Divergence-Free Wavelet Analysis of Turbulent Flows

In this paper we study the application of divergence-free wavelet bases for the analysis of incompressible turbulent flows and perform several experiments. In particular, we analyze various nominally incompressible fields and study the influence of compressible perturbations due to experimental and computational errors. In addition, we investigate the multiscale structure of modes obtained from the Proper Orthogonal Decomposition (POD) method. Finally, we study the divergence-free wavelet compression of turbulent flow data and present results on the energy recovery. Moreover, we utilize wavelet decompositions to investigate the regularity of turbulent flow fields in certain non-classical function spaces, namely Besov spaces. In our experiments, we have observed significantly higher Besov regularity than Sobolev regularity, which indicates the potential for adaptive numerical simulations.