On the influences of nonlinear bottom friction on the topographic rectification of tidal currents

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Abstract
The influences of nonlinear bottom friction on the along-isobath mean current associated with the topographic rectification of tidal currents are examined in the limit of depth-independence (no vertical structure in the horizontal currents), weak friction and weak nonlinearity. These influences are discussed in terms of the effects of spatial gradients and temporal variations in the effective friction coefficient relating bottom stress to velocity. For typical parameter values, spatial gradients in the coefficient enhance the mean current and temporal variations reduce it. The first influence is the source of Loder's (1980) suggestion that the mean current is enhanced by nonlinear friction. The second influence accounts for the mean current reduction upon the inclusion of nonlinear friction in the example considered by Huthnance (1981). However, it is shown that each of these influences can have the opposite effect for extreme parameter values. Additionally, the inclusion of mean current contributions to the friction coefficient can significantly increase the effective mean friction coefficient and hence also reduce the mean current. The results confirm that the form of bottom friction is important in models for the topographic rectification of tidal currents.