Pressure-Strain Correlation Modeling: Towards Achieving Consistency with Rapid Distortion Theory

In turbulence closure modeling, it is widely accepted that the rapid pressure-strain correlation (RPSC) model be consistent with the rapid distortion theory (RDT). It is desirable to achieve this consistency with a closure model that is computationally tractable and satisfies the requisite mathematical constraints of realizability and linearity in the appropriate variables. In this investigation, starting from a detailed modal analysis of two-dimensional mean flows, we identify important flow features to be incorporated into the model. However, the dynamical system analysis shows that the suggested physics cannot be embodied in a model with all desired computational and mathematical attributes. To resolve this conflict, we propose a slight compromise in the physical requirement and ease one of the linearity constraints leading to a best possible tractable model. Overall, the present work provides important insight into RPSC closure modeling challenges-arising from the interplay among physical fidelity, computational viability and mathematical constraints-and proposes avenues for future improvement.