A Simple Model for Tidally Forced Standing Waves in a Submarine Canyon

Submarine canyons are recognized as energetic sites for internal tides and enhanced mixing, yet the mechanisms by which tidal forcing excites these motions remain poorly understood. To address this gap, we develop a simplified theoretical model that represents a canyon as a long, narrow rectangular box. The analysis reveals that the dominant wave modes in this idealized geometry are standing internal Kelvin waves, generated at the canyon-top interface by barotropic tides in the open ocean and accompanied by the radiation of internal tides back into the open ocean. The amplitude of these standing waves depends on the tidal forcing strength, the geometry-determined proximity to resonance with a given tidal frequency, and the width-to-length aspect ratio, which controls wave-radiation efficiency. Theoretical calculations indicate that the canyon’s tidal kinetic energy is sustained primarily by a balance between tidal energy input and losses through radiated internal tides, with bottom drag and turbulent mixing contributing an order of magnitude less. Idealized MITgcm simulations forced by barotropic tides at the boundaries support these theoretical predictions. While the model adopts a simplified geometry, the framework can be extended to more realistic continental slope settings, providing new insight into internal tide dynamics within submarine canyons.