Acoustic mode coupling induced by shallow water nonlinear internal waves: sensitivity to environmental conditions and space-time scales of internal waves.

While many results have been intuited from numerical simulation studies, the precise connections between shallow-water acoustic variability and the space-time scales of nonlinear internal waves (NLIWs) as well as the background environmental conditions have not been clearly established analytically. Two-dimensional coupled mode propagation through NLIWs is examined using a perturbation series solution in which each order n is associated with nth-order multiple scattering. Importantly, the perturbation solution gives resonance conditions that pick out specific NLIW scales that cause coupling, and seabed attenuation is demonstrated to broaden these resonances, fundamentally changing the coupling behavior at low frequency. Sound-speed inhomogeneities caused by internal solitary waves (ISWs) are primarily considered and the dependence of mode coupling on ISW amplitude, range width, depth structure, location relative to the source, and packet characteristics are delineated as a function of acoustic frequency. In addition, it is seen that significant energy transfer to modes with initially low or zero energy involves at least a second order scattering process. Under moderate scattering conditions, comparisons of first order, single scattering theoretical predictions to direct numerical simulation demonstrate the accuracy of the approach for acoustic frequencies upto 400 Hz and for single as well as multiple ISW wave packets.