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

TL;DR

This review paper discusses wavelet analysis techniques and their diverse applications in studying magnetohydrodynamic (MHD) and plasma turbulence, including diagnostics, denoising, and multiscale simulations.

Contribution

It provides a comprehensive overview of wavelet transforms and introduces new methods for analyzing and simulating turbulent plasma flows using wavelet-based tools.

Findings

Wavelet transforms effectively extract coherent structures from turbulent flows.

Wavelet-based denoising improves the analysis of turbulent plasma data.

Multiscale wavelet schemes enable advanced numerical simulations of MHD turbulence.

Abstract

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.