Coastal Applications

Abstract

It was noted in Section 2.3 that a semigeostrophic channel flow that has become separated from the northern hemisphere left sidewall becomes immune to changes in the position of the right sidewall. As the position of the right wall changes the current moves with it, undergoing no other change in cross-sectional form. Only variations in bottom elevation influence the flow in a meaningful way. This aspect has been demonstrated under the usual conditions of gradually varying geometry, implying that the radius of curvature ρ ^* of the wall or coastline is large compared to the characteristic width of the current. (This variable should not be confused with density.) As we discuss below, the effects of coastal curvature begin to become nontrivial once this restriction is relaxed. In order to make analytical progress, and thereby gain a better physical understanding, the ratio of the Rossby radius of deformation, though finite, must be kept small. Topographic effects continue to dominate in this limit if the flow contacts the bottom, but topography is irrelevant if the coastal flow takes place in a surface layer, insulated from the bottom by an inactive deeper layer. Sidewall curvature then provides the only forcing mechanism.