Statistical mechanics of the shallow water system

We extend the formalism of the statistical theory developed for the 2D Euler equation to the case of shallow water system. Relaxation equations towards the maximum entropy state are proposed, which provide a parametrization of sub-grid scale eddies in 2D compressible turbulence.Comment: submitted to Phys. Fluid

A coalescence model for freely decaying two-dimensional turbulence

We propose a ballistic coalescence model (punctuated-Hamiltonian approach) mimicking the fusion of vortices in freely decaying two-dimensional turbulence. A temporal scaling behaviour is reached where the vortex density evolves like $t^{-\xi}$. A mean-field analytical argument yielding the approximation $\xi=4/5$ is shown to slightly overestimate the decay exponent $\xi$ whereas Molecular Dynamics simulations give $\xi =0.71\pm 0.01$, in agreement with recent laboratory experiments and simulations of Navier-Stokes equation.Comment: 6 pages, 1 figure, to appear in Europhysics Letter

Is turbulent mixing a self convolution process ?

Experimental results for the evolution of the probability distribution function (PDF) of a scalar mixed by a turbulence flow in a channel are presented. The sequence of PDF from an initial skewed distribution to a sharp Gaussian is found to be non universal. The route toward homogeneization depends on the ratio between the cross sections of the dye injector and the channel. In link with this observation, advantages, shortcomings and applicability of models for the PDF evolution based on a self-convolution mechanisms are discussed.Comment: 4 page

On the properties of steady states in turbulent axisymmetric flows

We experimentally study the properties of mean and most probable velocity fields in a turbulent von K\'arm\'an flow. These fields are found to be described by two families of functions, as predicted by a recent statistical mechanics study of 3D axisymmetric flows. We show that these functions depend on the viscosity and on the forcing. Furthermore, when the Reynolds number is increased, we exhibit a tendency for Beltramization of the flow, i.e. a velocity-vorticity alignment. This result provides a first experimental evidence of nonlinearity depletion in non-homogeneous non-isotropic turbulent flow.Comment: latex prl-stationary-051215arxiv.tex, 9 files, 6 figures, 4 pages (http://www-drecam.cea.fr/spec/articles/S06/008/

Time-reversible Dynamical Systems for Turbulence

Dynamical Ensemble Equivalence between hydrodynamic dissipative equations and suitable time-reversible dynamical systems has been investigated in a class of dynamical systems for turbulence. The reversible dynamics is obtained from the original dissipative equations by imposing a global constraint. We find that, by increasing the input energy, the system changes from an equilibrium state to a non-equilibrium stationary state in which an energy cascade, with the same statistical properties of the original system, is clearly detected.Comment: 16 pages Latex, 4 PS figures, on press on J. Phy