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

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 <F_E>, and energy flux divergence ∂_x <F_E>. Since we observe that dissipation <D> ≈ ∂_x<F_E>, we also interpret our estimate of ∂_x<F_E> 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>, <F_E>, and ∂_x<F_E> 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.