Whispering-gallery-mode trapping of sound in shallow water between an up-slope region and internal wave solitons

Abstract

Double-trapping of sound occurs in shallow water when the ocean has a sloping bottom and when a packet of high amplitude internal wave solitons is propagating either up-slope or down-slope. The phase velocity of an adiabatic mode increases in the up-slope direction and also as one approaches the front of the soliton packet, so the mode’s horizontal rays can be trapped for propagation that is nominally cross-slope. Because the variation of the horizontal phase velocity is considerably slower in the up-slope direction than it is in the vicinity of the soliton front, an analogy exists with the whispering-gallery effect (found near concave surfaces in architectural spaces). The equivalent radius of curvature of the ‘‘reflecting surface’’ is found in accord with the earth-flattening approximation to equal the phase velocity divided by its derivative with respect to the up-slope distance. Quantitative substantiation is given for models of sound and solitons in a realistic ocean (two constant sound speed layers separated by a thermocline). Double-trapped propagation has some attenuation because of energy leakage out through the width of the soliton packet.