Towards the development of second-order closure models for nonequilibrium turbulent flows

A new approach for the development of second-order closure models suitable for nonequilibrium turbulent shear flows is presented. The central idea is based on the implementation of a relaxation time approximation to the nonequilibrium extension of an explicit algebraic stress model. Here, the algebraic stress model is systematically derived from the full Speziale et al. 1991 (SSG) second-order closure in the equilibrium limit of homogeneous turbulence. It is then extended to nonequilibrium turbulent flows by means of a Padé approximation, whereby approximate consistency with the rapid distortion theory (RDT) solution for homogeneous shear flow is established. The resulting model is tested in homogeneous shear flow turbulence under a wide range of shear rates. Substantially improved results are obtained in comparison to conventional second-order closure models that are based on the direct modeling of terms in the Reynolds stress transport equation.