Research of the rapid pressure-strain correlation model in the rapid distortion limit

Even though a number of rapid pressure-strain models have been suggested and successfully tested for different flow situations by various authors, the model proposals still exhibit some apparent deficiencies when subjected to the flows with rapid distortion. From Mansour's relatively straightforward rapid distortion analysis, if an initially anisotropic flow undergoes a purely rapid rotation, the anisotropy measures will exhibit the behavior of the damped oscillations. Within the current framework of modeling the rapid pressure-strain correlation, i.e., the models based on the assumption that the M-tensor for the rapid pressure-strain term is expandable in the Reynolds-stress anisotropy tensor alone, all the model predictions fail to give the damped oscillations in the turbulence anisotropy. In the case of initially isotropic turbulence subjected to rapid distortion, Sjogren and Johansson showed that all the existing rapid pressure-strain models would deliver the identical path in the anisotropy-invariant map for both homogeneous plane strain and shear flows. The rapid distortion analysis shows two distinct curves reflecting different flow physics. In this work, we try to present a possible way to create a system that can overcome these deficiencies with the aid of the rapid distortion theory (RDT).