A wavelet-based method for multifractal analysis of 3D random fields: application to turbulence simulation data

摘要: older exponent, fractional Brownian motion, multifractal cascade mod- els, 3D continuous wavelet transform, Wavelet Transform Modulus Max- ima (WTMM) method, fully developed turbulence, Direct Numerical Simula- tions (DNS), intermittency, dissipation field. Abstract: We generalize the so-called transform modulus maxima method to analysis of data. This has been origi- nally designed describe statistically roughness fluctuations fractal signals like turbulent 1D and 2D rough surfaces. The WTMM consists in performing a multi-scale edge detection. can be achieved using con- tinuous provided one chooses an appropriate analyzing wavelet. filtering step takes advantage from recursive filter techniques which, for data analysis, are much less time consuming that FFT algorithms. After linking across scales local WT modulus, obtains skele- ton which provides space-scale partitioning considered From this skeleton computes, at each scale , some partition functions heart analysis. Then scaling behavior these func- tions, extracts spectra including singularity spectrum. report results test applications on synthetic monofractal fields realizations singular measures as well fractionally integrated cascades analytic properties known. is applied field issue isotropic turbulence simulation departure monofractality intermittent nature dissipa- tion clearly shown quantified. A comparative with obtained box-counting reveals classical indeed fail estimate correctly corresponding because their intrinsic inability master non-conservative measures. conclude by emphasizing wide range potential WTMMmethod, e.g. geophysical data, molecular cloud structure astrophysics, medical imaging many other areas fundamental sciences.