On the nonlinear, three-dimensional structure of equatorial oceanic flows

Abstract

A systematic development, based on the construction of an asymptotic solution of the Euler equation, written in rotating, spherical coordinates (φ, θ, r), is used to investigate the flows of the type seen in the neighborhood of the Pacific equator. First, it is shown that the observed poleward surface-flow structure away from the line of the equator is possible only if the flow evolves (changes) in the azimuthal direction. Then, allowing for variations in the azimuthal direction, the shallow-water, small-Rossby-number version of the problem, approximated close to the equator, leads to an asymptotic formulation that admits any prescribed azimuthal velocity profile u(θ, r) at some fixed longitude φ. The maximum extent of the flow region inside which we can describe in detail the velocity field is restricted by the size of the Rossby number. The analysis demonstrates that the meridional y and vertical w velocity components are nonlinearly connected to u, and that all three velocity components appear at the same order in the leading (scaled) equations, even though the physical size of w is very much smaller than that of the other two components. An appropriate choice is made for u,at a given φ, and the corresponding complete three-dimensional flow field, which emerges from the interlinkage of the velocity components, is described; the thermocline is also added to the flow configuration. We compare these results with the available field data, demonstrating that this formulation captures all the main structures of the flow field, but also allows for many choices to be made that can be used to adjust the details of the flow and to model other, similar flows.