The Experts below are selected from a list of 270 Experts worldwide ranked by ideXlab platform
Angelo Vulpiani - One of the best experts on this subject based on the ideXlab platform.
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On the strong anomalous diffusion
Physica D: Nonlinear Phenomena, 1999Co-Authors: P. Castiglione, Andrea Mazzino, Paolo Muratore-ginanneschi, Angelo VulpianiAbstract:The superdiffusion behavior, i.e. $ \sim t^{2 \nu}$, with $\nu > 1/2$, in general is not completely characherized by a unique exponent. We study some systems exhibiting strong anomalous diffusion, i.e. $ \sim t^{q \nu(q)}$ where $\nu(2)>1/2$ and $q \nu(q)$ is not a linear function of $q$. This feature is different from the weak superdiffusion regime, i.e. $\nu(q)=const > 1/2$, as in random shear flows. The strong anomalous diffusion can be generated by nontrivial chaotic dynamics, e.g. Lagrangian Motion in $2d$ time-dependent incompressible velocity fields, $2d$ symplectic maps and $1d$ intermittent maps. Typically the function $q \nu(q)$ is piecewise linear. This corresponds to two mechanisms: a weak anomalous diffusion for the typical events and a ballistic transport for the rare excursions. In order to have strong anomalous diffusion one needs a violation of the hypothesis of the central limit theorem, this happens only in a very narrow region of the control parameters space.
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Dispersion of passive tracers in closed basins: beyond the diffusion coefficient
Physics of Fluids, 1997Co-Authors: Vincenzo Artale, Massimo Cencini, Guido Boffetta, Antonio Celani, Angelo VulpianiAbstract:We investigate the spreading of passive tracers in closed basins. If the characteristic length scale of the Eulerian velocities is not very small compared with the size of the basin the usual diffusion coefficient does not give any relevant information about the mechanism of spreading. We introduce a finite size characteristic time τ(δ) which describes the diffusive process at scale δ. When δ is small compared with the typical length of the velocity field one has τ(δ)∼λ−1, where λ is the maximum Lyapunov exponent of the Lagrangian Motion. At large δ the behavior of τ(δ) depends on the details of the system, in particular the presence of boundaries, and in this limit we have found a universal behavior for a large class of system under rather general hypothesis. The method of working at fixed scale δ makes more physical sense than the traditional way of looking at the relative diffusion at fixed delay times. This technique is displayed in a series of numerical experiments in simple flows.
A Fouxon - One of the best experts on this subject based on the ideXlab platform.
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Universal long-time properties of Lagrangian statistics in the Batchelor regime and their application to the passive scalar problem.
Physical Review E, 1999Co-Authors: E Balkovsky, A FouxonAbstract:We consider transport of dynamically passive quantities in the Batchelor regime of smooth in space velocity field. For the case of arbitrary temporal correlations of the velocity we formulate the statistics of relevant characteristics of Lagrangian Motion. This allows to generalize many results obtained previously for the delta-correlated in time strain, thus answering the question of universality of these results.Comment: 11 pages, revtex; added references, typos correcte
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Universal long-time properties of Lagrangian statistics in the Batchelor regime and their application to the passive scalar problem.
Physical review. E Statistical physics plasmas fluids and related interdisciplinary topics, 1999Co-Authors: E Balkovsky, A FouxonAbstract:We consider the transport of dynamically passive quantities in the Batchelor regime of a smooth in space velocity field. For the case of arbitrary temporal correlations of the velocity, we formulate the statistics of relevant characteristics of Lagrangian Motion. This allows us to generalize many results obtained previously for strain delta correlated in time, thus answering a question about the universality of these results.
R M Samelson - One of the best experts on this subject based on the ideXlab platform.
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Lagrangian Motion coherent structures and lines of persistent material strain
Annual Review of Marine Science, 2013Co-Authors: R M SamelsonAbstract:Lagrangian Motion in geophysical fluids may be strongly influenced by coherent structures that support distinct regimes in a given flow. The problems of identifying and demarcating Lagrangian regime boundaries associated with dynamical coherent structures in a given velocity field can be studied using approaches originally developed in the context of the abstract geometric theory of ordinary differential equations. An essential insight is that when coherent structures exist in a flow, Lagrangian regime boundaries may often be indicated as material curves on which the Lagrangian-mean principal-axis strain is large. This insight is the foundation of many numerical techniques for identifying such features in complex observed or numerically simulated ocean flows. The basic theoretical ideas are illustrated with a simple, kinematic traveling-wave model. The corresponding numerical algorithms for identifying candidate Lagrangian regime boundaries and lines of principal Lagrangian strain (also called Lagrangian ...
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Lagrangian Motion, Coherent Structures, and Lines of Persistent Material Strain
Annual review of marine science, 2012Co-Authors: R M SamelsonAbstract:Lagrangian Motion in geophysical fluids may be strongly influenced by coherent structures that support distinct regimes in a given flow. The problems of identifying and demarcating Lagrangian regime boundaries associated with dynamical coherent structures in a given velocity field can be studied using approaches originally developed in the context of the abstract geometric theory of ordinary differential equations. An essential insight is that when coherent structures exist in a flow, Lagrangian regime boundaries may often be indicated as material curves on which the Lagrangian-mean principal-axis strain is large. This insight is the foundation of many numerical techniques for identifying such features in complex observed or numerically simulated ocean flows. The basic theoretical ideas are illustrated with a simple, kinematic traveling-wave model. The corresponding numerical algorithms for identifying candidate Lagrangian regime boundaries and lines of principal Lagrangian strain (also called Lagrangian coherent structures) are divided into parcel and bundle schemes; the latter include the finite-time and finite-size Lyapunov exponent/Lagrangian strain (FTLE/FTLS and FSLE/FSLS) metrics. Some aspects and results of oceanographic studies based on these approaches are reviewed, and the results are discussed in the context of oceanographic observations of dynamical coherent structures.
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Time-Periodic Flows in Geophysical and Classical Fluid Dynamics
Handbook of Numerical Analysis, 2009Co-Authors: R M SamelsonAbstract:Abstract Time-periodic flows form an important special class of fluid Motions. This class includes, for example, the many well-known families of linear propagating waves. Recently, nonlinear time-periodic flows have received increased attention in several contexts in geophysical and classical fluid mechanics. Despite the relative simplicity of their Eulerian representation, time-periodic velocity fields can give rise to complex, aperiodic Lagrangian Motion; models of this type can be useful for understanding fluid transport processes in the ocean and atmosphere. One approach to the analysis of chaotic dynamical systems, including certain models of geophysical flows, is based on the identification of a large set of unstable periodic cycles, each of which corresponds to an independent time-periodic flow. Time-periodic flows provide accessible examples in which to explore mechanisms of disturbance growth in general time-dependent flows, a problem of practical interest in numerical weather and ocean prediction. Recent advances in the theory of the transition to turbulence in classical pipe flow involve bifurcation analysis for a special class of time-periodic flows.
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Lagrangian characteristics of continental shelf flows forced by periodic wind stress
Nonlinear Processes in Geophysics, 2004Co-Authors: B. T. Kuebel Cervantes, John S. Allen, R M SamelsonAbstract:Abstract. The coastal ocean may experience periods of fluctuating along-shelf wind direction, causing shifts between upwelling and downwelling conditions with responses that are not symmetric. We seek to understand these asymmetries and their implications on the Eulerian and Lagrangian flows. We use a two-dimensional (variations across-shelf and with depth; uniformity along-shelf) primitive equation numerical model to study shelf flows in the presence of periodic, zero-mean wind stress forcing. The model bathymetry and initial stratification is typical of the broad, shallow shelf off Duck, NC during summer. After an initial transient adjustment, the response of the Eulerian fields is nearly periodic. Despite the symmetric wind stress forcing, there exist both mean Eulerian and Lagrangian flows. The mean Lagrangian displacement of parcels on the shelf depends both on their initial location and on the initial phase of the forcing. Eulerian mean velocities, in contrast, have almost no dependence on initial phase. In an experiment with sinusoidal wind stress forcing of maximum amplitude 0.1Nm and period of 6 days, the mean Lagrangian across-shelf displacements are largest in the surface and bottom boundary layers. Parcels that originate near the coast in the top 15m experience complicated across-shelf and vertical Motion that does not display a clear pattern. Offshore of this region in the top 10m a rotating cell feature exists with offshore displacement near the surface and onshore displacement below. A mapping technique is used to help identify the qualitative characteristics of the Lagrangian Motion and to clarify the long time nature of the parcel displacements. The complexity of the Lagrangian Motion in a region near the coast and the existence of a clear boundary separating this region from a more regular surface cell feature offshore are quantified by a calculation from the map of the largest Lyapunov exponent.
Leonid I. Piterbarg - One of the best experts on this subject based on the ideXlab platform.
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Hamiltonian description of vortex systems
Theoretical and Mathematical Physics, 2020Co-Authors: Leonid I. PiterbargAbstract:In the framework of 2D ideal Hydrodynamics a vortex system is defined as a smooth vorticity function having few positive local maxima and negative local minima separated by curves of zero vorticity. Invariants of such structures are discussed following from the vorticity conservation law and invertibility of Lagrangian Motion. Hamiltonian formalism for vortex systems is developed by introducing new functional variables diagonalizing the original non-canonical Poisson bracket.
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Parameter estimation in multi particle Lagrangian stochastic models
Monte Carlo Methods and Applications, 2006Co-Authors: Leonid I. PiterbargAbstract:A class of multi particle Lagrangian stochastic models is considered mimicking 2D turbulence. The maximum likelihood approach is used to estimate their parameters. An error analysis is carried out by Monte Carlo means. The method allows to estimate some physically important characteristics of Lagrangian Motion such as relative dispersion and Lyapunov exponent by observing only one particle pair. An illustrative example is given based on real data.
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a simple prediction algorithm for the Lagrangian Motion in two dimensional turbulent flows
Siam Journal on Applied Mathematics, 2002Co-Authors: Leonid I. Piterbarg, Tamay M. ÖzgökmenAbstract:A new algorithm is suggested for prediction of a Lagrangian particle position in a stochastic flow, given observations of other particles. The algorithm is based on linearization of the Motion equations and appears to be efficient for an initial tight cluster and small prediction time. A theoretical error analysis is given for the Brownian flow and a stochastic flow with memory. The asymptotic formulas are compared with simulation results to establish their applicability limits. Monte Carlo simulations are carried out to compare the new algorithm with two others: the center-of-mass prediction and a Kalman filter--type method. The algorithm is also tested on real data in the tropical Pacific.
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Short-Term Prediction of Lagrangian Trajectories
Journal of Atmospheric and Oceanic Technology, 2001Co-Authors: Leonid I. PiterbargAbstract:Abstract Lagrangian particles in a cluster are divided in two groups: observable and unobservable. The problem is to predict the unobservable particle positions given their initial positions and velocities based on observations of the observable particles. A Markov model for Lagrangian Motion is formulated. The model implies that the positions and velocities of any number of particles form a multiple diffusion process. A prediction algorithm is proposed based on this model and Kalman filter ideas. The algorithm performance is examined by the Monte Carlo approach in the case of a single predictand. The prediction error is most sensitive to the ratio of the velocity correlation radius and the initial cluster radius. For six predictors, if this parameter equals 5, then the relative error is less than 0.1 for the 15-day prediction, whereas for the ratio close to 1, the error is about 0.9. The relative error does not change significantly as the number of predictors increases from 4–7 to 20.
E Balkovsky - One of the best experts on this subject based on the ideXlab platform.
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Universal long-time properties of Lagrangian statistics in the Batchelor regime and their application to the passive scalar problem.
Physical Review E, 1999Co-Authors: E Balkovsky, A FouxonAbstract:We consider transport of dynamically passive quantities in the Batchelor regime of smooth in space velocity field. For the case of arbitrary temporal correlations of the velocity we formulate the statistics of relevant characteristics of Lagrangian Motion. This allows to generalize many results obtained previously for the delta-correlated in time strain, thus answering the question of universality of these results.Comment: 11 pages, revtex; added references, typos correcte
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Universal long-time properties of Lagrangian statistics in the Batchelor regime and their application to the passive scalar problem.
Physical review. E Statistical physics plasmas fluids and related interdisciplinary topics, 1999Co-Authors: E Balkovsky, A FouxonAbstract:We consider the transport of dynamically passive quantities in the Batchelor regime of a smooth in space velocity field. For the case of arbitrary temporal correlations of the velocity, we formulate the statistics of relevant characteristics of Lagrangian Motion. This allows us to generalize many results obtained previously for strain delta correlated in time, thus answering a question about the universality of these results.
