On the behavior of two-equation models in nonequilibrium homogeneous turbulence

Abstract

The class of turbulence models that utilize two-equation differential transport equations is investigated. A dynamical systems analysis is performed on these transport equations to identify the various critical points and associated stability characteristics. The goal is to understand the transient solution behavior and to identify the possible solution fixed points. The analysis is restricted to homogeneous flows with constant and time-dependent mean shear. The transient behavior of the turbulence variables identifies possible pseudolaminar solutions that can be generated. These solutions are unphysical and need to be avoided. The present study provides the necessary framework for analyzing such two-equation turbulence models. Finally it is shown that models rigorously derived from Reynolds-stress transport models by utilizing the algebraic stress approximation, e.g., explicit algebraic stress models, still constitute a justifiable method also when the mean shear varies in time, provided that the time variation is sufficiently slow. Closed form algebraic time dependent solutions are derived for some commonly used models in homogeneous shear flows.