AXIAL WAVE IN LONG-RANGE PROPAGATION IN A RANGE-INDEPENDENT OCEAN

Abstract

In many long-range propagation experiments the source and receiver are placed close to the depth of the waveguide (SOFAR) axis to minimize the interaction of the acoustic field with the ocean's surface and bottom. The time-of-arrival patterns of these experiments consist of resolvable, geometrical-like arrivals followed by an axial crescendo of unresolved energy. It is impossible to explain this late-arriving energy using the geometrical acoustics because of the presence of cusp caustics repeatedly along the waveguide axis. The interference of the wave fields corresponding to the rays located in the vicinity of the caustics near the waveguide axis produces a special "axial wave" that propagates along this axis. The purpose of the paper is to obtain the integral representation of the axial wave for an arbitrary deep-water waveguide in a range-independent medium in long-range acoustic propagation in the ocean when the source and receiver are located close to the depth of the sound-channel axis. The integral representation for the axial wave is derived with the use of solutions of the Helmholtz equation concentrated near the sound-channel axis and which decrease exponentially outside a strip containing the axis. These solutions have the form of the exponentials multiplied by parabolic cylinder functions whose arguments are sections of series in powers of ω-1/2, where ω is a cyclic frequency. Numerical results are obtained for the Munk canonical sound-speed profile.