An analytical model of capped turbulent oscillatory bottom boundary layers

Abstract

An analytical model of capped turbulent oscillatory bottom boundary layers (BBLs) is proposed using eddy viscosity of a quadratic form. The common definition of friction velocity based on maximum bottom shear stress is found unsatisfactory for BBLs under rotating flows, and a possible extension based on turbulent kinetic energy balance is proposed. The model solutions show that the flow may slip at the top of the boundary layer due to capping by the water surface or stratification, reducing the bottom shear stress, and that the Earth's rotation induces current and bottom shear stress components perpendicular to the interior flow with a phase lag (or lead). Comparisons with field and numerical experiments indicate that the model predicts the essential characteristics of the velocity profiles, although the agreement is rather qualitative due to assumptions of quadratic eddy viscosity with time‐independent friction velocity and a well‐mixed boundary layer. On the other hand, the predicted linear friction coefficients, phase lead, and veering angle at the bottom agreed with available data with an error of 3%–10%, 5°–10°, and 5°–10°, respectively. As an application of the model, the friction coefficients are used to calculate e‐folding decay distances of progressive internal waves with a semidiurnal frequency.