DIRECT NUMERICAL-SIMULATION OF ISOTROPIC TURBULENCE INTERACTING WITH A WEAK SHOCK-WAVE

Interaction of isotropic quasi-incompressible turbulence with a weak s hock wave was studied by direct numerical simulations. The effects of the fluctuation Mach number M(t) of the upstream turbulence and the sh ock strength M1(2)-1 on the turbulence statistics were investigated. T he ranges investigated were 0.0567 less-than-or-equal-to M(t) less-tha n-or-equal-to 0.110 and 1.05 less-than-or-equal-to M1 less-than-or-equ al-to 1.20. A linear analysis of the interaction of isotropic turbulen ce with a normal shock wave was adopted for comparisons with the simul ations. Both numerical simulations and the linear analysis of the inte raction show that turbulence is enhanced during the interaction with a shock wave. Turbulent kinetic energy and transverse vorticity compone nts are amplified, and turbulent lengthscales are decreased. The predi ctions of the linear analysis compare favourably with simulation resul ts for flows with M(t)2 < a(M1(2)-1) with a almost-equal-to 0.1, which suggests that the amplification mechanism is primarily linear. Simula tions also showed a rapid evolution of turbulent kinetic energy just d ownstream of the shock, a behaviour not reproduced by the linear analy sis. Investigation of the budget of the turbulent kinetic energy trans port equation shows that this behaviour can be attributed to the press ure transport term. Shock waves were found to be distorted by the upst ream turbulence, but still had a well-defined shock front for M(t)2 < a(M1(2)-1) with a almost-equal-to 0.1). In this regime, the statistics of shock front distortions compare favourably with the linear analysi s predictions. For flows with M(t)2 > a(M1(2)-1) with a almost-equal-t o 0.1, shock waves no longer had well-defined fronts: shock wave thick ness and strength varied widely along the transverse directions. Multi ple compression peaks were found along the mean streamlines at locatio ns where the local shock thickness had increased significantly.