Generalizing the wavelet-based multifractal formalism to vector-valued random fields: application to turbulent velocity and vorticity 3D numerical data

TL;DR

This paper extends the wavelet-based multifractal formalism to analyze vector-valued random fields, specifically applied to turbulent velocity and vorticity data, revealing new insights into their intermittency and singularity spectra.

Contribution

The authors generalize the wavelet transform modulus maxima method for vector fields using singular value decomposition, enabling more accurate multifractal analysis of turbulence data.

Findings

Velocity and vorticity fields are more intermittent than previously estimated.

Existence of a close relationship between the singularity spectra of velocity and vorticity.

Method successfully calibrated on synthetic and fractional Brownian vector fields.

Abstract

We use singular value decomposition techniques to generalize the wavelet transform modulus maxima method to the multifractal analysis of vector-valued random fields. The method is calibrated on synthetic multifractal 2D vector measures and monofractal 3D fractional Brownian vector fields. We report the results of some application to the velocity and vorticity fields issued from 3D isotropic turbulence simulations. This study reveals the existence of an intimate relationship between the singularity spectra of these two vector fields which are found significantly more intermittent than previously estimated from longitudinal and transverse velocity increment statistics.