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Theory and analysis of acoustic-gravity waves in a free-surface compressible and stratified ocean

Francis Auclair 1, * Laurent Debreu 2 Emilie Duval 2 Margot Hilt 1 Patrick Marchesiello 3 Eric Blayo 2 Franck Dumas 4 Yves Morel 3
* Corresponding author
2 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Inria Grenoble - Rhône-Alpes, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
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 rays 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, capillarity waves 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. Wave solutions are identified and visually analyzed 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 rays, internal modes, acoustic waves or acoustic modes, and also provides modification of these solutions due to stratification and compressibility.
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Submitted on : Thursday, March 18, 2021 - 4:53:31 PM
Last modification on : Monday, May 16, 2022 - 8:20:19 AM

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Francis Auclair, Laurent Debreu, Emilie Duval, Margot Hilt, Patrick Marchesiello, et al.. Theory and analysis of acoustic-gravity waves in a free-surface compressible and stratified ocean. Ocean Modelling, Elsevier, 2021, 168, pp.1-20. ⟨10.1016/j.ocemod.2021.101900⟩. ⟨hal-02958158v2⟩

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