A one-way coupled mode solution, Huygens’ principle and mode coupling coefficients

Abstract

The normal mode formulation for waveguide propagation has physical appeal since sound propagates in discrete entities—namely modes—and an understanding of the progression of modes sheds light on arrival times of pulses and features of ocean ducting. In the development of the range-dependent version several researchers employ the conservation of normal pressure and normal particle velocity along the z axis in the mean as the conserved quantity that allows for an algorithm to couple the modes as sound progresses in range. The usual derivations are based on R. Evan’s seminal work on the two-way coupled mode formulation. Here it is shown that Huygens’ principle and an approximate form of the Green’s function in the waveguide leads to a suitable algorithm as long as reflected or backward going flux is small relative to forward flux. The derivation, moreover, leads to expressions for mode coupling amplitudes that allow one to follow the distribution of flux along specific modal tracts. [Work supported by the Office of Naval Research and Naval Research Laboratory.]