Rubén A. Pasmanter

On long‐lived vortices in 2‐D viscous flows, most probable states of inviscid 2‐D flows and a soliton equation

This paper considers, in contraposition to the most probable states of quasi‐inviscid theories, the status of the vorticity(ω)–streamfunction(ψ) relations satisfied by the long‐lived vortices observed in some numerical simulations of decaying two‐dimensional turbulence and in experiments in stratified fluids. For the case ω=−Δψ=sinh ψ, the circular solutions can be expressed in terms of the IIIrd Painleve transcendent and dipolar solutions can be constructed by means of a Backlund transform.

A mean field prediction of the asymptotic state of decaying 2D turbulence

We compare the quasi-stationary state obtained from a numerical integration of the two-dimensional Navier-Stokes equation, performed by Matthaeus et al. [Phys. Rev. Lett. 66, 2731 (1991)] with predictions of a mean field theory based on inviscid dynamics. We find that over a relatively short initial period, the theory does not apply, whereas at later stages its prediction for the quasi-stationary state is very good. We relate the failure and success of the inviscid theory to the relevance of viscous effects in the dynamics.

Symbolic dynamics of fully developed chaos

Abstract By discerning levels k of statistical description it is shown that the level- k Boltzmann entropy h ( k ) ∝ log (# possibilities on level k ) of two-symbol sequences equals the information theoretical conditional entropy kS ( k ) -( k -1) S ( k -1) , with S ( k ) the average Shannon entropy on level k . A mixing measure μ is introduced by means of an appropriate demixing procedure. From the properties of the two-symbol sequence an expression for a symbolic 2 x 2 correlation matrix is derived.

Variational search of periodic motions in complex dynamical systems

Abstract We present a method for the detection and characterization of periodic motions in the dynamics of complex systems. In contrast to other commonly used approaches, e.g., empirical orthogonal functions, principal oscillation patterns, singular spectrum analyses, this method is oriented towards scalar quantities, therefore, it does not require the introduction of an arbitrary metric in the space of the dynamical variables. Nonlinear effects are included; needless to say, the higher the non-linearities included the longer and more complicated the actual calculations become. We are trying the method on a Lorenz model and on a simple model of the dynamics of the atmosphere.

Symbolic dynamics of fully developed chaos. II: Random and order-1 Markovian two-symbol sequences

Abstract The relations between three different symbolic descriptions of fully developed chaos in iterated one-hump maps on the interval are investigated in the case of short memory time.

Stochastic selfsimilar branching and turbulence

A new stochastic multifractal cascade model for inertial-subrange turbulence is introduced which can be fitted to a recent experimental determination of the spectrum of generalized dimensions. The local scaling behaviour (set of scale-invariant multiplier distributions) is close to the observed one. The model also produces realistic energy-dissipation-rate signals and displays the correct square-root exponentional tails in the energy-flux probability densities.

Symbolic dynamics of fully developed chaos III. Infinite-memory sequences and phase transitions

A special type of dynamical phase transitions which arises in a particular one-dimensional fully developed chaotic iterated map is studied by means of a symbolic dynamics. Exact analytical expressions for the probabilities of words are found on both sides of the critical value, making it possible to give a statistical description of the critical behaviour at the phase transition in terms of Boltzmann entropies, correlation functions and generalized dimensions.

Anomalous diffusion and patchiness generated by Lagrangian chaos in shallow tidal flows

As a simplified model of the currents generated by a tidal wave propagating over a shallow region with bottom irregularities, i.e., the Wadden Sea in The Netherlands, we used a two‐dimensional incompressible flow, periodic both in space and time. In previous work we have reported that the paths of passive particles advected by nonrandom, laminar, 2‐D tidal flows are often chaotic if the spatial inhomogeneity and time dependence are not negligible. Moreover, the numerical calculations showed that the deterministic advection of particles by such a velocity field leads to the following. (1) Patchiness, i.e., parts of the solute cloud that (in the absence of diffusion) do not disperse at all. Different patches may drift with different velocities. These patches coexist with the chaotic areas described next. (2) Chaotic paths with properties similar to those of random walks; i.e., the variance of the solute cloud grows in time like tα. The value of α depends upon the parameters that characterize the flow, e.g.,...

Markov Chain Approach to a Process with Long-Time Memory

Abstract The authors show that long-term memory effects, present in the chaotic dispersion process generated by a meandering jet model, can be nonetheless taken into account by a first-order Markov process, provided that the states of the phase-space “partition,” conceived in a wider sense, are appropriately defined.

Evolution of the vorticity-area density during the formation of coherent structures in two-dimensional flows

It is shown: (1) that in two-dimensional, incompressible, viscous flows the vorticity-area distribution evolves according to an advection-diffusion equation with a negative, time dependent diffusion coefficient and (2) how to use the vorticity-stream function relations, i.e., the so-called scatter-plots, of the quasi-stationary coherent structures in order to quantify the experimentally observed changes of the vorticity distribution moments leading to the formation of these structures.