Vertical structure of residual slope circulation driven by JEBAR and tides: an idealised model

The residual circulation over the continental slope, and in particular, its vertical structure, is analysed by means of an idealised hydrodynamic model. The model is based on the depth-dependent shallow-water equations under uniform along-isobath conditions and is forced by a prescribed meridional density gradient and tidal velocities. By means of expansion in the small Rossby number ε solutions are analysed for conditions representative for the continental slopes off the Hebrides and in the Bay of Biscay. The steady solution at zeroth order consists of a linear density-driven flow. At order ε a tidally rectified flow is found and a stationary flow due to self-interaction of the zeroth-order density-driven flow. At order ε2 the leading-order effect of the interaction between the zeroth-order density-driven flow and the tides is found: the ‘interaction current’. The solutions up to and including order ε2 constitute an along-isobath steady slope current which is comparable to field data. The slope current and the accompanying cross-shelf circulation depend strongly on the shelf and flow characteristics. For the Hebridean case the density forcing predominates, but for the Biscay case the tidal effects are of the same order of magnitude as the density effects. Under those conditions the interaction current is significant which implies that linear superposition of density and tidal effects differs from the non-linear combination of both. It is also shown that the depth-average of the interaction current differs essentially from the solution obtained from a depth-averaged model.