A two-layer model with a rigid lid and a flat bottom on an f plane is employed to study a flow field driven by a density flux through the sea surface or the coast; for example, freshwater discharged from a river. The negative (positive) density flux into the upper layer is represented by the water beneath (over) the interface changing from the lower (upper) layer to the upper (lower) layer, that is entrainment of the lower (upper) layer by the upper (lower) layer. The subinertial flow pattern constrained by the coast has two components: one is the baroclinic eddy nearby that matches the entrainment region, and the other is a forced, internal Kelvin wave along the appropriate half of the coast.