: quasi-steady and laminar, transition from laminar to turbulent, vortex development, large-scale vortex shedding, and reverting to laminar. The observation of LCS and Lagrangian particle tracers elucidates that the trailing edge vortex is nearly attached and stable during the vortex development stage and the interaction between the leading and trailing edge vortex caused by the adverse pressure gradient forces the vortexes to shed downstream during the large-scale vortex shedding stage, which corresponds to obvious fluctuations of the hydrodynamic response. For the rapidly pitching case, the inflection is hardly to be observed and the stall is delayed. The vortex formation, interaction, and shedding occurred once instead of being repeated three times, which is responsible for just one fluctuation in the hydrodynamic characteristics. The numerical results also show that the FTLE field has the potential to identify the transient flows, and the LCS can represent the divergence extent of infinite neighboring particles and capture the interface of the vortex region.
Characterizing two-timescale nonlinear dynamics using finite-time Lyapunov exponents and subspaces
NASA Astrophysics Data System (ADS)
Mease, K. D.; Topcu, U.; Aykutluğ, E.; Maggia, M.
2016-07-01
Finite-time Lyapunov exponents and subspaces are used to define and diagnose boundary-layer type, two-timescale behavior in the tangent linear dynamics and to determine the associated manifold structure in the flow of a finite-dimensional nonlinear autonomous dynamical system. Two-timescale behavior is characterized by a slow-fast splitting of the tangent bundle for a state space region. The slow-fast splitting is defined using finite-time Lyapunov exponents and vectors, guided by the asymptotic theory of partially hyperbolic sets, with important modifications for the finite-time case; for example, finite-time Lyapunov analysis relies more heavily on the Lyapunov vectors due to their relatively fast convergence compared to that of the corresponding exponents. The splitting is used to characterize and locate points approximately on normally hyperbolic center manifolds via tangency conditions for the vector field. Determining manifolds from tangent bundle structure is more generally applicable than approaches, such as the singular perturbation method, that require special normal forms or other a priori knowledge. The use, features, and accuracy of the approach are illustrated via several detailed examples.
A three-dimensional robust nonlinear terminal guidance law with ISS finite-time convergence
NASA Astrophysics Data System (ADS)
Li, Guilin; Ji, Haibo
2016-05-01
This paper presents a novel three-dimensional nonlinear terminal guidance law with finite-time convergence for intercepting manoeuvring targets. Different from the usual method of decoupling the missile-target relative motion into two-dimensional planes, this law is designed via using the coupled dynamics. The guidance law is derived based on the theory of finite-time input-to-state stability (ISS), which needs no assumption of the linearisation and the estimation of target accelerations. Under this law, the line-of-sight angular rates can be stabilised to a small domain of convergence around zero in finite time. The convergence rate and convergence domain can be adjusted by changing the guidance parameters. First, a sufficient condition on finite-time ISS of the guidance system is given, and is subsequently used to design the guidance law. Finally, simulation results are provided to show that the proposed guidance law possesses fast convergence rate and strong robustness to target manoeuvres.
Asymptotic Behavior of the Finite Time Ruin Probability of a Gamma Levy Process
NASA Astrophysics Data System (ADS)
Michna, Z.; Weron, A.
2007-05-01
In this paper we consider a jump-diffusion type approximation of the classical risk process by a gamma Lévy process. We derive here the asymptotic behavior (lower and upper bounds) of the finite time ruin probability for any gamma Lévy process.
NASA Astrophysics Data System (ADS)
Kim, Y. H.; Choi, B.; Son, Y. B.; Shim, W. J.; Hwang, J. H.; Park, Y.
2012-12-01
Series of satellite images show that the development and migration of green macroalgal bloom (known as Ulva prolifera) in the Yellow Sea (YS) and Eastern China Sea (ECS). This presentation will utilize the Lagrangian Coherent Structures (LCS) analysis to demonstrate the dispersion pattern of algal bloom patches. Analyzing LCS such as stable and unstable manifolds is one of emerging technologies for characterizing Lagrangian pathways in aquatic environments. This approach is based on the assumption that unstable manifolds such as ridges (i.e., high values) in the finite-time Lyapunov exponent (FTLE) fields coincide with material transport barriers. In this study, the FTLE fields were computed from gridded trajectories using flow fields provided by Regional Ocean Modeling System (ROMS) in the YS/ECS during summer 2011. The results show that there exist two strong transport barriers that lie along the east-west direction, at least, for the simulation period; one is located from the north of Changjiang River mouth to the middle of the Yellow Sea and the other one is stretched from the south of Shandong Peninsular toward east/southeast. This LCS analysis suggests that patches of green algae developed in the coastal region of Jiangsu Province during summer may migrate toward east into the middle of the YS or even toward Korean coast rather than extending along the Jiangsu coast, which is consistent with the observation results derived from the satellite ocean color data. In the very same manner, the utilization of LCS results to evaluate the distribution/transport pattern of marine debris in the YS/ECS will also be discussed during the presentation.
Lagrangian statistics in laboratory 2D turbulence
NASA Astrophysics Data System (ADS)
Xia, Hua; Francois, Nicolas; Punzmann, Horst; Shats, Michael
2014-05-01
Turbulent mixing in liquids and gases is ubiquitous in nature and industrial flows. Understanding statistical properties of Lagrangian trajectories in turbulence is crucial for a range of problems such as spreading of plankton in the ocean, transport of pollutants, etc. Oceanic data on trajectories of the free-drifting instruments, indicate that the trajectory statistics can often be described by a Lagrangian integral scale. Turbulence however is a state of a flow dominated by a hierarchy of scales, and it is not clear which of these scales mostly affect particle dispersion. Moreover, coherent structures often coexist with turbulence in laboratory experiments [1]. The effect of coherent structures on particle dispersion in turbulent flows is not well understood. Recent progress in scientific imaging and computational power made it possible to tackle this problem experimentally. In this talk, we report the analysis of the higher order Lagrangian statistics in laboratory two-dimensional turbulence. Our results show that fluid particle dispersion is diffusive and it is determined by a single measurable Lagrangian scale related to the forcing scale [2]. Higher order moments of the particle dispersion show strong self-similarity in fully developed turbulence [3]. Here we introduce a new dispersion law that describes single particle dispersion during the turbulence development [4]. These results offer a new way of predicting dispersion in turbulent flows in which one of the low energy scales are persistent. It may help better understanding of drifter Lagrangian statistics in the regions of the ocean where small scale coherent eddies are present [5]. Reference: 1. H. Xia, H. Punzmann, G. Falkovich and M. Shats, Physical Review Letters, 101, 194504 (2008) 2. H. Xia, N. Francois, H. Punzmann, and M. Shats, Nature Communications, 4, 2013 (2013) 3. R. Ferrari, A.J. Manfroi , W.R. Young, Physica D 154 111 (2001) 4. H. Xia, N. Francois, H. Punzmann and M. Shats, submitted (2014
Local Stable and Unstable Manifolds and Their Control in Nonautonomous Finite-Time Flows
NASA Astrophysics Data System (ADS)
Balasuriya, Sanjeeva
2016-08-01
It is well known that stable and unstable manifolds strongly influence fluid motion in unsteady flows. These emanate from hyperbolic trajectories, with the structures moving nonautonomously in time. The local directions of emanation at each instance in time is the focus of this article. Within a nearly autonomous setting, it is shown that these time-varying directions can be characterised through the accumulated effect of velocity shear. Connections to Oseledets spaces and projection operators in exponential dichotomies are established. Availability of data for both infinite- and finite-time intervals is considered. With microfluidic flow control in mind, a methodology for manipulating these directions in any prescribed time-varying fashion by applying a local velocity shear is developed. The results are verified for both smoothly and discontinuously time-varying directions using finite-time Lyapunov exponent fields, and excellent agreement is obtained.
Finite-time synchronization of fractional-order memristor-based neural networks with time delays.
Velmurugan, G; Rakkiyappan, R; Cao, Jinde
2016-01-01
In this paper, we consider the problem of finite-time synchronization of a class of fractional-order memristor-based neural networks (FMNNs) with time delays and investigated it potentially. By using Laplace transform, the generalized Gronwall's inequality, Mittag-Leffler functions and linear feedback control technique, some new sufficient conditions are derived to ensure the finite-time synchronization of addressing FMNNs with fractional order α:1<α<2 and 0<α<1. The results from the theory of fractional-order differential equations with discontinuous right-hand sides are used to investigate the problem under consideration. The derived results are extended to some previous related works on memristor-based neural networks. Finally, three numerical examples are presented to show the effectiveness of our proposed theoretical results. PMID:26547242
Distributed robust finite-time nonlinear consensus protocols for multi-agent systems
NASA Astrophysics Data System (ADS)
Zuo, Zongyu; Tie, Lin
2016-04-01
This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.
Input-output finite-time stabilisation of nonlinear stochastic system with missing measurements
NASA Astrophysics Data System (ADS)
Song, Jun; Niu, Yugang; Jia, Tinggang
2016-09-01
This paper considers the problem of the input-output finite-time stabilisation for a class of nonlinear stochastic system with state-dependent noise. The phenomenon of the missing measurements may occur when state signals are transmitted via communication networks. An estimating method is proposed to compensate the lost state information. And then, a compensator-based controller is designed to ensure the input-output finite-time stochastic stability (IO-FTSS) of the closed-loop system. Some parameters-dependent sufficient conditions are derived and the corresponding solving approach is given. Finally, numerical simulations are provided to demonstrate the feasibility and effectiveness of the developed IO-FTSS scheme.
Local Stable and Unstable Manifolds and Their Control in Nonautonomous Finite-Time Flows
NASA Astrophysics Data System (ADS)
Balasuriya, Sanjeeva
2016-03-01
It is well known that stable and unstable manifolds strongly influence fluid motion in unsteady flows. These emanate from hyperbolic trajectories, with the structures moving nonautonomously in time. The local directions of emanation at each instance in time is the focus of this article. Within a nearly autonomous setting, it is shown that these time-varying directions can be characterised through the accumulated effect of velocity shear. Connections to Oseledets spaces and projection operators in exponential dichotomies are established. Availability of data for both infinite- and finite-time intervals is considered. With microfluidic flow control in mind, a methodology for manipulating these directions in any prescribed time-varying fashion by applying a local velocity shear is developed. The results are verified for both smoothly and discontinuously time-varying directions using finite-time Lyapunov exponent fields, and excellent agreement is obtained.
Finite-time H∞ filtering for non-linear stochastic systems
NASA Astrophysics Data System (ADS)
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
Kibble-Zurek mechanism beyond adiabaticity: Finite-time scaling with critical initial slip
NASA Astrophysics Data System (ADS)
Huang, Yingyi; Yin, Shuai; Hu, Qijun; Zhong, Fan
2016-01-01
The Kibble-Zurek mechanism demands an initial adiabatic stage before an impulse stage to have a frozen correlation length that generates topological defects in a cooling phase transition. Here we study such a driven critical dynamics but with an initial condition that is near the critical point and that is far away from equilibrium. In this case, there is no initial adiabatic stage at all and thus adiabaticity is broken. However, we show that there again exists a finite length scale arising from the driving that divides the evolution into three stages. A relaxation-finite-time-scaling-adiabatic scenario is then proposed in place of the adiabatic-impulse-adiabatic scenario of the original Kibble-Zurek mechanism. A unified scaling theory, which combines finite-time scaling with critical initial slip, is developed to describe the universal behavior and is confirmed with numerical simulations of a two-dimensional classical Ising model.
Gao, Fangzheng; Wu, Yuqiang; Zhang, Zhongcai
2015-11-01
This paper investigates the problem of finite-time stabilization by output feedback for a class of nonholonomic systems in chained form with uncertainties. Comparing with the existing relevant literature, a distinguishing feature of the systems under investigation is that the x-subsystem is a feedforward-like rather than feedback-like system. This renders the existing control methods inapplicable to the control problems of the systems. A constructive design procedure for output feedback control is given. The designed controller renders that the states of closed-loop system are regulated to zero in a finite time. Two simulation examples are provided to illustrate the effectiveness of the proposed approach. PMID:26434417
Finite Time Thermodynamic Optimization or Entropy Generation Minimization of Energy Systems
NASA Astrophysics Data System (ADS)
Chen, Lingen; Wu, Chih; Sun, Fengrui
1999-12-01
The historical background, research development, and the state-of-the-art of finite time thermodynamic theory and applications are reviewed from the point of view of both physics and engineering. The emphasis is on the performance optimization of thermodynamic processes and devices with finite-time and/or finite-size constraints, including heat engines, refrigerators, heat pumps, chemical reactions and some other processes, with respect to the following aspects: the study of Newton's law systems, an analysis of the effect of heat resistance and other irreversible loss models on the performance, an analysis of the effect of heat reservoir models on the performance, as well as the application for real thermodynamic processes and devices. It is pointed out that the generalized thermodynamic optimization theory is the development direction of finite thermodynamics in the future.
Applications the Lagrangian description in aperiodic flows
NASA Astrophysics Data System (ADS)
Mendoza, Carolina; Mancho, Ana Maria
2012-11-01
We use several recently developed Lagrangian tools for describing transport in general aperiodic flows. In our approach the first step is based in a Lagrangian descriptor (the so called function M). It measures the length of particle trajectories on the ocean surface over a given interval of time. We describe its output over satellite altimetry data on the Kuroshio current. The technique is combined with the direct computation of manifolds of Distinguished Hyperbolic trajectories and a very detailed description of transport is achieved across an eddy and a jet on the Kuroshio current,. A second velocity data set is examined with the M function tool. These are obtained from the HYCOM project on the Gulf of Mexico during the time of the oil-spill. We have identified underlying Lagrangian structures and dynamics. We acknowledge to the hospitality of the university of Delaware and the assistance of Bruce Lipphardt and Helga Huntley in accessing the model data sets. We acknowledge to the grants: UPM-AL12-PAC-09, Becas de Movilidad de Caja Madrid 2011, MTM2011-26696 and ILINK-0145.
The finite time multi-level SU(2) Landau-Zener problems: exact analytical results
NASA Astrophysics Data System (ADS)
Mkam Tchouobiap, S. E.; Kenmoe, M. B.; Fai, L. C.
2015-10-01
The multi-level SU(2) Landau-Zener problem is analytically solved at finite time within the framework of the Bloch tensor formalism and with the help of the disentanglement Wei-Norman ordering technique. A generalized and exact analytical solution is achieved that accounts not only for all projections of an arbitrary spin S along the Zeeman field direction but also for non-adiabatic and adiabatic evolutions.
Finite Time Singularity of the Nematic Liquid Crystal Flow in Dimension Three
NASA Astrophysics Data System (ADS)
Huang, Tao; Lin, Fanghua; Liu, Chun; Wang, Changyou
2016-09-01
In this paper, we consider the initial and boundary value problem of a simplified nematic liquid crystal flow in dimension three and construct two examples of finite time singularity. The first example is constructed within the class of axisymmetric solutions, while the second example is constructed for any generic initial data {(u_0,d_0)} that has sufficiently small energy, and {d_0} has a nontrivial topology.
Jammazi, Chaker
2009-03-05
The paper gives Lyapunov type sufficient conditions for partial finite-time and asymptotic stability in which some state variables converge to zero while the rest converge to constant values that possibly depend on the initial conditions. The paper then presents partially asymptotically stabilizing controllers for many nonlinear control systems for which continuous asymptotically stabilizing (in the usual sense) controllers are known not to exist.
NASA Technical Reports Server (NTRS)
Eluszkiewicz, Janusz; Nehrkorn, Thomas; Wofsy, Steven C.; Matross, Daniel; Gerbig, Christoph; Lin, John C.; Freitas, Saulo; Longo, Marcos; Andrews, Arlyn E.; Peters, Wouter
2007-01-01
This paper evaluates simulations of atmospheric CO2 measured in 2004 at continental surface and airborne receptors, intended to test the capability to use data with high temporal and spatial resolution for analyses of carbon sources and sinks at regional and continental scales. The simulations were performed using the Stochastic Time-Inverted Lagrangian Transport (STILT) model driven by the Weather Forecast and Research (WRF) model, and linked to surface fluxes from the satellite-driven Vegetation Photosynthesis and Respiration Model (VPRM). The simulations provide detailed representations of hourly CO2 tower data and reproduce the shapes of airborne vertical profiles with high fidelity. WRF meteorology gives superior model performance compared with standard meteorological products, and the impact of including WRF convective mass fluxes in the STILT trajectory calculations is significant in individual cases. Important biases in the simulation are associated with the nighttime CO2 build-up and subsequent morning transition to convective conditions, and with errors in the advected lateral boundary condition. Comparison of STILT simulations driven by the WRF model against those driven by the Brazilian variant of the Regional Atmospheric Modeling System (BRAMS) shows that model-to-model differences are smaller than between an individual transport model and observations, pointing to systematic errors in the simulated transport. Future developments in the WRF model s data assimilation capabilities, basic research into the fundamental aspects of trajectory calculations, and intercomparison studies involving other transport models, are possible venues for reducing these errors. Overall, the STILT/WRF/VPRM offers a powerful tool for continental and regional scale carbon flux estimates.
Yang, Yana; Hua, Changchun; Guan, Xinping
2016-03-01
Due to the cognitive limitations of the human operator and lack of complete information about the remote environment, the work performance of such teleoperation systems cannot be guaranteed in most cases. However, some practical tasks conducted by the teleoperation system require high performances, such as tele-surgery needs satisfactory high speed and more precision control results to guarantee patient' health status. To obtain some satisfactory performances, the error constrained control is employed by applying the barrier Lyapunov function (BLF). With the constrained synchronization errors, some high performances, such as, high convergence speed, small overshoot, and an arbitrarily predefined small residual constrained synchronization error can be achieved simultaneously. Nevertheless, like many classical control schemes only the asymptotic/exponential convergence, i.e., the synchronization errors converge to zero as time goes infinity can be achieved with the error constrained control. It is clear that finite time convergence is more desirable. To obtain a finite-time synchronization performance, the terminal sliding mode (TSM)-based finite time control method is developed for teleoperation system with position error constrained in this paper. First, a new nonsingular fast terminal sliding mode (NFTSM) surface with new transformed synchronization errors is proposed. Second, adaptive neural network system is applied for dealing with the system uncertainties and the external disturbances. Third, the BLF is applied to prove the stability and the nonviolation of the synchronization errors constraints. Finally, some comparisons are conducted in simulation and experiment results are also presented to show the effectiveness of the proposed method. PMID:25823053
Lagrangian computation of inviscid compressible flows
NASA Technical Reports Server (NTRS)
Klopfer, G. H.
1978-01-01
A Lagrangian method is developed to solve the Euler equations of gas dynamics. The solution of the equations is obtained by a numerical computation with the well-known Flux-Corrected-Transport (FCT) numerical method. This procedure is modified so that the boundary treatment is accurate and relatively simple. Shock waves and other flow discontinuities are captured monotonically without any type of fitting procedures. The Lagrangian method is employed so that the problem of mesh generation is completely avoided. The method is applicable to all Mach numbers except the low subsonic range where compressibility effects are small. The method is applied to a one-dimensional Riemann problem (shock tube) and to a two-dimensional supersonic channel flow with reflecting shock waves.
Stochastic Lagrangian dynamics for charged flows in the E-F regions of ionosphere
Tang Wenbo; Mahalov, Alex
2013-03-15
We develop a three-dimensional numerical model for the E-F region ionosphere and study the Lagrangian dynamics for plasma flows in this region. Our interest rests on the charge-neutral interactions and the statistics associated with stochastic Lagrangian motion. In particular, we examine the organizing mixing patterns for plasma flows due to polarized gravity wave excitations in the neutral field, using Lagrangian coherent structures (LCS). LCS objectively depict the flow topology-the extracted attractors indicate generation of ionospheric density gradients, due to accumulation of plasma. Using Lagrangian measures such as the finite-time Lyapunov exponents, we locate the Lagrangian skeletons for mixing in plasma, hence where charged fronts are expected to appear. With polarized neutral wind, we find that the corresponding plasma velocity is also polarized. Moreover, the polarized velocity alone, coupled with stochastic Lagrangian motion, may give rise to polarized density fronts in plasma. Statistics of these trajectories indicate high level of non-Gaussianity. This includes clear signatures of variance, skewness, and kurtosis of displacements taking polarized structures aligned with the gravity waves, and being anisotropic.
Coherent Lagrangian vortices in three-dimensional unsteady flows
NASA Astrophysics Data System (ADS)
Blazevski, Daniel; Haller, George
2014-05-01
Detecting barriers to, and facilitators of, transport is a fundamental problem in studying the behavior of Lagrangian trajectories in a fluid. A recent extension of two-dimensional results provides transport barriers in 3D flows as locally most attracting, repelling or shearing surfaces. This provides an objective definition of a Lagrangian vortex boundary as an outermost member of a family of most shearing cylindrical material surfaces. The detection of such a 3D vortex boundary yields an accurate estimate on the volume the vortex transports. We compute 3D Lagrangian vortices in kinematic models, and also use a global circulation model to extract sharp boundaries for coherent three-dimensional Agulhas rings in the South Atlantic.
Lagrangian Coherent Structures in the Trieste Gulf
NASA Astrophysics Data System (ADS)
Besio, G.; Enrile, F.; Magaldi, M. G.; Mantovani, C.; Cosoli, S.; Gerin, R.; Poulain, P. M.
2013-12-01
One serious issue in Environmental Science and Engineering concerns the prediction of the fate of contaminants released in a water body. A possible way to tackle this problem consists in forecasting pollutant trajectories from velocity-field data sets obtained by measurements or numerical simulations. A shortcoming of such a traditional approach is the high sensitivity to initial conditions. Another way to understand transport in complex fluid flows comes from a new mathematical tool: Lagrangian Coherent Structures (LCS). The idea of using Lagrangian Structures rose as a meeting point between non-linear dynamics and fluid mechanics. It provides the means to identify material lines that shape trajectory patterns, dividing the flow field into regions with different dynamical behaviours. The objective of this study is the detection of Lagrangian Coherent Structures in the Gulf of Trieste. LCS are calculated from the 2D surface velocity field measured by the coastal radars of the TOSCA (Tracking Oil Spills & Coastal Awareness network) project. Blobs of simulated particles are subjected to chaotic stirring (transport and stretching) that is in agreement with the detected LCS. In the TOSCA project drifters were deployed, too. Therefore, a simple simulation of some of these drifters was carried out. The trajectory of the simulated drifters diverge from the real one: this result is due to the chaotic transport of passive tracers. However, the separation becomes more evident when velocity fields are less accurate because of lack of measurements, previously filled with nearest neighbourhood interpolation. In the light of such results, the use of LCS could be helpful in understanding the trajectory followed by drifters and passive tracers in general, because they can point out the directions along which transport is likely to develop.
Stochastic modeling of Lagrangian accelerations
NASA Astrophysics Data System (ADS)
Reynolds, Andy
2002-11-01
It is shown how Sawford's second-order Lagrangian stochastic model (Phys. Fluids A 3, 1577-1586, 1991) for fluid-particle accelerations can be combined with a model for the evolution of the dissipation rate (Pope and Chen, Phys. Fluids A 2, 1437-1449, 1990) to produce a Lagrangian stochastic model that is consistent with both the measured distribution of Lagrangian accelerations (La Porta et al., Nature 409, 1017-1019, 2001) and Kolmogorov's similarity theory. The later condition is found not to be satisfied when a constant dissipation rate is employed and consistency with prescribed acceleration statistics is enforced through fulfilment of a well-mixed condition.
Occurrence of discontinuities in the performance of finite-time quantum Otto cycles
NASA Astrophysics Data System (ADS)
Zheng, Yuanjian; Hänggi, Peter; Poletti, Dario
2016-07-01
We study a quantum Otto cycle in which the strokes are performed in finite time. The cycle involves energy measurements at the end of each stroke to allow for the respective determination of work. We then optimize for the work and efficiency of the cycle by varying the time spent in the different strokes and find that the optimal value of the ratio of time spent on each stroke goes through sudden changes as the parameters of this cycle vary continuously. The position of these discontinuities depends on the optimized quantity under consideration such as the net work output or the efficiency.
NASA Astrophysics Data System (ADS)
Dasgupta, Sambarta
Transient stability and sensitivity analysis of power systems are problems of enormous academic and practical interest. These classical problems have received renewed interest, because of the advancement in sensor technology in the form of phasor measurement units (PMUs). The advancement in sensor technology has provided unique opportunity for the development of real-time stability monitoring and sensitivity analysis tools. Transient stability problem in power system is inherently a problem of stability analysis of the non-equilibrium dynamics, because for a short time period following a fault or disturbance the system trajectory moves away from the equilibrium point. The real-time stability decision has to be made over this short time period. However, the existing stability definitions and hence analysis tools for transient stability are asymptotic in nature. In this thesis, we discover theoretical foundations for the short-term transient stability analysis of power systems, based on the theory of normally hyperbolic invariant manifolds and finite time Lyapunov exponents, adopted from geometric theory of dynamical systems. The theory of normally hyperbolic surfaces allows us to characterize the rate of expansion and contraction of co-dimension one material surfaces in the phase space. The expansion and contraction rates of these material surfaces can be computed in finite time. We prove that the expansion and contraction rates can be used as finite time transient stability certificates. Furthermore, material surfaces with maximum expansion and contraction rate are identified with the stability boundaries. These stability boundaries are used for computation of stability margin. We have used the theoretical framework for the development of model-based and model-free real-time stability monitoring methods. Both the model-based and model-free approaches rely on the availability of high resolution time series data from the PMUs for stability prediction. The problem of
Occurrence of discontinuities in the performance of finite-time quantum Otto cycles.
Zheng, Yuanjian; Hänggi, Peter; Poletti, Dario
2016-07-01
We study a quantum Otto cycle in which the strokes are performed in finite time. The cycle involves energy measurements at the end of each stroke to allow for the respective determination of work. We then optimize for the work and efficiency of the cycle by varying the time spent in the different strokes and find that the optimal value of the ratio of time spent on each stroke goes through sudden changes as the parameters of this cycle vary continuously. The position of these discontinuities depends on the optimized quantity under consideration such as the net work output or the efficiency. PMID:27575106
Fast computation of Lagrangian coherent structures: algorithms and error analysis
NASA Astrophysics Data System (ADS)
Brunton, Steven; Rowley, Clarence
2009-11-01
This work investigates a number of efficient methods for computing finite time Lyapunov exponent (FTLE) fields in unsteady flows by approximating the particle flow map and eliminating redundant particle integrations in neighboring flow maps. Ridges of the FTLE fields are Lagrangian coherent structures (LCS) and provide an unsteady analogue of invariant manifolds from dynamical systems theory. The fast methods fall into two categories, unidirectional and bidirectional, depending on whether flow maps in one or both time directions are composed to form an approximate flow map. An error analysis is presented which shows that the unidirectional methods are accurate while the bidirectional methods have significant error which is aligned with the opposite time coherent structures. This relies on the fact that material from the positive time LCS attracts onto the negative time LCS near time-dependent saddle points.
Attracting and repelling Lagrangian coherent structures from a single computation
NASA Astrophysics Data System (ADS)
Farazmand, Mohammad; Haller, George
2013-06-01
Hyperbolic Lagrangian Coherent Structures (LCSs) are locally most repelling or most attracting material surfaces in a finite-time dynamical system. To identify both types of hyperbolic LCSs at the same time instance, the standard practice has been to compute repelling LCSs from future data and attracting LCSs from past data. This approach tacitly assumes that coherent structures in the flow are fundamentally recurrent, and hence gives inconsistent results for temporally aperiodic systems. Here, we resolve this inconsistency by showing how both repelling and attracting LCSs are computable at the same time instance from a single forward or a single backward run. These LCSs are obtained as surfaces normal to the weakest and strongest eigenvectors of the Cauchy-Green strain tensor.
NASA Astrophysics Data System (ADS)
Han, Lu; Xiao, Jian; Qiu, Cunyong; Huang, Jingchun
2016-07-01
Many actual engineering applications can be modelled as large-scale switched system, while switching behaviours often occur in some short finite time intervals; thus, it is significant to ensure the finite-time boundedness of large-scale switched system in practical terms. In this paper, the problems of finite-time stability analysis and stabilisation for large-scale switched system are addressed. First, considering different switching signals for subsystems, the concepts of decentralised finite-time boundedness (DFTB) and decentralised finite-time H∞ controllers are introduced, which focus on the dynamical transient behaviour of large-scale switched system during finite intervals. Under these concepts, several sufficient conditions are given to ensure a class of large-scale systems decentralised finite-time stable based on the decentralised average dwell times, and then the results are extended to H∞ finite-time boundedness of large-scale switched system. Finally, based on the results on DFTB, optimal decentralised H∞ controllers and average dwell times are designed under the minimum value of H∞ performance. Numerical examples are given to illustrate the effectiveness of the proposed approaches in this paper.
DG-FTLE: Lagrangian coherent structures with high-order discontinuous-Galerkin methods
NASA Astrophysics Data System (ADS)
Nelson, Daniel A.; Jacobs, Gustaaf B.
2015-08-01
We present an algorithm for the computation of finite-time Lyapunov exponent (FTLE) fields using discontinuous-Galerkin (dG) methods in two dimensions. The algorithm is designed to compute FTLE fields simultaneously with the time integration of dG-based flow solvers of conservation laws. Fluid tracers are initialized at Gauss-Lobatto quadrature nodes within an element. The deformation gradient tensor, defined by the deformation of the Lagrangian flow map in finite time, is determined per element with high-order dG operators. Multiple flow maps are constructed from a particle trace that is released at a single initial time by mapping and interpolating the flow map formed by the locations of the fluid tracers after finite time integration to a unit square master element and to the quadrature nodes within the element, respectively. The interpolated flow maps are used to compute forward-time and backward-time FTLE fields at several times using dG operators. For a large finite integration time, the interpolation is increasingly poorly conditioned because of the excessive subdomain deformation. The conditioning can be used in addition to the FTLE to quantify the deformation of the flow field and identify subdomains with material lines that define Lagrangian coherent structures. The algorithm is tested on three benchmarks: an analytical spatially periodic gyre flow, a vortex advected by a uniform inviscid flow, and the viscous flow around a square cylinder. In these cases, the algorithm is shown to have spectral convergence.
NASA Astrophysics Data System (ADS)
Borsten, L.; Duff, M. J.; Ferrara, S.; Marrani, A.
2013-12-01
The global U-dualities of extended supergravity have played a central role in differentiating the distinct classes of extremal black hole solutions. When the U-duality group satisfies certain algebraic conditions, as is the case for a broad class of supergravities, the extremal black holes enjoy a further symmetry known as Freudenthal duality (F-duality), which although distinct from U-duality preserves the Bekenstein-Hawking entropy. Here it is shown that, by adopting the doubled Lagrangian formalism, F-duality, defined on the doubled field strengths, is not only a symmetry of the black hole solutions, but also of the equations of motion themselves. A further role for F-duality is introduced in the context of world-sheet actions. The Nambu-Goto world-sheet action in any (t, s) signature spacetime can be written in terms of the F-dual. The corresponding field equations and Bianchi identities are then related by F-duality allowing for an F-dual formulation of Gaillard-Zumino duality on the world-sheet. An equivalent polynomial ‘Polyakov-type’ action is introduced using the so-called black hole potential. Such a construction allows for actions invariant under all groups of type E7, including E7 itself, although in this case the stringy interpretation is less clear.
Lagrangian Modeling of the Atmosphere
NASA Astrophysics Data System (ADS)
Schultz, Colin
2013-08-01
Like watching a balloon borne by the breeze, a Lagrangian model tracks a parcel of air as it flows through the atmosphere. Whether running forward or backward in time, Lagrangian models offer a powerful tool for tracking and understanding the fates, or origins, of atmospheric flows. In the AGU monograph Lagrangian Modeling of the Atmosphere, editors John Lin, Dominik Brunner, Christoph Gerbig, Andreas Stohl, Ashok Luhar, and Peter Webley explore the nuances of the modeling technique. In this interview Eos talks to Lin about the growing importance of Lagrangian modeling as the world settles on climate change mitigation strategies, the societal value of operational modeling, and how recent advances are making it possible to run these complex calculations at home.
Weyl's Lagrangian in teleparallel form
Burnett, James; Vassiliev, Dmitri
2009-10-15
The Weyl Lagrangian is the massless Dirac Lagrangian. The dynamical variable in the Weyl Lagrangian is a spinor field. We provide a mathematically equivalent representation in terms of a different dynamical variable - the coframe (an orthonormal tetrad of covector fields). We show that when written in terms of this dynamical variable, the Weyl Lagrangian becomes remarkably simple: it is the wedge product of axial torsion of the teleparallel connection with a teleparallel lightlike element of the coframe. We also examine the issues of U(1)-invariance and conformal invariance. Examination of the latter motivates us to introduce a positive scalar field (equivalent to a density) as an additional dynamical variable; this makes conformal invariance self-evident.
Lagrangian postprocessing of computational hemodynamics
Shadden, Shawn C.; Arzani, Amirhossein
2014-01-01
Recent advances in imaging, modeling and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform Lagrangian particle tracking, and other Lagrangian-based postprocessing. As described herein, Lagrangian methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review Lagrangian methods that have been used in post-processing velocity data of cardiovascular flows. PMID:25059889
Species doubling and effective Lagrangians
Creutz, M.; Tytgat, M.
1996-09-01
Coupling gauge fields to the chiral currents from an effective Lagrangian for pseudoscalar mesons naturally gives rise to a species doubling phenomenon similar to that seen with fermionic fields in lattice gauge theory. 17 refs.
Finite-time quantum-to-classical transition for a Schroedinger-cat state
Paavola, Janika; Hall, Michael J. W.; Paris, Matteo G. A.; Maniscalco, Sabrina
2011-07-15
The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schroedinger-cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum-to-classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well-defined physical meaning and allow a deeper understanding of the quantum-to-classical transition. Our analysis shows that, for most nonclassicality measures, the Schroedinger-cat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a ''sudden death''. In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.
NASA Astrophysics Data System (ADS)
Utembe, S. R.; Cooke, M. C.; Archibald, A. T.; Shallcross, D. E.; Derwent, R. G.; Jenkin, M. E.
2011-03-01
A secondary organic aerosol (SOA) code, coupled to the reduced Common Representative Intermediates chemical mechanism (CRI v2-R5), has been used in the global 3-D chemistry-transport model, STOCHEM, to simulate the global distribution of organic aerosol (OA) mass loadings. The SOA code represents the gas-to-aerosol partitioning of products formed over several generations of oxidation of a variety of organic precursors emitted from anthropogenic, biogenic and biomass burning sources. The model also includes emissions of primary organic aerosol (POA), based on the AeroCom inventory and the Global Fire Emissions database (GFED). The calculated burdens for POA, 0.89 Tg, and SOA, 0.23 Tg, are well within the range of values that have been reported in previous modelling studies. The calculated SOA annual in-situ production of 22.5 Tg yr -1 also falls within the 8-110 Tg yr -1 range calculated by other models, but is somewhat lower than observationally-constrained top-down estimates which have been reported recently. The oxidation of biogenic precursors is found to account for about 90% of the global SOA burden, and this makes a substantial contribution to the highest annual mean surface OA concentrations (up to 8 μg m -3), which are simulated in tropical forested regions. Comparison of the simulated OA mass loadings with surface observations from a variety of locations indicate a good description of the OA distribution, but with an average underestimation of about a factor of 3. Sustained formation of SOA into the free troposphere is simulated, with important contributions from second and third-generation products of terpene oxidation in the upper troposphere. Comparison of the simulated OA mass loadings with vertical profiles from the ACE-Asia campaign indicates a very good description of the relative variation of OA with altitude, but with consistent underestimation of about a factor of 5. Although the absolute magnitude of the global source strength is underestimated
Davis, W.E.; Olsen, A.R.; Erb, T.A.
1989-01-01
The 1987 Across North America Tracer Experiment (ANATEX), for the study of regional to continental-scale transport and diffusion, released perfluorocarbon tracers for three hours every 2.5 days in January, February and March (Draxler et. al. 1985, 1987). The experiment resulted in 33 days of releases at two sites; Glasgow, Montana and St. Cloud, Minnesota. Each release consisted of approximately 50 kg of perfluoro-ortho-dimenthoyl-cyclohexane (PDCH) at St. Cloud and 83 kg of perfluoro-trimethyl-cyclohexane (PTCH) at Glasgow. The experiment included the release of a third tracer, 50 kg of perfluoro-methyl-cyclohexane (PMCH), every five days from St. Cloud; designed to serve as a means to distinguish consecutive releases from St. Cloud. A surface sampling network of 77 sampling sites, located east of 105/degree/ longitude in the United States and Canada, measured 24-hour average tracer concentrations out to a distance of 3000 km from Glasgow. The network, organized in eight arcs east of Glasgow, collected daily concentrations of each tracer from January 5 through March 29, 1987. The network design provides average daily surface footprint information for the three tracers. 8 refs., 2 figs.
NASA Astrophysics Data System (ADS)
Davis, William E.; Olsen, Anthony R.; Erb, Trudy A.
1989-01-01
The 1987 Across North America Tracer Experiment (ANATEX), for the study of regional to continental-scale transport and diffusion, released perfluorocarbon tracers for three hours every 2.5 days in January, February and March (Draxler et. al. 1985, 1987). The experiment resulted in 33 days of releases at two sites; Glasgow, Montana and St. Cloud, Minnesota. Each release consisted of approximately 50 kg of perfluoro ortho-dimenthoyl cyclohexane (PDCH) at St. Cloud and 83 kg of perfluoro trimethyl cyclohexane (PTCH) at Glasgow. The experiment included the release of a third tracer, 50 kg of perfluoro methyl cyclohexane (PMCH), every five days from St. Cloud; designed to serve as a means to distinguish consecutive releases from St. Cloud. A surface sampling network of 77 sampling sites, located east of 105 degree longitude in the United States and Canada, measured 24-hour average tracer concentrations out to a distance of 3000 km from Glasgow. The network, organized in eight arcs east of Glasgow, collected daily concentrations of each tracer from January 5 through March 29, 1987. The network design provides average daily surface footprint information for the three tracers.