Sonic boom interaction with turbulence

A recently developed transonic small-disturbance model is used to analyze the interactions of random disturbances with a weak shock. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. It shows that diffraction effects, nonlinear steepening effects, focusing and caustic effects and random induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite-difference algorithm to solve the mixed-type elliptic hyperbolic flows around the shock wave is presented. Numerical calculations of shock wave interactions with various deterministic vorticity and temperature disturbances result in complicate shock wave structures and describe peaked as well as rounded pressure signatures behind the shock front, as were recorded in experiments of sonic booms running through atmospheric turbulence.