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Spatio-temporal spectra in the logarithmic layer of wall turbulence: large-eddy simulations and simple models

Published online by Cambridge University Press:  13 March 2015

Michael Wilczek*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Max Planck Institute for Dynamics and Self-Organization, D-37077 Göttingen, Germany
Richard J. A. M. Stevens
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Department of Science and Technology and J.M. Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Charles Meneveau
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
*
Email address for correspondence: michael.wilczek@ds.mpg.de

Abstract

Motivated by the need to characterize the spatio-temporal structure of turbulence in wall-bounded flows, we study wavenumber–frequency spectra of the streamwise velocity component based on large-eddy simulation (LES) data. The LES data are used to measure spectra as a function of the two wall-parallel wavenumbers and the frequency in the equilibrium (logarithmic) layer. We then reformulate one of the simplest models that is able to reproduce the observations: the random sweeping model with a Gaussian large-scale fluctuating velocity and with additional mean flow. Comparison with LES data shows that the model captures the observed temporal decorrelation, which is related to the Doppler broadening of frequencies. We furthermore introduce a parameterization for the entire wavenumber–frequency spectrum $E_{11}(k_{1},k_{2},{\it\omega};z)$, where $k_{1}$, $k_{2}$ are the streamwise and spanwise wavenumbers, ${\it\omega}$ is the frequency and $z$ is the distance to the wall. The results are found to be in good agreement with LES data.

Type
Rapids
Copyright
© 2015 Cambridge University Press 

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