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Highlights • An original time-split approach is implemented in a free-surface ocean model. • NH flows are simulated in a natural way, propagating acoustic waves. • The three-mode algorithm is detailed and its performances are evaluated. • Acoustic, surface-gravity and internal-gravity waves are studied Abstract A three-mode time-split algorithm is proposed to simulate non-hydrostatic ocean processes in a natural way: fast pressure adjustments via acoustic waves are explicitly represented. The full set of compressible Navier–Stokes equations is integrated for a free-surface ocean with three time-steps respectively associated to the internal, external and compressible (non Boussinesq) modes. The resulting three-mode algorithm can be implemented either in a fully compressible configuration or in a "pseudo-compressible" configuration by artificially lowering acoustic-wave velocities to reduce computational costs. The present description of the three-mode algorithm focuses in the first place on the simulation of non-hydrostatic processes in free-surface ocean models. Several test simulations related to linear and non-linear acoustic, surface and internal gravity waves are studied in details with the proposed three-mode algorithm. [ABSTRACT FROM AUTHOR]

We show that a time-varying bathymetry can be implemented in a σ-coordinate free-surface ocean model with only slight modifications to the original numerical algorithm. A consistent choice of variables for the height of the water column is proposed. The resulting algorithm creates new opportunities in ocean model configurations in which bathymetry changes at time scales comparable with those of ocean dynamics (e.g., near shore bed motion and seismic or volcanic catastrophes) or in direct modeling of laboratory experiments with a moving bottom. The new numerical implementation is carefully compared with a laboratory experiment involving internal wave generation by an oscillating, ridge-shaped topography. An energy formulation of the time-varying bathymetry is proposed, and energy fluxes are computed to characterize and quantify the cascade of energy leading to the generation of internal waves by an oscillating ridge. [ABSTRACT FROM AUTHOR]