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. To describe in a simple model case the interference of near-axial waves which resulted in forming the so-called axial wave and propose formulas for the axial wave in more general cases, the two-dimensional reference point source problem for the parabolic index of refraction squared is investigated. The integral representation for the exact solution is transformed in such a way to extract ray summands corresponding to rays radiated from the source at angles less than a certain angle, the axial wave, and a term corresponding to a sum of all the rays having launch angles greater than the indicated angle. Numerical results for the axial wave are obtained for parameters corresponding to long-range ocean acoustic propagation experiments.
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