A Review of Reynolds Stress Models for Turbulent Shear Flows

A detailed review of recent developments in Reynolds stress modeling for incompressible turbulent shear ows is provided. The mathematical foundations of both two-equation models and full second-order closures are explored in depth. It is shown how these models can be systematically derived for two-dimensional mean turbulent ows that are close to equilibrium. A variety of examples are provided to demonstrate how well properly calibrated versions of these models perform for such ows. However, substantial problems remain for the description of more complex turbulent ows where there are large departures from equilibrium. Recent e orts to extend Reynolds stress models to non-equilibrium turbulent ows are discussed brie y along with the major modeling issues relevant to practical Naval Hydrodynamics applications. Research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-0001. Funding was also provided by the O ce of Naval Research under Grant N00014-94-1-0088 (ARI on NonequilibriumTurbulence, Dr. L. P. Purtell, Program O cer).