Implementation of a time-dependent bathymetry in a free-surface ocean model: Application to internal wave generation

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. rgy 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.