Stationary Sea Surface Height Anomalies in Cyclonic Boundary Currents: Conservation of Potential Vorticity and Deviations from Strict Topographic Steering

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Abstract
In high-latitude subpolar seas, such as the Nordic Seas and the Labrador Sea, time-mean geostrophic currents mediate the bulk of the meridional oceanic heat transport. These currents are primarily encountered along the continental slopes as intense cyclonic boundary currents, which due to the relatively weak stratification should be strongly steered by the bottom topography. However, analyses of hydrographic and satellite altimetric data along depth contours in Nordic Seas boundary currents reveal some remarkable stationary along-stream variations in the depth-integrated buoyancy and bottom pressure. A closer examination shows that these variations are linked to changes in steepness and curvature of the continental slope. 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. Based on potential vorticity conservation, equations for the zeroth and first order pressure and buoyancy fields are derived. To the lowest order, the flow is completely aligned with the bottom topography. However, the first order results show that where the lowest-order flow increases (decreases) its relative vorticity along a depth contour, the first order pressure and depth-integrated buoyancy increase (decrease). This response is associated with cross-isobath flows, which induce stretching/compression of fluid elements that compensates for the changes in relative vorticity. The model-predicted along-isobath variations in pressure and depth-integrated buoyancy are comparable in magnitude to the ones found in the observational data from the Nordics Seas.

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