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

摘要

We generalize the wavelet transform modulus maxima (WTMM) method tomultifractal analysis of 3D random fields. This method is calibrated onsynthetic 3D monofractal fractional Brownian fields and on 3D multifractalsingular cascade measures as well as their random function counterpart obtainedby fractional integration. Then we apply the 3D WTMM method to the dissipationfield issue from 3D isotropic turbulence simulations. We comment on the need torevisiting previous box-counting analysis which have failed to estimatecorrectly the corresponding multifractal spectra because of their intrinsicinability to master non-conservative singular cascade measures.