Interfering modes and an axial wave in an underwater sound channel

Experiments on long-range propagation of low-frequency sound that were conducted starting from the mid-1980s indicate a complex character of propagation in an underwater sound channel, in which a source and a receiver are located close to the channel axis. A burst of energy propagating along the axis follows early arrivals, which are well described by the formulas of geometrical acoustics, in plots of acoustic intensity as a function of propagation time and hydrophone depth. This energy burst cannot be described using geometrical acoustics because of caustics with caustic beaks located near the channel axis. Very complex interference processes occur near these caustics. As the distance from the source grows, the dimensions of the interference vicinity increase and start to overlap producing a peculiar "axial wave." For an arbitrary two-dimensional underwater sound channel, the axial wave can be represented as a sum of the first normal modes and a residue. This conclusion is based on the use of two representations for an acoustic field. The first of them includes the sum of ray components and an axial wave. The second representation consists of ray addends, the sum of the first normal modes, and a residue. Numerical results are obtained for a canonical profile of sound velocity at the frequency of 200 Hz for the distances of 1600-1650 km.