Amplification and attenuation of shock wave strength caused by homogeneous isotropic turbulence

We study the pressure increase across a planar shock wave with shock Mach numbers M_s of 1.1, 1.3, and 1.5 propagating through homogeneous isotropic turbulence at a low turbulent Mach number (M_t ∼ 10^-4) based on direct numerical simulations (DNSs). Fluctuation in the pressure increase, Δp′, on a given shock ray is induced by turbulence around the ray. A local amplification of the shock wave strength, measured with the pressure increase, is caused by the velocity fluctuation opposed to the shock wave propagating direction with a time delay, while the velocity in the opposite direction attenuates the shock wave strength. The turbulence effects on the shock wave are explained based on shock wave deformation due to turbulent shearing motions. The spatial distribution of Δp′ on the shock wave has a characteristic length of the order of the integral scale of turbulence. The influence of turbulent velocity fluctuation at a given location on Δp′ becomes most significant after the shock wave propagates from the location for a distance close to the integral length scale for all shock Mach numbers, demonstrating that the shock wave properties possess strong memory even during the propagation in turbulence. A lower shock Mach number M_s results in a smaller rms value of Δp′, stronger influences on Δp′ by turbulence far away from the shock ray, and a larger length scale in the spatial profile of Δp′ on the shock wave. Relative intensity of Δp′ increases with [Mt/(Ms-1)]α, where DNS and experimental results yield α ≈ 0.73.