Search Results
You are looking at 1 - 2 of 2 items for
- Author or Editor: Dave Ramsden x
- Refine by Access: All Content x
Abstract
The behavior of 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: S = N 2sin2θ/f 2, 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.
Two regimes are considered. The first is for cases where the eddy coefficients are constant in time but variable in space and the interior flow is allowed to adjust to the boundary mixing. The numerical results agree with analytic theory for two limiting cases. The first case is when the mixing extends into the fluid interior, and the second is when the mixing is limited to a slab region.
The second regime involves cases in which the eddy coefficients are determined from a gradient Richardson number hypothesis. The interior alongslope flow is fixed in time. Two cases are considered, and it is shown that the resultant Ekman layer shutdown from downwelling favorable flows can be parameterized in terms of the Burger number and a “stratification drag” number, similar to that used by Trowbridge and Lentz, D = CdN/f, where Cd is the bottom drag coefficient.
Cases favorable to downwelling flow are shown to shut down in a time proportional to S −3/2 D −1 f −1 for small S. Cases favorable to upwelling flow are also investigated. The results are shown to depend on the values of diffusivity in the well-mixed and far-field region. The results, though not conclusive, suggest upwelling favorable flows shut down in a time proportional to S −1 D −1/2 f −1.
Abstract
The behavior of 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: S = N 2sin2θ/f 2, 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.
Two regimes are considered. The first is for cases where the eddy coefficients are constant in time but variable in space and the interior flow is allowed to adjust to the boundary mixing. The numerical results agree with analytic theory for two limiting cases. The first case is when the mixing extends into the fluid interior, and the second is when the mixing is limited to a slab region.
The second regime involves cases in which the eddy coefficients are determined from a gradient Richardson number hypothesis. The interior alongslope flow is fixed in time. Two cases are considered, and it is shown that the resultant Ekman layer shutdown from downwelling favorable flows can be parameterized in terms of the Burger number and a “stratification drag” number, similar to that used by Trowbridge and Lentz, D = CdN/f, where Cd is the bottom drag coefficient.
Cases favorable to downwelling flow are shown to shut down in a time proportional to S −3/2 D −1 f −1 for small S. Cases favorable to upwelling flow are also investigated. The results are shown to depend on the values of diffusivity in the well-mixed and far-field region. The results, though not conclusive, suggest upwelling favorable flows shut down in a time proportional to S −1 D −1/2 f −1.
Abstract
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.
Abstract
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.
