Direct Numerical Simulations of Interactions between Spherical Shock Wave and Homogeneous Isotropic Turbulence

Shock waves in the real world often propagate in free space with radial curvature. This study aims to clarify the characteristic changes of such shock waves caused by the interaction with turbulence. For this purpose, direct numerical simulations of the interaction between a spherical shock wave and homogeneous isotropic turbulence are carried out. The first analysis is about the deformation of the shock wave. The local positions of the shock wave were defined as the position of the maximum pressure, and its variation was taken as the deformation. The results show that the deformation monotonically increases, which differs from the case of the planar shock wave. Next, the ratio of the local pressure increase to the average pressure increase was defined to investigate the variation of the pressure increase. The ratio increases with propagation as well as the deformation. Thus, it was found that the pressure increase varies with the interaction and that the intensity of the variation grows as well as the deformation. Finally, to investigate the relationship between the deformation and the pressure increase, we computed the pressure distribution conditioned on whether the local shock wave position is in front of or behind the mean position. The results showed that when the shock wave was behind the mean position, the overpressure was higher, and vice versa. This behavior is similarly observed in the planar shock wave.