On the Gaussian beam tracing method for long-distance sound wave propagation in non-uniform mean flows

This paper presents an improved Gaussian beam tracing method to efficiently compute long-distance sound wave propagation in non-uniform mean flows. New dynamic ray tracing equations are derived from the convected wave equation in the vicinity of the ray path under the high-frequency asymptotic and paraxial conditions, based on which the solutions of acoustic potential and the corresponding Gaussian beams are developed. The sound pressure at the observer is accurately computed by an integral superposition of all vicinal beams, through a revised weighting function that considers the convection effect on each beam. The proposed method is valid at caustics and can capture the wave diffractions at different sound frequencies. Benchmark problems of the acoustic monopole radiation and the broadband pulse propagation in a free space uniform flow, sound wave interactions with a semi-infinite rigid plate in a moving medium, sound propagations in inhomogeneous stratified flows and in a large-scale vortex flow are studied to validate the proposed method. The results are compared with analytical solutions and high-fidelity numerical results using the finite element method or the fast field program. Good agreements are obtained, showing its potential for the effective assessment of the long-distance sound propagation in complex inhomogeneous flows.