Influence of thermal non-equilibrium on the dynamics of velocity gradient in turbulent flows

Dynamics of velocity gradient is a useful tool for understanding several non-linear turbulent processes of interest and has been widely employed to investigate various fundamental aspects of incompressible turbulent flows. However, such research on compressible turbulence and that, especially, under thermal non-equilibrium (TNE) conditions is minimal. Flow fields associated with TNE are characterized by complexities including but not limited to (i) a significant level of divergence in the velocity field, (ii) thermodynamic nature of pressure evolution (iii) vibrational excitation and subsequent dissociation of the constituent air molecules. These challenges are often encountered in hypersonic flows that exist past objects/vehicles re-entering the earth's (or other planetary) atmosphere. The primary focus of the present work is to first develop the exact theoretical formulation of the evolution equations of the velocity gradient and the pressure-hessian tensor. Subsequently, we identify the dominant unclosed processes in this formulation. Finally, we make attempts to model these dominant processes to capture the essential influence of TNE on compressible velocity gradient dynamics.