Spin-up of a source-sink flow over a model continental shelf

Results of analytical and experimental models are presented in which the role of various forms of bottom topography on externally driven continental shelf currents has been investigated. The shelf currents are generated in a relating cylindrical geometry by means of a source-sink technique. A linear analytical model for a homogeneous fluid in this configuration predicts that the azimuthal (swirl) velocity above a flat bottom is inversely proportional to the radial distance from the origin. This velocity profile is shown to be altered if the bottom boundary consists of a model continental shelf and slope. Then a geometrical function has to be included to describe the azimuthal velocity profile above the sloping bottom. This function depends only on the slope angle alpha and differs only significantly from unity for large values of alpha (alpha > 30 degrees). As a result, a free Stewartson layer is generated above the shelf break to account for the azimuthal velocity shear between the two interior regions. The net vertical transport in this shear layer is again only important for large slope angles.

Some aspects of the analytical model were verified in laboratory experiments on source-sink driven hows in both homogeneous and weakly linearly stratified fluids. The results show that the stratification was sufficiently weak not to have a significant effect on the dynamics in the interior regions. Reference experiments were carried out to measure the azimuthal velocity profiles above a flat bottom. Then, a part of the bottom profile was replaced by a slope with a slope angle of 25 degrees or 55 degrees. Comparison of the azimuthal velocity profiles of the 25 degrees slope with its equivalent reference case reveals no measurable difference, as predicted by the analytial model. However, with the 55 degrees slope, the difference between the interior regions above the slope and the flat bottom is significant and in quantitative agreement with the results of the analytical model. In addition to the analytical description of the steady state flow, the experiments also provided information on the spin-up phase of the flow. The experimentally obtained spin-up times confirm the theoretical results of Greenspan and Howard (1963) when the local fluid depth is taken into account.