Acoustic mode propagation in a range-dependent ocean

Analytical approximate solutions to the Helmholtz’s equation are obtained for acoustic mode propagation in a slowly varying ocean waveguide. Specific calculations are displayed for the particular case of propagation through mesoscale eddies in the western North Atlantic. An asymptotic expansion of the solution to the coupled equations governing the range variations of the modal amplitudes gives explicit expressions for the correction terms to the adiabatic approximation, which is discussed in detail. The validity of the adiabatic and asymptotic approximations is found to depend strongly on acoustic frequency, mode number, and propagation range. It is also found to depend on the particular acoustic quantity considered, such as magnitude, phase, and travel time.