Spherical nonlinear wave propagation in a dissipative stratified atmosphere

Abstract

Nonlinear acoustic wave propagation is considered, for a signal which is initially sinusoidal at the input radius, subject to the effects of spherical spreading, exponential density stratification with altitude, and thermoviscous dissipation. A model equation is derived giving the signal variation along each straight line ray from centre of symmetry, and in the form of a Generalized Burgers Equation. This equation is studied in the small-dissipation limit. It is shown that along rays above the horizontal, shocks quickly form, but then rapidly thicken, the wave eventually dying in linear old age, with amplitude saturation. On rays below the horizontal shocks may or may not form, depending on the relation of the ray to an “initial shock curve” which is determined analytically. When shocks do form, they become increasingly thin with increasing distance, while outside them nonlinear effects become small and the main part of the wave evolves under linear non-dissipative mechanisms alone, displaying no trace of amplitude saturation.