Computing and Analyzing Turbulent Flows Using Wavelets

  • Schneider K
  • Farge M
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Abstract

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 introduc- ing the continuous and discrete wavelet transforms we present classi- cal 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 equa- tions and apply it to compute a time-developing turbulent mixing layer. Finally we draw some conclusions and present some perspec- tives for turbulence modelling.

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Schneider, K., & Farge, M. (2001). Computing and Analyzing Turbulent Flows Using Wavelets. In Wavelet Transforms and Time-Frequency Signal Analysis (pp. 181–216). Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-0137-3_7

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