Flat-bottomed Ocean Research Articles

Topographic Coupling of Surface and Internal Kelvin Waves

An analytical method is developed to compute the diffraction of a barotropic Kelvin wave by a localized topographic irregularity on an otherwise flat-bottom ocean with an arbitrary vertical stratification. The bump topography is assumed to be small in height compared to the water depth of the flat-bottom ocean. It is found that all baroclinic mode Kelvin waves will be generated downstream of the bump, with the first baroclinic mode having the largest amplitude. At subinertial frequencies (ω<f) localized disturbances are also generated with higher vertical modes trapped nearer to the bump. At superinertial frequencies (ω>f) cylindrical Poincard waves with certain anisotropy are generated at (x = x0, y = 0) and (x = −x0, y = 0), where (x0,0) is the center of the bump topography, and the y axis is the coastline. The Poincaré waves favor the lowest few modes, with the baroclinic modes having stronger tendencies to be directionally anisotropic. The baroclinic Poincaré waves radiating offshore from the bump topography could contribute to the internal wave field in the open ocean and provide an alternative mechanism to dissipate the barotropic tides. Order-of-magnitude estimates show that an energy flux of ∼0.09 W per centimeter coastline could be converted from the M2 tide in the eastern Pacific.

Effects of bottom topography and density stratification on the formation of western boundary currents

A wind-driven, general circulation for a two-layer ocean with continental shelf-slope along the western boundary is studied numerically. Special attention is focused on the formation process of the western boundary current in the subtropical gyre. The western boundary current develops in the upper layer along the western boundary on the shelf-slope with a bottom trapped poleward flow in the lower layer. The poleward undercurrent is concentrated approximately along the contour lines of the potential vorticity,f/D, wheref is the Coriolis parameter andD the depth of the ocean. The separation of upper- and lower-layer flows on the shelf-slope represents a typical transient response. As the response approaches a steady state, the poleward undercurrent decreases in amplitude, and the motion tends to be confined to the upper layer. The flow pattern becomes similar to that found in a flat bottom ocean. A steady-state response is expected to be isostatic (no motion in the lower layer), even on the shelf-slope, as conservation of potential vorticity would suggest.

Combined effects of wind stress and topography in a two-layer model of the Southern Ocean

Abstract Recent observations for the Southern Ocean suggest that bottom topography may play an important role in the dynamics of the Antarctic Circumpolar Current. In the following paper, a two-layer model of the Antarctic Circumpolar Current is used to assess the importance of Southern Ocean bathymetry. Both barotropic and baroclinic components of the velocity field have a tendency to follow contours of constant (H/|f|) (H is the depth, f the Coriolis parameter). If the flow over an isolated ridge is considered, the zonal component is significantly increased over the northern flank, whereas a weak westerly counter-current is induced over the southern portion of the ridge, mainly in the upper layer of the ocean. Behaviour at the interface shows many similarities with the observed features of the Antarctic Polar Front. Whereas the interface in a flat-bottomed ocean rises steadily towards the south, a ridge induces the interface to rise sharply over its northern flank and to flatten out over the southern side. This is consistent with the observed behaviour of surfaces of constant density in the Southern Ocean. The importance of different wind systems, the β-effect, and the size of specific ridges are qualitatively assessed.

A three-dimensional model of the Southern Ocean with bottom topography

A three-dimensional theory is presented of the steady wind-driven flow in a homogeneous circumpolar ocean. The bottom topography is a function of longitude and may consist of a series of ridges. The results of Kamenkovich ( Trudy Institut Okeanologiya, 56, 241–293, 1962) for a transport theory are reproduced here for the three-dimensional velocity field. The model ocean is subdivided into an interior region between surface and bottom Ekman layers. The circumpolar current in the interior to lowest order follows the contours of H/ f where H is the depth and f is the Coriolis parameter. The theory shows that in general any deviation from a flat bottom ocean leads to a reduction in transport in the circumpolar current. This decrease in transport can be traced in the theory to an increase in bottom friction as the current turns northward and accelerates over the sloping bottom.

On the existence and structure of inertial boundary currents in a stratified ocean

An investigation is made of the properties of inertial boundary currents in a stably stratified, inviscid, non-diffusive ocean. The Boussinesq and β-plane approximations are adopted. The formalism developed by Robinson (1965) is used: the equations are transformed so that density replaces the vertical coordinate as an independent variable, and after a suitable non-dimensionalization of variables, the various fields are expanded as power series in the downstream co-ordinate η. The motion is shown to conserve potential vorticity. The equations and boundary conditions are obtained to order η2. Solutions are obtained in the region of formation of the coastal jet (i.e. the case of no mass flux through the plane η = 0) for several cases in which the potential vorticity function depends on stream function and density in a simple way. For these cases, it is found that in a constant depth ocean, a boundary current can exist only if the geostrophic drift at the boundary-layer edge is westward at all depths. This constraint is relaxed if the depth increases rapidly enough in the downstream (northward) direction. For slopes just in excess of the critical value, a deep onshore counter-current is predicted. Solutions of the first-order problem, using realistic values of the various parameters, have been computed and are found to be in qualitative agreement with observed features of the Florida Current.In an appendix, it is shown that the constraint of westward geostrophic drift at all levels must hold in a flat-bottomed ocean for arbitrary potential vorticity distributions consistent with stable stratification.