Augmented adiabatic mode theory for upslope propagation from a point source in variable‐depth shallow water overlying a fluid bottom

Abstract

A uniform asymptotic solution is presented for sound propagation from a constant frequency point source in shallow water whose depth H(r) decreases monotonically with cylindrical distance r. The water has constant sound speed c1 and density ρ1; the bottom fluid extends indefinitely in depth and has sound speed c2 and density ρ2, where c2>c1. The interface depth has constant value H0 up to range r0 and thereafter decreases linearly to zero. The solution appears as a sum of modal terms, each such mode eventually encountering a critical depth Hc(n) (at which modal phase velocity equals c2) at a critical range rc(n). A previously derived local solution for a modal term near its critical range is modified such that it automatically reduces to the adiabatic mode solution at nearer ranges and such that it is valid at arbitrary distances beyond the critical range. Bulk attenuation is incorporated into the model using an appropriate modal average over depth. Numerical results are compared with four parabolic equat...