Divergence-free wavelet analysis of turbulent flows (Q1610515)

The paper describes the application of divergence-free wavelets to the analysis of turbulent flows. First, biorthogonal wavelets and the construction of divergence-free wavelets and wavelet thresholding are reviewed, followed by a short presentation of proper orthogonal decomposition. Subsequently, the divergent-free wavelet decomposition is applied to a periodic two-dimensional flow computed by direct numerical simulation, and to two-dimensional slices of three-dimensional experimental velocity fields of a flow past an airfoil obtained by particle image velocity. The compression properties of wavelets are studied, and the contributions of divergent and non-divergent components in the flow at different scales are quantified. Finally, the authors investigate the regularity of turbulent flow fields.