On inertial currents over a sloping continental shelf

Using simple mathematical models, it is shown that an equatorward flowing coastally confined eastern boundary current (or poleward flowing western boundary current) may have two conjugate forms which transport the same flux of each water type. In a slowly varying environment, these two conjugate forms coalesce at some critical latitude which depends on the flow. For lower latitudes there is no defined form. As the coalescence latitude is approached from higher latitudes, one of the two conjugate forms narrows, while the other widens. Furthermore, in the neighborhood of the critical latitude the wider form is subcritical and the narrower form is supercritical to possible long small amplitude shelf waves. It is also shown that a poleward flowing coastally confined eastern boundary current (or an equatorward flowing western boundary current) may be traced poleward to some critical latitude beyond which the possibility of a current in juxtaposition with the coast terminates. For latitudes higher than this terminating latitude the current separates from the coast.