Title: Influence of vibrational non-equilibrium on velocity gradient dynamics of compressible flows

In hypersonic flows, the phenomenon of turbulence tends to become more complex because of high levels of compressibility and elevated temperature levels. These complexities, in turn, lead to the emergence of many processes, such as vibrational energy excitation, dissociation and ionization of molecules. Such novel phenomena observed in vibrational non-equilibrium flows may affect various non-linear turbulent processes like scalar mixing, energy cascading, intermittency, and material element deformation. Tracking the evolution of velocity gradient dynamics is indeed a means to examine and understand the behaviour of these non-linear processes in a turbulent flow field. To clearly identify and understand the interaction of vibrational non-equilibrium with velocity gradient dynamics, in this work, we first derive the exact evolution equation of the velocity gradient and the pressure Hessian tensor for a flow field which is in a state of vibrational non-equilibrium. As expected, several “new” and unclosed mechanisms appear in the evolution equation of the pressure Hessian equation. To gain some more physical insights into these new mechanisms, as well as, to understand their relative importance in the dynamics of compressible velocity gradients, in the second part of this study, we employ direct numerical simulation database of compressible homogeneous turbulence. This study is expected to contribute towards the development of improved closure models for vibrationally excited compressible flows.





Key words: Compressible flows, Pressure-Hessian tensor, Velocity gradient tensor, Vibrational non-equilibrium