Propagation of sonic booms and other weak nonlinear waves through turbulence

The structure of weak shocks propagating over long distances through turbulence modeled by sound speed fluctuations is investigated. The equilibrium wave shape is governed by a balance between non‐linear steepening and a dissipative mechanism due to acoustic scattering of high‐frequency energy out of the incident wave direction. This scattered energy appears as perturbations arriving behind the shock. For conditions representative of sonic boom and explosion wave propagation over long distances the mean wave structure is governed by a Burgers' equation similar to that describing viscous shocks, the difference being that parameters describing the turbulent scattering appear in the dissipative term. The theoretical predictions agree in order of magnitude with experiments on atmospheric propagation of sonic boom and explosion waves.