Abstract
Understanding the conversion of surface tides into internal tides and resulting turbulence is important for oceanic mixing. This study investigates internal tide generation over shallow supercritical obstacles in flows where Nh/U0 ∼ O(1), with N is background stratification, h obstacle height, and U0 far-field tidal velocity amplitude, particularly relevant in shallow, fjord-like environments where tidal currents become much faster. Previous work has focused on Nh/U0 ≫ 1, showing that internal tide generation roughly follows h2N, and local dissipation follows . Here, a faster, linear stratified flow regime is investigated using idealized simulations. Tidal energy conversion follows the power law until crest-top Froude number Frc = Uc/c1 ≈ 1 (where Uc = U0H / (H − h) is the barotropic flow speed at the crest, H is total water depth and c1 = 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 Frc > 1 at the crest resembles approach-controlled flow in two layers (Lawrence 1993). Radiation from the crest transitions from relatively linear response with well-defined internal tidal beams to strongly non-linear response with diffuse beam as Frc > 1. However, significant mode-1 internal tides are still radiated into the farfield, contradicting the traditional dichotomy that basins with Frc > 1 do not generate internal tides (Stigebrandt and Aure 1989). Simulations with realistic or asymmetric stratification exhibit the same general characteristics as constant-stratification simulations. This saturation conversion when Frc > 1 should be considered when devising wave drag parameterization used in the models, especially in fjord regions where large Frc are likely to be found.
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