Density-driven exchange flow in terms of the Kelvin and Ekman numbers

The pattern of density-induced flow influenced by basin's width, friction, and Earth's rotation is investigated as a function of the Ekman (E-k) and Kelvin (K-e) numbers. A semianalytical solution is used to determine the conditions under which the density-induced exchange flow is vertically sheared or horizontally sheared. Solutions are obtained over diverse laterally varying bathymetries. It is found that the exchange flow is horizontally sheared under high frictional conditions (E-k > 1) independently of the width of the basin (K-e). The horizontally sheared pattern describes inflow in the channel and outflow over shoals, with the inflow occupying the entire water column. The exchange flow pattern is also horizontally sheared under weak friction (E-k -> 0) and in wide (K-e > 2) basins. In that case, however, the outflow is concentrated on the left (looking into the basin in the Northern Hemisphere) portion of the cross section and inflow appears on the right. Also, under weak friction, the exchange pattern becomes more vertically sheared, with outflow at surface and inflow underneath as the width of the basin becomes small (K-e < 1). Bathymetry is not very influential in the weak friction exchange patterns. Finally, under moderate friction (0.01 < E-k < 0.1), the exchange pattern is both horizontally and vertically sheared for all widths. The horizontally sheared pattern is best defined in wide basins (high Ke), whereas the vertically sheared pattern practically dominates in narrow basins (low Ke). These findings allow classification of various estuaries in the E-k-K-e parameter space.