Topographic Rectification of Tidal Currents

Abstract

The rectification of oscillatory tidal currents on the sloping sides of a low submarine bank is discussed using the moment method. This method has been previously used in shear dispersion studies where it is used to analyze the advection-diffusion equation. In the present problem it is applied to the barotropic potential vorticity equation linearized about an oscillatory, spatially uniform tidal velocity. To apply the method it is necessary to assume that the topography produces only a small change in depth. The method economically provides the most important qualitative properties (e.g., transport, location and width) of the time averaged current. These results are obtained without making an harmonic truncation. They can then be used to assess the accuracy of the harmonic truncation approximation used by other authors. It is shown that harmonic truncation correctly predicts the transport and location of the rectified current when the bank is low. However if the width of the bank is much less than a tidal excursion distance, harmonic truncation may give a very mistaken impression of the width of the rectified current. Finally, lateral vorticity diffusion is included in the moment calculation. It is shown that this dissipative process does not change the transport or location of the rectified current. It does however increase its width.