Wavelet transforms and their applications to MHD and plasma turbulence: a review

Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics based on the wavelet coefficients. We then show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising. Finally some multiscale numerical simulation schemes using wavelets are described. Several examples for analyzing, compressing and computing one, two and three dimensional turbulent MHD or plasma flows are presented.Comment: Journal of Plasma Physics, 201

Conditional vorticity budget of coherent and incoherent flow contributions in fully developed homogeneous isotropic turbulence

We investigate the conditional vorticity budget of fully developed three-dimensional homogeneous isotropic turbulence with respect to coherent and incoherent flow contributions. The Coherent Vorticity Extraction based on orthogonal wavelets allows to decompose the vorticity field into coherent and incoherent contributions, of which the latter are noise-like. The impact of the vortex structures observed in fully developed turbulence on statistical balance equations is quantified considering the conditional vorticity budget. The connection between the basic structures present in the flow and their statistical implications is thereby assessed. The results are compared to those obtained for large- and small-scale contributions using a Fourier decomposition, which reveals pronounced differences

Foreword for the special issue on ‘Large Eddy Simulation, Coherent Vortex Simulation & Vortex Methods’ dedicated to the memory of Joel Ferziger

This is the introduction of the special issue of the Journal of Turbulence, which was dedicated to the memory of Joel Ferziger who died on 16 August 2004. It contains 11 papers which were presented during the Euromech Colloquium 454 on ‘Large Eddy Simulation, Coherent Vorticity Simulation and Vortex Methods’ that we organised at CIRM (Centre International de Rencontres Mathématiques) in Marseilles (France) from 14 to 16 April 2004

Craya decomposition using compactly supported biorthogonal wavelets

Special Issue on Continuous Wavelet Transform in Memory of Jean Morlet, Part IIInternational audienceWe present a new local Craya--Herring decomposition of three-dimensional vector fields using compactly supported biorthogonal wavelets. Therewith vector-valued function spaces are split into two orthogonal components, i.e., curl-free and divergence-free spaces. The latter is further decomposed into toroidal and poloidal parts to decorrelate horizontal from vertical contributions which are of particular interest in geophysical turbulence. Applications are shown for isotropic, rotating and stratified turbulent flows. A comparison between isotropic and anisotropic orthogonal Craya--Herring wavelets, built in Fourier space and thus not compactly supported, is also given

The role of coherent vorticity in turbulent transport in resistive drift-wave turbulence

The coherent vortex extraction method, a wavelet technique for extracting coherent vortices out of turbulent flows, is applied to simulations of resistive drift-wave turbulence in magnetized plasma (Hasegawa-Wakatani system). The aim is to retain only the essential degrees of freedom, responsible for the transport. It is shown that the radial density flux is carried by these coherent modes. In the quasi-hydrodynamic regime, coherent vortices exhibit depletion of the polarization-drift nonlinearity and vorticity strongly dominates strain, in contrast to the quasiadiabatic regime

Wavelet-based density estimation for noise reduction in plasma simulations using particles

For given computational resources, the accuracy of plasma simulations using particles is mainly held back by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on wavelet analysis is proposed and tested to reduce this noise. The method, known as wavelet based density estimation (WBDE), was previously introduced in the statistical literature to estimate probability densities given a finite number of independent measurements. Its novel application to plasma simulations can be viewed as a natural extension of the finite size particles (FSP) approach, with the advantage of estimating more accurately distribution functions that have localized sharp features. The proposed method preserves the moments of the particle distribution function to a good level of accuracy, has no constraints on the dimensionality of the system, does not require an a priori selection of a global smoothing scale, and its able to adapt locally to the smoothness of the density based on the given discrete particle data. Most importantly, the computational cost of the denoising stage is of the same order as one time step of a FSP simulation. The method is compared with a recently proposed proper orthogonal decomposition based method, and it is tested with three particle data sets that involve different levels of collisionality and interaction with external and self-consistent fields

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

Wavelet Analysis of Vortex Breakdown

We study the quasi-periodic turbulent bursting of a laboratory produced isolated vortex immersed in laminar flow. We analyze the experimentally measured flow field using orthogonal wavelets to observe the time evolution of the bursting. The discrete wavelet transform is used to separate the flow field into a coherent component, capturing the dynamics and statistics of the vortex during bursting, and an incoherent component, which is structureless and exhibits a different statistical behavior