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 hAPEi, energy flux hFEi, and energy flux divergence partial derivative(x) < F-E >. Since we observe that dissipation < D > approximate to partial derivative(x) < F-E >, we also interpret our estimate of partial derivative(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. Asummary result is that the crossshelf depth dependencies of hAPEi, < F-E >, and partial derivative(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. Atest of our simple parameterization against a range of datasets suggests that it is broadly applicable.