ON THE CONSISTENCY OF REYNOLDS STRESS TURBULENCE CLOSURES WITH HYDRODYNAMIC STABILITY THEORY

The consistency of second-order closure models with results from hydro dynamic stability theory is analyzed for the simplified case of homoge neous turbulence. In a recent study, Speziale, Gatski, and Mac Giolla Mhuiris [Phys. Fluids A 2, 1678 (1990)] showed that second-order closu res are capable of yielding results that are consistent with linear st ability theory for the case of homogeneous shear flow in a rotating fr ame. It is demonstrated in this paper that this success is due to the fact that the stability boundaries for rotating homogeneous shear flow are not dependent on the details of the spatial structure of the dist urbances. For those instances where they are-such as in the case of el liptical flows where the instability mechanism is more subtle-the resu lts are not so favorable. The origins and extent of this modeling prob lem are examined in detail along with a possible resolution based on R apid Distortion Theory (RDT) and its implications for turbulence model ing. (C) 1996 American Institute of Physics.