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

Fermat's principle of least time is used to derive an improved law of refra ction for a stratified medium moving horizontally with different temperatur es in each layer and includes velocity of sound, wind speed, and the angle (vertical directed) between the vectorial sum of sound velocity and the win d speed. The new equations are compared with the usual approximations for t he different laws of refraction of a moving medium occasionally mentioned i n literature as "Snell's law for a moving media". The propagation of sound rays is calculated with the improved law of refraction and compared with th e classical results. For upward-orientated sound rays and a moderate thermi cal stratification with high wind speeds the difference in the angle of ref raction between the improved refraction law and the "usual approximation" i s roughly 3 degrees and neglectable for grazing incidence. The sound ray trajectories are expressed as analytical equations for a cons tant sound velocity combined with a wind speed profile proportional to heig ht; the results are shown in a figure. Furthermore, the sound ray trajector ies for a linear sound speed profile combined with a linear height-dependen t wind speed profile are calculated and the results are shown graphically. An approximation of the sound ray trajectories in a moving medium is given for the three-dimensional case.