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A model for large-scale structures in turbulent shearflows

Published online by Cambridge University Press:  26 April 2006

Andrew C. Poje and
J. L. Lumley
Andrew C. Poje
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14855, USAPresent address: IGPP, University of California, Los Alamos National Laboratory, Los Alamos, NM 87544 USA.
J. L. Lumley
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14855, USA
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Abstract

A procedure based on energy stability arguments is presented as amethod for extracting large-scale, coherent structures from fullyturbulent shear flows. By means of two distinct averaging operators,the instantaneous flow field is decomposed into three components: aspatial mean, coherent field and random background fluctuations. Theevolution equations for the coherent velocity, derived from theNavier–Stokes equations, are examined to determine the mode thatmaximizes the growth rate of volume-averaged coherent kineticenergy. Using a simple closure scheme to model the effects of thebackground turbulence, we find that the spatial form of the maximumenergy growth modes compares well with the shape of the empiricaleigenfunctions given by the proper orthogonal decomposition. Thediscrepancy between the eigenspectrum of the stability problem andthe empirical eigenspectrum is explained by examining the role ofthe mean velocity field. A simple dynamic model which captures theenergy exchange mechanisms between the different scales of motion isproposed. Analysis of this model shows that the modes which attainthe maximum amplitude of coherent energy density in the modelcorrespond to the empirical modes which possess the largestpercentage of turbulent kinetic energy. The proposed method providesa means for extracting coherent structures which are similar tothose produced by the proper orthogonal decomposition but whichrequires only modest statistical input.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 285 , 25 February 1995, pp. 349 - 369
Copyright
© 1995 Cambridge University Press

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