Analysing and Computing Turbulent Flows Using Wavelets

These lecture notes are a review on wavelet techniques for analyzing and computing fully-developed turbulent flows, which correspond to the regime where nonlinear instabilities are dominant. The wavelet-based techniques we have been developing during the last decade are explained and the main results are presented. After introducing the continuous and discrete wavelet transforms we present classical and wavelet-based statistical diagnostics to study turbulent flows. We then present wavelet methods for extracting coherent vortices in two- and three-dimensional turbulent flows. Afterwards we present an adaptive wavelet solver for the two-dimensional Navier—Stokes equations and apply it to compute a time-developing turbulent mixing layer. Finally we draw some conclusions and present some perspectives for turbulence modelling.