Propagation of finite amplitude sound through turbulence: modeling with geometrical acoustics and the parabolic approximation.

Sonic boom propagation can be affected by atmospheric turbulence. It has been shown that turbulence affects the perceived loudness of sonic booms, mainly by changing its peak pressure and rise time. The models reported here describe the nonlinear propagation of sound through turbulence. Turbulence is modeled as a set of individual realizations of a random temperature or velocity field. In the first model, linear geometrical acoustics is used to trace rays through each realization of the turbulent field. A nonlinear transport equation is then derived along each eigenray connecting the source and receiver. The transport equation is solved by a Pestorius algorithm. In the second model, the KZK equation is modified to account for the effect of a random temperature field and it is then solved numerically. Results from numerical experiments that simulate the propagation of spark-produced N waves through turbulence are presented. It is observed that turbulence decreases, on average, the peak pressure of the N waves and increases the rise time. Nonlinear distortion is less when turbulence is present than without it. The effects of random vector fields are stronger than those of random temperature fields. The location of the caustics and the deformation of the wave front are also presented. These observations confirm the results from the model experiment in which spark-produced N waves are used to simulate sonic boom propagation through a turbulent atmosphere.