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92-13271REPORT DOCUMENTATION PAGE As a first step to understand the compressibility effects, interaction of isotropic quasi-incompressible turbulence with a weak shock wave was studied by threedimensional time-dependent direct numerical simulations. In addition, linear analysis was used to study interaction of isotropic turbulence with shock waves of a wide range of strengths. The effects of the fluctuation Mach number Aft and the average Mach number A'f of the upstream turbulence on turbulence statistics were investigated.Both numerical simulations and linear analyses of the interaction show that turbulence is enhanced during the interaction with a shock wave.
ABSTRACTAs a first step to understand the compressibility effects, interaction of isotropic quasi-incompressible turbulence with a weak shock wave was studied by threedimensional time-dependent direct numerical simulations. In addition, linear analysis was used to study interaction of isotropic turbulence with shock waves of a wide range of strengths. The effects of the fluctuation Mach number M and the average Mach number M17 of the upstream turbulence on turbulence statistics were investigated.Both numerical simulations and linear analyses of the interaction show that turbulence is enhanced during the interaction with a shock wave. Turbulent kinetic energy (TKE) and transverse vorticity components are amplified, and turbulent length scales are decreased. The predictions of the linear analyses compare favorably with simulation results for flows with M < M~r -1, which suggests that the amplification mechanism is mainly linear.Rapid evolution of TKE just downstream of the shock was not, however, reproduced by the linear analysi-Investigation of the budget of the TKE transport equation shows that this beiiavior of TKE is manifested in the pressure transport term (pf" ' 1 ) ,i , which is nonlinear. The budgets of enstrophy components W' 2 show that their amplifications through the shock are mainly caused by the distortion due to the mean flow compression, and that effect of baroclinic torque is not significant. Shock waves were found to be distorted by the upstream turbulence, but still have a well-defined shock front for Mt < M17 -1. In this regime, the statistics of the displacement and inclination of the shock front compare favorably with the linear analysis predictions. For flows with M1 > M(T -1, shock waves no longer have well-defined fronts. shock wave thickness and strength vary widely in the transverse directions. Multiple peaks in pressure are found along the mean streamline where the local thickness of the shock wave has increased significantly.
iv AcknowledgementsThe authors would like to acknowledge the financial support from the Air Force