Objective Model for the Fluctuating Pressure-Strain-Rate Correlations

Abstract

Representation theorems for isotropic functions are used to construct a closure model for the fluctuating pressure-strain-rate correlation tensor. In contrast to alternative proposals in the literature, the present model does not include a dependence on the vorticity in inertial frames or on the intrinsic spin tensor in noninertial frames because it is shown that this dependence violates objectivity which has been previously suggested to be an essential property of a turbulence closure. The proposed model is calibrated using data from homogeneous shear flows in inertial frames and is tested against data from a variety of turbulent shear flow, in both fixed and rotating frames, with generally very encouraging results. In particular, the results conclusively demonstrate that the absence of dependence on vorticity and intrinsic spin in the model for the pressure-strain-rate correlations does not adversely impact its ability to accurately predict the effects of system rotation on the turbulence.