Propagation of weak shock waves through turbulence

Abstract

The effect of turbulence on the structure of weak shock waves is investigated. The equilibrium structure is shown to be governed by a balance between nonlinear steepening and the turbulent scattering of acoustic energy out of the main wave direction. The scattered energy appears as perturbations behind the shock front. For conditions typical of sonic booms in atmospheric turbulence the wave structure is governed by a Burgers equation similar to that describing viscous shocks, except that parameters related to the turbulence appear instead of the viscosity coefficient. The magnitude of the perturbations following a shock is estimated from first-order scattering applied to a thickened shock. Predictions of shock thicknesses and perturbations compare favourably with available experimental data. The approach used in the analysis of shock structure is to account for energy scattered from a single wave propagating a long distance through turbulence. This avoids difficulties of physical interpretation which arise if an ensembleaveraged structure is calculated, which is the usual approach in turbulent scattering analysis.