A nonlinear, three-dimensional model for ocean flows, motivated by some observations of the Pacific Equatorial Undercurrent and thermocline

Abstract

Using the salient properties of the flow observed in the equatorial Pacific as a guide, an asymptotic procedure is applied to the Euler equation written in a suitable rotating frame. Starting from the single overarching assumption of slow variations in the azimuthal direction in a two-layer, steady flow that is symmetric about the equator, a tractable, fully nonlinear, and three-dimensional system of model equations is derived, with the Coriolis terms consistent with the β-plane approximation retained. It is shown that this asymptotic system of equations can be solved exactly. The ability of this dynamical model to capture simultaneously fundamental oceanic phenomena, which are closely inter-related (such as upwelling/downwelling, zonal depth-dependent currents with flow reversal, and poleward divergence along the equator), is a novel and compelling feature that has hitherto been elusive. While details are presented for the equatorial flow in the Pacific, the analysis demonstrates that other flow configurations can be accommodated within the framework of this approach, depending on the choice of the underlying velocity profile and of the various parameters; the method is therefore applicable to a range of ocean flows with a similar three-dimensional structure.