Bounded energy states in homogeneous turbulent shear flow: An alternative view
Abstract
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 vortex stretching is accounted for 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 present for a kepsilon model modified to account for 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 productionequalsdissipation equilibrium with bounded energy states. The validity of this result is further supported by an independent theoretical argument. It is concluded that the generally accepted structural equilibrium for homogeneous shear flow with unbounded component energies is in need of reexamination.
 Publication:

Final Report Institute for Computer Applications in Science and Engineering
 Pub Date:
 October 1990
 Bibcode:
 1990icas.rept.....B
 Keywords:

 Equilibrium;
 Homogeneous Turbulence;
 KEpsilon Turbulence Model;
 Kinetic Energy;
 Shear Flow;
 Turbulent Flow;
 Anisotropy;
 Energy Dissipation;
 Mathematical Models;
 Stretching;
 Tensors;
 Vortices;
 Fluid Mechanics and Heat Transfer