Extracting singularities in turbulent flow with real and complex wavelets

Abstract

In order to contribute to an understanding of the nature of turbulent intermittency the multifractal properties of turbulent velocity fields are explored on the basis of real and complex wavelets. The wavelet transform modulus maxima method (WTMM) is nowadays a well developed procedure to extract the singularity spectrum D(h) if the signal does not contain oscillating singularities like vortex tubes. However, the presence of oscillating singularities leads to an underestimation of Holder exponents h and thus to wrong results. In general, two exponents h, β are necessary to characterize the singular behaviour, where the oscillation exponent β describes the local power law divergence of the instantaneous frequency. To determine h and β we propose an improved WTMM method based on real and complex wavelets in which the maxima lines are traced directly. An appropriate partition function allows to calculate a general singularity spectrum D(h, β)