Direct Numerical Simulation of the Interaction between a Shock Wave and Various Types of Isotropic Turbulence

Direct Numerical Simulation (DNS) is used to study the interaction between normal shock waves of moderate strength (M1= 1.2 and M1 = 1.5) and isotropic turbulence. A complete description of the turbulence behaviour across the shock is provided and the influence of the nature of the incoming turbulence on the interaction is investigated. The presence of upstream entropy fluctuations satisfying the Strong Reynolds Analogy enhances the amplification of the turbulent kinetic energy and transverse vorticity variances across the shock compared to the solenoidal (pure vorticity) case. Budgets for the fluctuating-vorticity variances are computed, showing that the baroclinic torque is responsible for this additional production of transverse vorticity. More reduction of the transverse Taylor microscale and integral scale is also observed in the vorticity-entropy case while no influence can beseen on the longitudinal Taylor microscale. When the upstream turbulence is dominated by acoustic and vortical fluctuations, less amplification of the kinetic energy (for Mach numbers between 1.25 and 1.8), less reduction of the transverse microscale and more amplification of the transverse vorticity variance are observed through the shock compared to the solenoidal case. In all cases, the classic estimation of Batchelor relating the dissipation rate and the integral scale of the flow proves to be invalid. These results are obtained with the same numerical tool and similar flow parameters, and they are in good agreement with Linear Interaction Analysis (LIA).