Abstract
The behavior of time-dependent oceanic boundary layers on a sloping bottom in the presence of stratification is investigated by the method of direct numerical simulations. The Navier–Stokes equations are decomposed into mean and turbulent components with the mean equations involving a slope Burger number:
SN22f2
where N is the buoyancy frequency, θ is the bottom slope angle, and f is the Coriolis parameter. The influence of the turbulent fluctuations is parameterized as eddy coefficients of viscosity and diffusivity.
The interior alongslope flow is allowed to be time dependent, and boundary conditions are derived for two possibilities: one where the interior alongslope responds to an interior pressure gradient, and the second where the flow is in balance with other model prognostic variables. Sinusoidal forcing is used to drive the model. The response of the system to the two forms of forcing is found to be quite different and consistent with the forms of the forcing.
When the frequency of forcing ω is much less than N, the system exhibits the asymmetric response in mixed layer height observed in oceanic regimes. When ω is of tidal frequency, the measured buoyancy fluxes and upslope transport working against mean background gradients of buoyancy produce secondary mixing rates of the same order as maximum prescribed values of diffusivity. It is concluded that this mechanism is probably not vigorous enough to generate observed oceanic interior mixing rates.
