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Extraction of coherent vortex tubes in a 3D turbulent mixing layer using orthogonal wavelets

  • Kai Schneider
  • Marie Farge
Conference paper
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 71)

Abstract

We present a new technique to extract coherent vortex tubes out of turbulent flows. The method is based on an orthogonal vector-valued wavelet decomposition of the vorticity field using the fast wavelet transform. A nonlinear thresholding of the wavelet coefficients is applied, where the threshold depends on the Reynolds number and on the total enstrophy of the flow, only. The coherent vortex tubes are reconstructed from the strong wavelet coefficients while the remaining weak coefficients correspond to an incoherent background flow. As example we present an application of this method to a turbulent mixing layer computed by high resolution direct numerical simulation. We find that only few wavelet coefficients are necessary to represent the coherent vortex tubes of the flow. The incoherent background flow reconstructed from the remaining weak coefficients is structureless and exhibits an energy equipartition.

Keywords

Wavelet Coefficient Vortex Tube Vorticity Field Orthogonal Wavelet Coherent Vortex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Daubechies, I. 1992 Ten Lectures on wavelets, SIAM, Philadelphia.zbMATHGoogle Scholar
  2. Donoho, D. 1993 Unconditionnal bases are optimal bases for data compression and statistical estimation. Appl. Comp. Harmonic Analysis, 1, 100–115.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Farge, M. 1992 Wavelet Transforms and their Applications to Turbulence. Ann. Rev. of Fluid Mech., 24, 395–457.MathSciNetzbMATHADSCrossRefGoogle Scholar
  4. Farge, M., Schneider, K. & Kevlahan, N. 1999 Non-Gaussianity and Coherent Vortex Simulation for two-dimensional turbulence using an adaptive orthonormal wavelet basis. Phys. Fluids, 11(8), 2187–2201.CrossRefMathSciNetADSzbMATHGoogle Scholar
  5. Farge, M., Pellegrino, G. & Schneider, K. 2001 Coherent Vortex Extraction in 3D Turbulent Flows using orthogonal wavelets. Phys. Rev. Lett., 87(5), 054501Google Scholar
  6. Farge, M. & Schneider, K. 2001 Coherent Vortex Simulation (CVS), a semi-deterministic turbulence model. Flow, Turbulence and Combustion, in pressGoogle Scholar
  7. Jimenez J. & Wray A. A. 1993, The structure of intense vorticity in isotropic turbulence, J. Fluid Mech., 255, 65–90.MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. Rogers, M. & Moser, R. 1994 Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids, 6(2), 903–923.CrossRefADSzbMATHGoogle Scholar
  9. Schneider, K. & Farge, M. 2000 Numerical simulation of temporally growing mixing layer in an adaptive wavelet basis. C. R. Acad. Sci. Paris Série II b, 328, 263–269.zbMATHADSGoogle Scholar
  10. Schneider, K., Farge, M., Pellegrino, G. & Rogers, M. 2000 CVS filtering of 3D turbulent mixing layers using orthogonal wavelets. Proceedings of the 2000 Summer Program, Center for Turbulence Research, Nasa Ames and Stanford University, 319–330.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Kai Schneider
    • 1
  • Marie Farge
    • 2
  1. 1.Centre de Mathématiques et d’InformatiqueUniversité de ProvenceMarseille Cedex 13France
  2. 2.LMD-CNRS, Ecole Normale Supérieure, ParisParis Cedex 9France

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