94 research outputs found

    Introduction to chaos and diffusion

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    This contribution is relative to the opening lectures of the ISSAOS 2001 summer school and it has the aim to provide the reader with some concepts and techniques concerning chaotic dynamics and transport processes in fluids. Our intention is twofold: to give a self-consistent introduction to chaos and diffusion, and to offer a guide for the reading of the rest of this volume.Comment: 39 page

    Evidence for a k^{-5/3} spectrum from the EOLE Lagrangian balloons in the low stratosphere

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    The EOLE Experiment is revisited to study turbulent processes in the lower stratosphere circulation from a Lagrangian viewpoint and resolve a discrepancy on the slope of the atmospheric energy spectrum between the work of Morel and Larcheveque (1974) and recent studies using aircraft data. Relative dispersion of balloon pairs is studied by calculating the Finite Scale Lyapunov Exponent, an exit time-based technique which is particularly efficient in cases where processes with different spatial scales are interfering. Our main result is to reconciliate the EOLE dataset with recent studies supporting a k^{-5/3} energy spectrum in the range 100-1000 km. Our results also show exponential separation at smaller scale, with characteristic time of order 1 day, and agree with the standard diffusion of about 10^7 m^2/s at large scales. A still open question is the origin of a k^{-5/3} spectrum in the mesoscale range, between 100 and 1000 km.Comment: 19 pages, 1 table + 5 (pdf) figure

    The predictability problem in systems with an uncertainty in the evolution law

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    The problem of error growth due to the incomplete knowledge of the evolution law which rules the dynamics of a given physical system is addressed. Major interest is devoted to the analysis of error amplification in systems with many characteristic times and scales. The importance of a proper parameterization of fast scales in systems with many strongly interacting degrees of freedom is highlighted and its consequences for the modelization of geophysical systems are discussed.Comment: 20 pages RevTeX, 6 eps figures (included

    Relaxation of finite perturbations: Beyond the Fluctuation-Response relation

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    We study the response of dynamical systems to finite amplitude perturbation. A generalized Fluctuation-Response relation is derived, which links the average relaxation toward equilibrium to the invariant measure of the system and points out the relevance of the amplitude of the initial perturbation. Numerical computations on systems with many characteristic times show the relevance of the above relation in realistic cases.Comment: 7 pages, 5 figure

    Non Asymptotic Properties of Transport and Mixing

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    We study relative dispersion of passive scalar in non-ideal cases, i.e. in situations in which asymptotic techniques cannot be applied; typically when the characteristic length scale of the Eulerian velocity field is not much smaller than the domain size. Of course, in such a situation usual asymptotic quantities (the diffusion coefficients) do not give any relevant information about the transport mechanisms. On the other hand, we shall show that the Finite Size Lyapunov Exponent, originally introduced for the predictability problem, appears to be rather powerful in approaching the non-asymptotic transport properties. This technique is applied in a series of numerical experiments in simple flows with chaotic behaviors, in experimental data analysis of drifter and to study relative dispersion in fully developed turbulence.Comment: 19 RevTeX pages + 8 figures included, submitted on Chaos special issue on Transport and Mixin

    Drifter dispersion in the Adriatic Sea: Lagrangian data and chaotic model

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    International audienceWe analyze characteristics of drifter trajectories from the Adriatic Sea with recently introduced nonlinear dynamics techniques. We discuss how in quasi-enclosed basins, relative dispersion as a function of time, a standard analysis tool in this context, may give a distorted picture of the dynamics. We further show that useful information may be obtained by using two related non-asymptotic indicators, the Finite-Scale Lyapunov Exponent (FSLE) and the Lagrangian Structure Function (LSF), which both describe intrinsic physical properties at a given scale. We introduce a simple chaotic model for drifter motion in this system, and show by comparison with the model that Lagrangian dispersion is mainly driven by advection at sub-basin scales until saturation sets in

    Dispersion of passive tracers in model flows: effects of the parametrization of small-scale processes

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    Abstract. A set of numerical experiments is presented, in which we study the dynamics of passive particles advected by given two-dimensional velocity fields and perturbed by a non-white noise with a characteristic time Ï„. Data and model results have shown that this kind of random perturbation is able to represent subgridscale processes for upper ocean mesoscale turbulence for regions of the world ocean where turbulence can be assumed to be homogeneous. Extensive computations in different fields characterized by cell-like structure, both stationary and time-dependent, representing very idealized geophysical flow situations, show that the presence of a finite correlation time scale does lead to enhanced or arrested dispersion, depending on the considered flow; however, it does not seem to affect the gross qualitative behaviour of the dispersion processes, which is primarily affected by the large-scale velocity field

    The Richardson's Law in Large-Eddy Simulations of Boundary Layer flows

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    Relative dispersion in a neutrally stratified planetary boundary layer (PBL) is investigated by means of Large-Eddy Simulations (LES). Despite the small extension of the inertial range of scales in the simulated PBL, our Lagrangian statistics turns out to be compatible with the Richardson t3t^3 law for the average of square particle separation. This emerges from the application of nonstandard methods of analysis through which a precise measure of the Richardson constant was also possible. Its values is estimated as C2∼0.5C_2\sim 0.5 in close agreement with recent experiments and three-dimensional direct numerical simulations.Comment: 15 LaTex pages, 4 PS figure
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