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WKB theory for rapid distortion of inhomogeneous turbulence

Published online by Cambridge University Press:  10 July 1999

S. NAZARENKO
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
N. K.-R. KEVLAHAN
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton L8S 4K1, Canada
B. DUBRULLE
Affiliation:
CNRS URA 2052, L'Orme des Merisiers, 709, 91191 Gif sur Yvette, France

Abstract

A WKB method is used to extend RDT (rapid distortion theory) to initially inhomogeneous turbulence and unsteady mean flows. The WKB equations describe turbulence wavepackets which are transported by the mean velocity and have wavenumbers which evolve due to the mean strain. The turbulence also modifies the mean flow and generates large-scale vorticity via the averaged Reynolds stress tensor. The theory is applied to Taylor's four-roller flow in order to explain the experimentally observed reduction in the mean strain. The strain reduction occurs due to the formation of a large-scale vortex quadrupole structure from the turbulent spot confined by the four rollers. Both turbulence inhomogeneity and three-dimensionality are shown to be important for this effect. If the initially isotropic turbulence is either homogeneous in space or two-dimensional, it has no effect on the large-scale strain. Furthermore, the turbulent kinetic energy is conserved in the two-dimensional case, which has important consequences for the theory of two-dimensional turbulence. The analytical and numerical results presented here are in good qualitative agreement with experiment.

Type
Research Article
Copyright
© 1999 Cambridge University Press

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