Modification of the nonlinear wave progressive equation model for sonic booms in a stratified atmosphere

The nonlinear progressive wave equation (NPE) model [McDonald and Kuperman, J. Acoust. Soc. Am. 81, 1406 (1987)] is modified to simulate sonic boom physics in a stratified atmosphere using a wave—following window whose dimensions are much less than atmospheric scale heights. (The NPE was originally formulated for time domain weak shock propagation in the ocean, where the ambient density is nearly constant.) This allows simulation of sonic boom propagation in a refracted ray tube in which the ambient density may vary considerably as the simulation window moves along. Energy conservation places a strong constraint on the form of the resulting nonlinear wave equation. Properties of the modified NPE and some illustrative solutions are presented. [Work supported by the Office of Naval Research.]