94 research outputs found
Introduction to chaos and diffusion
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
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
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
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
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
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
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
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 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
in close agreement with recent experiments and three-dimensional direct
numerical simulations.Comment: 15 LaTex pages, 4 PS figure
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