Journal of Fluid Mechanics

On mass transports generated by tides and long waves

J. M.  Huthnance a1
a1 Institute of Oceanographic Sciences, Bidston Observatory, Merseyside L43 7RA

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For small-amplitude barotropic wave motion in a shallow fluid, Moore (1970) found that the associated mean mass transport is geostrophic, but otherwise arbitrary in the absence of friction. We show how weak friction, or starting the motion from rest, determines the mass transport by restricting circulation around closed geostrophic (f/h) contours. The resulting transport is quadratic in oscillatory quantities and depends on the friction type, but not on its (weak) magnitude. Comparison is made with earlier results in particular geometries. A tendency for anticyclonic circulation around shallow regions is found, and extends to large-amplitude oscillations where particle excursions exceed the topographic length scale. We suggest that numerical schemes for calculating tidal residuals should conserve mass and vorticity.

(Published Online April 20 2006)
(Received November 3 1979)
(Revised May 19 1980)