University of Alberta
Edmonton, Alberta, Canada
In coastal seas where the bottom topography consists of a gently sloping shelf, currents flowing along the sea floor will tend to flow along the shelf with the shallower region to its right. Thus the Coriolis force and the force of gravity acting on the water mass associated with the current are in balance to leading order. Such flows have been observed to exist in nature (e.g. the Mid-Atlantic Bight), and are seen to persist over long periods of time.
Analytical models have been constructed to investigate such flows, such as in Swaters (JFM, 1991). There, the flow is described by a two-layer model in which the lower layer, while geostrophic, is not quasi-geostrophic, since the height variations of the current are not small as compared to its scale height. The model reproduces several key features of the observed flow.
Any laboratory investigations of such a flow will necessarily be in a rotating cylindrical geometry. To facilitate comparison with existing or future experimental data, the model is rederived in a cylindrical geometry. For a simple current configuration in which the height vanishes at two locations in the cross slope direction, an analytic solution is found, and its stability characteristics are investigated.