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COHERENT VORTICITY EXTRACTION IN TURBULENT BOUNDARY LAYERS USING ORTHOGONAL WAVELETS

George Khujadze
Universitat Siegen, Chair of Fluid Mechanics Paul-Bonatz-Str. 9-11, 57068 Siegen, Germany & Abastumani Astrophysical Observatory Ilia State University, Tbilisi 0160, Georgia

Romain Nguyen van yen
Institut fur Mathematik Freie Universitat Berlin Germany

Kai Schneider
Laboratoire de Modélisation et Simulation Numérique en Mécanique, CNRS et Universités d'Aix-Marseille & CMI, Université de Provence, 39 rue Frédéric Joliot-Curie, 13453 Marseille, France

Martin Oberlack
Department of Fluid Mechanics TU Darmstadt Otto-Bernd-Str. 2², 64287 Darmstadt, Germany, Graduate School CE, TU Darmstadt Dolivostrasse 15, 64293 Darmstadt, Germany

Marie Farge
LMD-IPSL-CNRS Ecole Normale Superieure 24 rue Lhomond, 75231 Paris Cedex 5, France

Abstract

High-resolution data obtained by direct numerical simulation of turbulent boundary layers are analysed by means of orthogonal wavelets. The data, originally given on a Chebychev grid, are first interpolated onto an adapted dyadic grid. Then, they are decomposed using a wavelet basis, which accounts for the anisotropy of the flow by using different scales in the wall-normal direction and in the planes parallel to the wall. Thus the vorticity field is decomposed into coherent and incoherent contributions using thresholding of the wavelet coefficients. It is shown that less than 1% of the coefficients retain the coherent structures of the flow, while the majority of the coefficients corresponds to a structureless, i.e., noise-like background flow. Scale- and direction-dependent statistics in wavelet space quantify the flow properties at different wall distances.