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Anisotropy and energy flux in wall turbulence

Published online by Cambridge University Press:  27 August 2003

D. C. DUNN
Affiliation:
Department of Aeronautics, Imperial College, London SW7 2AZ, UK Present address: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
J. F. MORRISON
Affiliation:
Department of Aeronautics, Imperial College, London SW7 2AZ, UK
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Abstract

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A term-by-term wavelet decomposition of the equation for turbulence kinetic energy in turbulent channel flow is used to provide a dual space-scale description of the production and flux of energy. Wavelet filtering, analogous to that used in large-eddy simulation, is performed on the nonlinear term that constitutes the energy flux. Meneveau's term, $\pi_{{sg}}^{(m)}[{\bm i}]$ is used to represent forward scatter and backscatter. This term is highly intermittent, much more so than the equivalent terms for production at the same scale. Virtually all of $\pi_{{sg}}^{(m)}[{\bm i}]$ appears in only two components that involve subgrid flux of streamwise momentum in the wall-normal and spanwise directions. An equivalent term that is the wavelet transform of the pressure-gradient term is shown to be several orders of magnitude smaller, consistent with its neglect in current subgrid modelling techniques. However, the mean-square pressure-gradient fluctuations (that reach a maximum in the range of wavenumbers in which the velocity spectra exhibit a −5/3 slope) are responsible for the significant spatial intermittency observed in the energy flux.

Type
Papers
Copyright
© 2003 Cambridge University Press