Bounded Energy States in Homogeneous Turbulent Shear Flow—An Alternative View

[+] Author and Article Information
P. S. Bernard

Department of Mechanical Engineering, University of Maryland, College Park, MD 20742

C. G. Speziale

Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23665

J. Fluids Eng 114(1), 29-39 (Mar 01, 1992) (11 pages) doi:10.1115/1.2909995 History: Received May 06, 1991; Online May 23, 2008


The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if a residual vortex stretching term is maintained in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are presented for a k–ε model modified to account for net vortex stretching. The calculations indicate an initial exponential time growth of the turbulent kinetic energy and dissipation rate for elapsed times that are as large as those considered in any of the previously conducted physical or numerical experiments on homogeneous shear flow. However, vortex stretching eventually takes over and forces a production-equals-dissipation equilibrium with bounded energy states. The plausibility of this result is further supported by independent calculations of isotropic turbulence which show that when this vortex stretching effect is accounted for, a much more complete physical description of isotropic decay is obtained. It is thus argued that the inclusion of vortex stretching as an identifiable process may have greater significance in turbulence modeling than has previously been thought and that the generally accepted structural equilibrium for homogeneous shear flow, with unbounded energy growth, could be in need of re-examination.

Copyright © 1992 by The American Society of Mechanical Engineers
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