Abstract
A comprehensive theoretical study of the nonlinear hemispheric-scale midlatitude and cross-equatorial steady-state dynamics of a grounded deep western boundary current is given. The domain considered is an idealized differentially rotating, meridionally aligned basin with zonally varying parabolic bottom topography so that the model ocean shallows on both the western and eastern sides of the basin. Away from the equator, the flow is governed by nonlinear planetary geostrophic dynamics on sloping topography in which the potential vorticity equation can be explicitly solved. As the flow enters the equatorial region, it speeds up and becomes increasingly nonlinear and passes through two distinguished inertial layers referred to as the “intermediate” and “inner” inertial equatorial boundary layers, respectively. The flow in the intermediate equatorial region is shown to accelerate and turn eastward, forming a narrow equatorial jet. The qualitative properties of the solution presented are consistent with the known dynamical characteristics of the deep western boundary currents as they flow from the midlatitudes into the tropics. The predominately zonal flow across the ocean basin in the inner equatorial region (and its exit from the equatorial region) is determined in Part II of this study.
