Stationary buoyancy variations along the depth contours in cyclonic boundary currents: analyzes of data and a simple potential vorticity model

In subpolar seas such as the Nordic Seas and the Labrador Sea, intense cyclonic boundary currents are frequently encountered on the continental slopes. Due to relatively weak vertical stratification, these boundary currents are strongly steered by the topography. However, analyzes of hydrographic and satellite-altimetry data reval some remarkable stationary variations in the depth-integrated heat content along the depth contours, which seem to be liked to changes in steepness and curvature of the topography. To examine the underlying dynamics, a steady-state model of a cyclonic stratified boundary current over a topographic slope is developed in the limit of small Rossby numbers. To the lowest order, the bottom velocities are aligned with the bottom topography. If the leading-order buoyancy field is a function of only the bottom depth and the vertical coordinate, an equation for the variations of the first-order buoyancy and pressure fields along the depth contours can be derived. This equation, based on the conservation of potential vorticity, shows that the pressure and depth-integrated buoyancy tend to increase/decrease where the leading-order isobath-following flow increases/decreases its relative vorticity. The predicted along-isobath variations in pressure and buoyancy are comparable in magnitude to the ones found in the data, and furthermore tend to be more pronounced for cyclonic anomalies in relative vorticity. In the absence of vertical shear, the dynamical response is essentially explained by the analysis presented by Rhines (1970) of edge and bottom waves in a stratified rotating fluid.