Compressibility effects on Reynolds stress amplification and shock structure in shock-isotropic turbulence interactions

Recent direct numerical simulation studies of canonical shock-isotropic turbulence interactions (SITIs) in the highly compressible regime exhibit streamwise Reynolds stress amplification that is significantly higher in some cases than in previous studies; an explanation is offered based on a relatively high Mach number combined with significant dilatational energy in the incident flow. Some cases exhibit a loss of amplification that is associated with a highly perturbed shock structure as the flow parameters approach the threshold between the wrinkled and broken shock regimes. The shock structure perturbations due to the highly compressible incident turbulence match those proposed by Donzis (Phys. Fluids, vol. 24, 2012, 126101) relatively well, but due to the presence of thermodynamic fluctuations in addition to velocity fluctuations in the incident flow, we propose a generalized parametrization based on the root-mean-square Mach number fluctuation in place of the turbulence Mach number. This is found to improve the collapse of the shock structure data, suggesting that the wrinkled-broken shock regime threshold determined previously for vortical turbulence (Donzis, Phys. Fluids, vol. 24, 2012, 126101; Larsson et al., J. Fluid Mech., vol. 717, 2013, pp. 293-321) can be applied to more general isotropic inflow fields using the proposed parametrization.

Automated summary

Recent direct numerical simulation studies have shown that in highly compressible regime, the amplification of streamwise Reynolds stress in canonical shock-isotropic turbulence interactions (SITIs) is higher than in previous studies. This can be explained by the relatively high Mach number and significant dilatational energy in the incident flow. Loss of amplification is observed as the flow parameters approach the threshold between wrinkled and broken shock regimes due to highly perturbed shock structure. The proposed parametrization based on root-mean-square Mach number fluctuation improves the collapse of shock structure data, suggesting its applicability to general isotropic inflow fields.