Symmetry and snell's law

A connection between the acoustic rays in a moving fluid medium (with a sound Speed and subsonic flow each depending arbitrarily on position and time) and the null geodesics of a pseudo-Riemannian manifold allows one to derive several well-known results used in underwater and atmospheric acoustic ray theory from one single underlying symmetry principle. isometry. These results being well known in cases with Cartesian symmetry generalize to any system of curvilinear coordinates and three-dimensional fluid flows. Snell's law, range, and travel time integrals for Cartesian and cylindrically symmetry systems are derived and an illustrative example presented. (c) 2005 Acoustical Society of America.