Uniform Ray Theory of Surface, Internal and Acoustic Wave Propagation in a Rotating Ocean or Atmosphere

First a short wavelength asymptotic expansion, employing rays, is presented for waves propagating in a rotating compressible fluid layer of nonuniform depth. This theory applies to surface, internal and acoustic waves in an ocean or atmosphere. It yields infinite amplitudes at caustics and shorelines. Therefore two different asymptotic expansions, uniform in a region containing a caustic and a shoreline respectively, are constructed. They yield the correct finite amplitude at the caustic and at the shoreline. In addition, expansions uniform in a region containing a caustic and a shoreline, or two or more caustics and shorelines, are constructed. Both general time-dependent waves and time-harmonic waves are considered. Linear theory is employed.