Rapid distortion analysis of homogeneous turbulence subjected to rotating shear

Abstract

We perform inviscid rapid distortion calculations of initially isotropic turbulence subject to unsteady shear. The mean strain-rate tensor is of constant magnitude but the eigendirections rotate at a uniform rate or frequency. When the forcing frequency is zero, constant-shear forcing is recovered. The results indicate that there are three distinct regimes of physical behavior for this kind of forcing: (1) at low frequencies, turbulence quickly becomes one-componential and fluctuation field attains statistical steady state; (2) at intermediate frequencies, kinetic energy exhibits sporadic growth spurts interspersed with the periods of no activity; and (3) at relatively high frequencies, kinetic energy evolution exhibits a purely periodic behavior. It is rather intriguing that turbulence decays at low frequencies but grows at intermediate frequencies of forcing. We investigate the physics underlying the observed behavior and examine the roles of production and pressure-strain correlation. Finally, a simple dynamical model that captures the observed regimes of behavior is proposed. In this model the different turbulence responses are reproduced by merely introducing different phase lags between applied strain and Reynolds stress.