When the source and receiver are located close to the depth of the waveguide axis, there exist cusped caustics repeatedly along the axis. A description of the propagation of energy along the waveguide axis in terms of geometrical acoustics is not valid in neighborhoods of cusped caustics, because in these neighborhoods the waves associated with individual ray paths interfere with one another. Neighborhoods of interference grow with range, and at long distances they overlap. This results in the formation of a diffractive (as opposed to ray, i.e., geometrical acoustics) component of the field — the axial wave — that propagates along the sound-channel axis. In this paper, the integral representation of the axial wave obtained before for an arbitrary deep-water waveguide in a three-dimensional range-independent medium is generalized to a range-dependent ocean. The integral representation of the axial wave is derived with the use of solutions of the homogeneous Helmholtz equation concentrated near the sound-channel axis and which decrease exponentially outside a narrow strip containing the axis. The observed time-of-arrival patterns from a number of long-range ocean acoustic propagation experiments show early geometrical-like arrivals followed by a crescendo of energy that propagates along the sound-channel axis and is not resolved into individual arrivals. The practical application of the developed analytic expression for the sound field near the axis of an ocean type waveguide is the discrimination of noninterfering (resolved) and interfering (nonresolved) arrivals. In this paper, the axial wave is simulated for a deterministic model of a range-dependent medium, where the range-dependence results for such things as change in geographic location. The model is based on the information about sound-speed profiles as a function of range between the source and receiving array for the AET experiment. The sound source frequency is taken equal to 75Hz. The propagation range is 3250 km.
