Detecting oscillating singularities in multifractal analysis: Application to hydrodynamic turbulence

Multifractal analysis describes data as a collection of singularities. However, its classical formulation does not account for their possibly oscillating nature, while, in a number of applications, distinguishing between oscillating and non oscillating singularities may significantly enrich the analysis. This is notably the case in hydrodynamic turbulence, of interest here, where two different important heuristic models contradictorily lead to predict the existence or absence of oscillating singularities. This contribution proposes a wavelet Leader oscillation formalism enabling to evidence the presence of oscillating singularities in real data. It is first validated on synthetic data both with and without oscillating singularities and second applied to high quality ID velocity turbulence data. This constitutes the first quantitative evidence against the presence of oscillating singularities in turbulence data.