Saturation of the Internal Tide over the Inner Continental Shelf. Part II: Parameterization

Abstract

Here, we develop a framework for understanding the observations presented in Part I. In this framework, the internal tide saturates as it shoals as a result of amplitude limitation with decreasing water depth H. From this framework evolves estimates of averaged energetics of the internal tide; specifically, energy ⟨APE⟩, energy flux ⟨FE⟩, and energy flux divergence ∂x⟨FE⟩. Since we observe that dissipation ⟨D⟩ ≈ ∂x⟨FE⟩, we also interpret our estimate of ∂x⟨FE⟩ as ⟨D⟩. These estimates represent a parameterization of the energy in the internal tide as it saturates over the inner continental shelf. The parameterization depends solely on depth-mean stratification and bathymetry. A summary result is that the cross-shelf depth dependencies of ⟨APE⟩, ⟨FE⟩, and ∂x⟨FE⟩ are analogous to those for shoaling surface gravity waves in the surf zone, suggesting that the inner shelf is the surf zone for the internal tide. A test of our simple parameterization against a range of datasets suggests that it is broadly applicable.