A three-dimensional wavelet based multifractal method : about the need of revisiting the multifractal description of turbulence dissipation data

TL;DR

This paper introduces a generalized 3D wavelet-based multifractal analysis method, demonstrating its effectiveness on synthetic data and turbulence dissipation fields, and highlights the limitations of previous box-counting approaches.

Contribution

The paper develops a new 3D WTMM method for multifractal analysis and applies it to turbulence data, addressing shortcomings of earlier techniques.

Findings

The 3D WTMM method accurately characterizes multifractal spectra.

Previous box-counting methods failed on non-conservative measures.

Revisiting turbulence data analysis improves understanding of dissipation fields.

Abstract

We generalize the wavelet transform modulus maxima (WTMM) method to multifractal analysis of 3D random fields. This method is calibrated on synthetic 3D monofractal fractional Brownian fields and on 3D multifractal singular cascade measures as well as their random function counterpart obtained by fractional integration. Then we apply the 3D WTMM method to the dissipation field issue from 3D isotropic turbulence simulations. We comment on the need to revisiting previous box-counting analysis which have failed to estimate correctly the corresponding multifractal spectra because of their intrinsic inability to master non-conservative singular cascade measures.