Comprehensive multifractal analysis of turbulent velocity using wavelet leaders Article - Janvier 2008

Bruno Lashermes, Stéphane Roux, Patrice Abry, Stéphane Jaffard

Bruno Lashermes, Stéphane Roux, Patrice Abry, Stéphane Jaffard, « Comprehensive multifractal analysis of turbulent velocity using wavelet leaders  », European Physical Journal B : Condensed Matter and Complex Systems, janvier 2008, pp. 201-215. ISSN 1434-6028

Abstract

The multifractal (MF) framework relates the scaling properties of turbulence to its local regu- larity properties through a statistical description as a collection of local singularities. The MF properties are moreover linked to the multiplicative cascade process that creates the peculiar properties of turbulence such as intermittency. A comprehensive estimation of the MF properties of turbulence from data analysis, using a tool valid for all kind of singularities (including oscillating singularities) and mathematically well- founded, is thus of first importance in order to extract a reliable information on the underlying physical processes. The MF formalism based on the wavelet leaders (WL) is a new MF formalism which is the first to meet all these requests. This paper aims at its description and at its application to experimental turbulent velocity data. After a detailed discussion of the practical use of the MF formalism based on the WL the following questions are carefully investigated : (1) What is the dependence of MF properties on the Reynolds number ? (2) Are oscillating singularities present in turbulent velocity data ? (3) Which MF model does correctly account for the observed MF properties ? Results from several data set analyses are used to discuss the dependence of the computed MF properties on the Reynolds number but also to assess their common or universal component. An exact though partial answer (no oscillating singularities are detected) to the issue of the presence of oscillating singularities is provided for the first time. Eventually an accurate parameterization with cumulants exponents up to order 4 confirms that the log-normal model (with c2 = −0.025 ± 0.002) correctly accounts for the universal MF properties of turbulent velocity.

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