WAVELET REGULARIZATION OF A FOURIER-GALERKIN METHOD FOR SOLVING THE 2D INCOMPRESSIBLE EULER EQUATIONS

International audienceWe employ a Fourier-Galerkin method to solve the 2D incompressible Euler equations, and study several ways to regularize the solution by wavelet filtering at each timestep. Real-valued orthogonal wavelets and complex-valued wavelets are considered, combined with either linear or non-linear filtering. The results are compared with those obtained via classical viscous and hyperviscous regularization methods. Wavelet regularization using complex-valued wavelets performs as well in terms of L2 convergence rate to the reference solution. The compression rate for homogeneous 2D turbulence is around 3 for this method, suggesting that memory and CPU time could be reduced in an adaptive wavelet computation. Our results also suggest L2 convergence to the reference solution without any regularization, in contrast to what is obtained for the 1D Burgers equation

The Lundgren-Monin-Novikov Hierarchy: Kinetic Equations for Turbulence

We present an overview of recent works on the statistical description of turbulent flows in terms of probability density functions (PDFs) in the framework of the Lundgren-Monin-Novikov (LMN) hierarchy. Within this framework, evolution equations for the PDFs are derived from the basic equations of fluid motion. The closure problem arises either in terms of a coupling to multi-point PDFs or in terms of conditional averages entering the evolution equations as unknown functions. We mainly focus on the latter case and use data from direct numerical simulations (DNS) to specify the unclosed terms. Apart from giving an introduction into the basic analytical techniques, applications to two-dimensional vorticity statistics, to the single-point velocity and vorticity statistics of three-dimensional turbulence, to the temperature statistics of Rayleigh-B\'enard convection and to Burgers turbulence are discussed.Comment: Accepted for publication in C. R. Acad. Sc

A finite volume-complete flux scheme for the singularly perturbed generalized Burgers-Huxley equation

In this paper the finite volume-complete flux scheme is proposed to numerically solve the generalized Burgers-Huxley equation. The scheme is applied in an iterative manner. Numerical computations are performed for traveling wave-type problems as a validation of the method. Convection-dominated problems are used to assess the method on boundary layers. The results are in good agreement with reference results

Stochastic Perturbations in Vortex Tube Dynamics

A dual lattice vortex formulation of homogeneous turbulence is developed, within the Martin-Siggia-Rose field theoretical approach. It consists of a generalization of the usual dipole version of the Navier-Stokes equations, known to hold in the limit of vanishing external forcing. We investigate, as a straightforward application of our formalism, the dynamics of closed vortex tubes, randomly stirred at large length scales by gaussian stochastic forces. We find that besides the usual self-induced propagation, the vortex tube evolution may be effectively modeled through the introduction of an additional white-noise correlated velocity field background. The resulting phenomenological picture is closely related to observations previously reported from a wavelet decomposition analysis of turbulent flow configurations.Comment: 16 pages + 2 eps figures, REVTeX