Propagation of images in an inhomogeneous fluid.

Abstract

A new class of exact scalar Green's functions is presented. These functions solve fluid dynamics problems analogous to lens design problems in optics. In particular, given a point signal at a specified location, the Green's functions discussed here describe waves that propagate asymptotically to specified image points. The geometry of the target determines the structure of the background medium, which may be interpreted to be an acoustic or optical fluid, or a curved space-time. There is no restriction to spherical or axial symmetry. Included in the class are the known propagators for massless fields in Rindler space and in a space of constant negative curvature. In the latter case, the Green's function derived here is the analog of the Green's function that describes free-particle nonrelativistic quantum mechanics in a space of constant negative curvature. In general, the waveforms of this class are multiple bubbles that separate from a spherical initial pulse and converge monotonically on point singularities or zero-equipotential surfaces of a pair of underlying electrostatic potentials.