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 Mt. DNSs were performed under five conditions. A polar coordinate system (r,θ,ϕ) was then defined for the analyses, with the center of the high-energy region as the origin. The local position of the shock wave rs was defined as the position of the maximum value PM of the radial pressure distribution P(r) at two declinations (θ,ϕ) in the polar coordinate system. Specifically, rs and PM were functions of (θ,ϕ), and their statistics were computed using data over all (θ,ϕ) at each time. The standard deviation of the fluctuation of rs 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 rs and joint probability density function of fluctuation of rs and PM 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.