Theory and analysis of acoustic-gravity waves in a free-surface compressible and stratified ocean. (December 2021) - Auclair, F.; Debreu, L.; Duval, E.; Hilt, M.; Marchesiello, P.; Blayo, E.; Dumas, F.; Morel, Y.
Abstract: Waves propagate in a free-surface ocean due to compressibility and gravity (and surface tension at much smaller scale). Analytical solutions have long been derived independently for acoustic and gravity waves, i.e., acoustic waves or internal-gravity waves in an unbounded ocean, surface-gravity waves in a free-surface-ocean, and acoustic or internal modes in a bounded ocean. In the present study, surface tension and earth-rotation are neglected and a simple, unified model based on inner and boundary dispersion relations is derived for waves propagating in a compressible, stratified, free-surface ocean. Branches of acoustic gravity wave solutions are identified and visually analysed in phase-space. Taylor developments are then carried out with respect to small parameters describing stratification and compressibility and are compared with numerical approximations of the intersection of inner and boundary dispersion surfaces. Finally, the model recovers the known approximations for swell, long-surface waves, internal-gravity waves, internal modes, acoustic waves or acoustic modes, and also provides information on the modifications of these solutions due to stratification and compressibility and on the coupling of acoustic and gravity waves. Two peculiar regions of the acoustic-gravity wave phase-space are more specifically highlighted and studied in detail: one for long waves shedding new light on the distinction between surface waves and low-order internal modes, the other for marginally stable surface waves of intermediate length-scale.