The authors present results from laboratory experiments and numerical simulations of the barotropic circulation in a basin with sloping boundaries forced by a surface stress. Focus is placed on flows with large-scale Rossby numbers that are significantly smaller than unity. The results of the laboratory experiments and simulations show that cyclonic circulation follows the isobaths, the flow pattern being independent of the strength of the forcing. For anticyclonic circulation, the flow pattern changes with forcing strength. It is similar to the cyclonic topographically steered pattern for weak forcing, and develops strong cross slope flows for strong forcing.
Linear dynamics are symmetric between cyclonic and anticyclonic circulation and give a good description of the cyclonic and weakly forced anticyclonic circulation. The analysis of the non-linear dynamics shows that topographically steered cyclonic flows are all stable and steady energy-minimum solutions to the inviscid non-linear equations. This implies that the non-linear terms (advection of relative vorticity) are always small for topographically steered cyclonic flow.
For anticyclonic flow, the situation is very different. It is possible that no anticyclonic topographically steered flow is ever a solution to the steady inviscid equations. And if such a steady anticyclonic flow does exist, it is likely to be unstable, since it must correspond to a saddle point in energy rather than to a minimum or a maximum. The non-linear terms are important when the Rossby number is larger than the Ekman number, which is the case for the anticyclonic experiments with strongest forcing. For these experiments, the advection of relative vorticity prevents the flow from following topography, creating locations with strong relative vorticity and cross slope flow. The development of cross slope flow can be understood from the conservation of potential vorticity in basins with irregular topography.
The separation of anticyclonic flow from steep topography shown in the laboratory experiments and the theoretical analysis herein are in agreement with features like the Gulf Stream separation from the continental slope at Cape Hatteras, North Carolina.
2008. Vol. 38, 771-787 p.