Snell’s law of refraction and sound rays for a moving medium

Abstract

Fermat’s principle of least time is used to calculate a new law of refraction for a stratified medium moving horizontally with different temperatures in each layer. This new law of refraction includes velocity of sound, wind speed, and the angle between the vectorial sum of sound velocity and the wind speed. This new equation is compared with the usual approximations for the different refraction laws of a moving medium occasionally mentioned in literature as ‘‘Snell’s law for a moving media.’’ The sound rays in a moving thermically stratified medium are refracted more or less (dependent on either upwind or downwind sound propagation), then calculated according to the ‘‘Snell’s law.’’ For upward-oriented sound rays and a moderate thermical stratification with high wind speeds, the difference in the angle of refraction between the new refraction law and the usual approximation is roughly 3 degrees and neglectable for grazing incidence. The sound ray trajectories expressed as analytical equations for a constant sound velocity combined with a wind speed profile proportional to height; the results are shown in a figure. Furthermore, the sound ray trajectories for a linear sound speed profile combined with a linear height-dependent wind speed profile are calculated and shown graphically.