Midlatitude–Equatorial Dynamics of a Grounded Deep Western Boundary Current. Part II: Cross-Equatorial Dynamics

Gordon E. Swaters Institute of Applied Mathematics, Department of Mathematical and Statistical Sciences, and Institute for Geophysical Research, University of Alberta, Edmonton, Alberta, Canada

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Abstract

This is Part II of a two-part theoretical study into the midlatitude–cross-equatorial dynamics of a deep western boundary current (DWBC) in an idealized meridionally aligned, differentially rotating ocean basin with zonally varying parabolic bottom topography. Part I determined the midlatitude flow across the planetary vorticity gradient and the dynamics of the DWBC as it begins to enter the equatorial region in the “intermediate equatorial region.” Part II determines the nonlinear dynamics of the DWBC as it flows across the basin along the equator in the “inner equatorial region.” The large-scale structure of the flow within the inner equatorial region corresponds to a zonally aligned nonlinear stationary planetary wave pattern that meanders about the equator in which the flow exits the equatorial region on the eastern side of the basin. In addition to numerically determining the pathlines for the large-scale equatorial flow, an approximate nonlinear model is introduced for which an analytical solution can be obtained for the nonlinear planetary wave along the equator. If the DWBC exits the equatorial region into the opposite hemisphere from its source hemisphere, the characteristic curves associated with the flow must necessarily intersect within the inner equatorial region. It is in the regions of intersecting characteristics that dissipation makes a leading-order contribution to the dynamics and induces the requisite potential vorticity adjustment permitting the cross-equatorial flow of a DWBC that is in planetary geostrophic dynamical balance in midlatitudes.

Corresponding author address: Gordon E. Swaters, Department of Mathematical and Statistical Sciences, University of Alberta, 632 Central Academic Building, Edmonton AB T6G2G1, Canada. E-mail: gswaters@ualberta.ca

Abstract

This is Part II of a two-part theoretical study into the midlatitude–cross-equatorial dynamics of a deep western boundary current (DWBC) in an idealized meridionally aligned, differentially rotating ocean basin with zonally varying parabolic bottom topography. Part I determined the midlatitude flow across the planetary vorticity gradient and the dynamics of the DWBC as it begins to enter the equatorial region in the “intermediate equatorial region.” Part II determines the nonlinear dynamics of the DWBC as it flows across the basin along the equator in the “inner equatorial region.” The large-scale structure of the flow within the inner equatorial region corresponds to a zonally aligned nonlinear stationary planetary wave pattern that meanders about the equator in which the flow exits the equatorial region on the eastern side of the basin. In addition to numerically determining the pathlines for the large-scale equatorial flow, an approximate nonlinear model is introduced for which an analytical solution can be obtained for the nonlinear planetary wave along the equator. If the DWBC exits the equatorial region into the opposite hemisphere from its source hemisphere, the characteristic curves associated with the flow must necessarily intersect within the inner equatorial region. It is in the regions of intersecting characteristics that dissipation makes a leading-order contribution to the dynamics and induces the requisite potential vorticity adjustment permitting the cross-equatorial flow of a DWBC that is in planetary geostrophic dynamical balance in midlatitudes.

Corresponding author address: Gordon E. Swaters, Department of Mathematical and Statistical Sciences, University of Alberta, 632 Central Academic Building, Edmonton AB T6G2G1, Canada. E-mail: gswaters@ualberta.ca
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  • Swaters, G. E., 2015: Midlatitude-equatorial dynamics of a grounded deep western boundary current. Part I: Midlatitude flow and the transition to the equatorial region. J. Phys. Oceanogr., 45, 24572469, doi:10.1175/JPO-D-14-0207.1.

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