THE EQUILIBRIUM STATES AND THE STABILITY ANALYSIS OF REYNOLDS STRESS EQUATIONS FOR HOMOGENEOUS TURBULENT SHEAR FLOWS

Abstract

An analysis is performed to examine the equilibrium states and the stability of modeled Reynolds stress equations for homogeneous turbulent shear flows. The system of the governing equations consists of four coupled ordinary differential equations for b(11), b(22), b(12), and epsilon/Sk. Depending on the model constants adopted, the solution of this system may converge, diverge, oscillate, or the equilibrium solution may not exist. It is shown that the rapid part of the pressure-strain correlation is most responsible for such different behaviors. Constraints for the model constants in various Reynolds stress models are obtained by stability conditions for the equilibrium states as well as by their physically realizable bounds. It is observed that most models for the pressure-strain correlation that are linear in the anisotropy tensor are stable and produce reasonable: equilibrium solutions. Whereas quadratic or cubic models often oscillate and converge onto unrealistic states, especially under high shear conditions. (C) 1995 American Institute of Physics.