Saturation of Internal Tide Generation over Shallow Supercritical Topography

Abstract Understanding the conversion of surface tides into internal tides and the resulting turbulence is important for oceanic mixing. This study investigates internal tide generation over shallow supercritical obstacles in flows, where Nh / U 0 ∼ O (1), with N being background stratification, h being obstacle height, and U 0 being far-field tidal velocity amplitude, particularly relevant in shallow, fjord-like environments where tidal currents become much faster. Previous work has focused on Nh / U 0 ≫ 1, showing that internal tide generation roughly follows and local dissipation follows . Here, a faster, linear stratified flow regime is investigated using idealized simulations. Tidal energy conversion follows the power law until the crest-top Froude number Fr c = U c / c 1 ≈ 1 [where U c = U 0 H /( H − h ) is the barotropic flow speed at the crest, H is the total water depth, and is the mode-1 phase speed in the deep water], beyond which internal tide generation stops increasing (saturates). Radiation saturates and local dissipation no longer grows as quickly as . Qualitatively, the fully stratified flow with Fr c > 1 at the crest resembles approach-controlled flow in two layers. Radiation from the crest transitions from a relatively linear response with well-defined internal tidal beams to a strongly nonlinear response with diffuse beam as Fr c > 1. However, significant mode-1 internal tides are still radiated into the far field, contradicting the traditional dichotomy that basins with Fr c > 1 do not generate internal tides. Simulations with realistic or asymmetric stratification exhibit the same general characteristics as constant-stratification simulations. This saturation conversion when Fr c > 1 should be considered when devising wave-drag parameterization used in the models, especially in fjord regions where large Fr c values are likely to be found. Significance Statement Tidal forcing of stratified flow over a submarine ridge produces internal waves at the tidal frequency and local turbulence. For moderate tides, the energy removed from the surface tide usually scales quadratically with the flow amplitude. Here, we show that when the flow speed above the ridge crest exceeds the speed of the lowest internal wave mode, the conversion rate stops increasing, and both internal tide radiation and local dissipation no longer increase with stronger forcing. This regime should be taken into account when parameterizing internal tidal drag and mixing, particularly when they are parameterized in shallow seas and fjords.