Becherer, J., Moum, J.N., Calantoni, J., Colosi, J.A., Barth, J.A., Lerczak, J.A., McSweeney, J.M., MacKinnon, J.A., & Waterhouse, A.F. (2021): Saturation of the internal tide over the inner continental shelf. Part I: Observations. Journal of Physical Oceanography, doi:10.1175/JPO-D-20-0264.1
Broadly-distributed measurements of velocity, density and turbulence spanning the inner shelf off central California indicate that (i) the average shoreward-directed internal tide energy flux (〈FE〉) decreases to near 0 at the 25 m isobath; (ii) the vertically-integrated turbulence dissipation rate (〈D〉) is approximately equal to the flux divergence of internal tide energy (∂x〈FE〉); (iii) the ratio of turbulence energy dissipation in the interior relative to the bottom boundary layer (BBL) decreases toward shallow waters; (iv) going inshore, 〈FE〉 becomes decorrelated with the incoming internal wave energy flux; and (v) 〈FE〉 becomes increasingly correlated with stratification toward shallower water.
Becherer, J., Moum, J.N., Calantoni, J., Colosi, J.A., Barth, J.A., Lerczak, J.A., McSweeney, J.M., MacKinnon, J.A., & Waterhouse, A. F. (2021): Saturation of the internal tide over the inner continental shelf. Part II: Parameterization. Journal of Physical Oceanography, doi:10.1175/JPO-D-21-0047.1
Here, we develop a framework for understanding the observations presented in the accompanying paper (Part I) by Becherer et al. (2021). In this framework, the internal tide saturates as it shoals due to 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 〈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 data sets suggests that it is broadly applicable.