Spherical shock wave modulation induced by interaction with homogeneous isotropic turbulence

In this study, we have performed direct numerical simulations (DNSs) of the interaction between a spherical shock wave and homogeneous isotropic turbulence to investigate shock wave modulation. We considered two parameters, the central pressure of the initial high-energy region that generates the shock wave and the turbulent Mach number M-t. DNSs were performed under five conditions. A polar coordinate system (r,theta,phi) was then defined for the analyses, with the center of the high-energy region as the origin. The local position of the shock wave r(s) was defined as the position of the maximum value P-M of the radial pressure distribution P(r) at two declinations (theta,phi) in the polar coordinate system. Specifically, r(s) and P-M were functions of (theta,phi), and their statistics were computed using data over all (theta,phi) at each time. The standard deviation of the fluctuation of r(s) increased monotonically with the shock-wave front propagation in turbulence. This shows that the shock-wave front deformation grew monotonically. The mean pressure distribution conditioned by the fluctuations of r(s) and joint probability density function of fluctuation of r(s) and P-M show that there is a negative correlation between the deformation of the shock-wave front and the local intensity of the shock wave. This indicates that the deformed shock-wave front tends to return to its original shape. However, the monotonous growth of the deformation indicates the presence of a counter-effect that allows it to grow.