Effects of Finite Amplitude Bottom Topography on Ocean Variability

The wind-driven oceanic circulation in the presence of bottom topography that isopycnals intersect is examined in an idealized setting. A modified quasi-geostrophic (QG) model has been designed and implemented. The model allows staircase bottom topography: topographic breaks decompose the lateral domain into subdomains consisting of fixed numbers of layers. Topographic shelves are placed within small (order Rossby number) vertical distances from the undisturbed layer interfaces. Each shelf can have topographic variations of the same scale. An elliptic solver inverting potential vorticity into geostrophic stream functions was designed based on the Capacitance matrix method. Solutions are matched at the topographic breaks by adding fictitious potential vorticity sources. The model has been tested against the problem of trapped topographic waves over a cliff. The results obtained for small-steepness disturbances agree with a weakly non-linear theory developed by Dewar and Leonov. Steeper disturbances break in a way that favors on shelf eddy detachment and transport of undiluted properties onto the shelf. The model has been further applied to the basin-scale wind-driven circulation problem in a 3-layer configuration with a continental shelf in the western part of the domain. Double-gyre wind forcing has been considered. The topographic shelves are responsible for dynamics absent in classical idealized eddy resolving QG models which have been the preferred numerical tool for the study of low frequency intrinsic ocean variability. The top-layer flow interacts with the shelf topography by means of vortex tube stretching and vorticity dissipation due to bottom drag. This mechanism reduces the role of horizontal friction as a controlling factor in the dynamics.The results obtained for different parameter regimes (free-slip, no-slip boundary condition, different values of the viscosity) show reduced sensitivity to the type of dynamic boundary condition, compared to classical results. The intrinsic variability of the flow is affected by the new mechanism of on- and off shelf transport of potential vorticity. The role of horizontal friction is again reduced, as shown by the modeling results. Spatiotemporal patterns of the variability have been analyzed. Most of the patterns are insensitive to the type of boundary condition (free-slip vs. no-slip), and qualitatively resemble classical no-slip results.