Two-way coupled long-wave isentropic ocean-atmosphere dynamics

The events following the 15 January 2022 explosions of the Hunga Tonga-Hunga Ha'apai volcano highlighted the need for a better understanding of ocean-atmosphere interactions when large amounts of energy are locally injected into one (or both). Starting from the compressible Euler equations, a two-way coupled (TWC) system is derived governing the long-wave behaviour of the ocean and atmosphere under isentropic constraint. Bathymetry and topography are accounted for along with three-dimensional atmospheric non-uniformities through their depth average over a spherical shell. A linear analysis, yielding two pairs of gravito-acoustic waves, offers explanations for phenomena observed during the Tonga event. A continuous transcritical regime (in terms of water depth) is identified as the source of large wave generation in deep water bodies, removing the singularity-driven Proudman-type resonance observed in one-way coupled models. The refractive properties, governing the interaction of the atmospheric wave with step changes in water depth, are derived to comment on mode-to-mode energy transfer. Two-dimensional global simulations modelling the propagation of the atmospheric wave (under realistic conditions on the day) and its worldwide effect on oceans are presented. Local maxima of water-height disturbance in the farfield from the volcano, linked to the atmospheric wave deformation (in agreement with observations), are identified, emphasising the importance of the TWC model for any daylong predictions. The proposed framework can be extended to include additional layers and physics, e.g. ocean and atmosphere stratification. With the aim of contributing to warning system improvement, the code necessary to simulate the event with the proposed model is made available.

Automated summary

The post-explosion events of the Hunga Tonga-Hunga Ha'apai volcano in January 15, 2022 highlighted the need for a better understanding of ocean-atmosphere interactions under large energy injections. A two-way coupled system was derived to describe the long-wave behavior of the ocean and atmosphere, taking into account bathymetry, topography, and atmospheric non-uniformities. Linear analysis explained the observed phenomena during the Tonga event, while a continuous transcritical regime and refractive properties were identified as key factors for wave generation and energy transfer. Global simulations demonstrated the worldwide effect of the atmospheric wave and emphasized the importance of the two-way coupled model for daylong predictions. The proposed framework can be extended to include additional layers and physics to improve warning systems, and the code for simulating the event is made available.