Losing the shock wave front profile due to interaction with turbulence

In this study, losing the shock wave profiles under interactions with grid turbulence was investigated experimentally and theoretically. We demonstrated that the shock wave contrast on side-view schlieren images gradually decreased to an undetectable level in the experiment. This shock wave 'vanishment' occurred at a low shock Mach number with a high turbulent Mach number. With a relatively strong shock wave, the contrast of the shock wave remained detectable although the shock wave profile region was expanded. To understand the shock wave vanishment phenomenon during interaction with turbulence, we established a shock wave vanishment model based on the solution of a one-dimensional interaction between a shock wave and forward induced flow. The criterion of the occurrence of local vanishment of the shock wave was derived as M-t >= (M-s(2) - 1)/M-s, where M-t is the turbulent Mach number and M-s is the shock Mach number. The proposed shock vanishment model involves the effect of the interaction length and the shock wave recovery characteristics. The derived model explains the vanishment of weak shock wave profile during turbulence with an interaction length of ten times the order of the integral scale of the turbulence, as observed in the experiment.