Dynamics of Nonlinear Cross-Equatorial Flow. Part I: Potential Vorticity Transformation
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The transformation of potential vorticity within nonlinear deep western boundary currents in an idealized tropical ocean is studied using a shallow-water model. In a rectangular domain forced by a localized, Northern Hemisphere mass source and a distributed sink that require a net, cross-equatorial mass flux, a series of numerical experiments investigate how potential vorticity changes sign as fluid crosses the equator. Dissipation is included as momentum diffusion, and the Reynolds number, defined as the ratio of the mass source per unit depth to the viscosity, determines the nature of the flow. For Re less than a critical value (approximately 30) the flow is laminar and well described by linear theory. For Reynolds numbers just above this value, the system becomes time-dependent with eddies of one sign developing adjacent to the boundary and propagating steadily across the equator. For very large Re, an extensive and complicated network of both positive and negative anomalies emerges. Analysis of vorticity fluxes, decomposed into mean, eddy, and frictional elements, reveals the growth with Reynolds number of a turbulent boundary layer that exchanges vorticity between the inertial portion of the boundary current and a frictional sublayer where it is expelled from the basin. Thus, the eddy field is established as an essential mechanism for potential vorticity transformation in nonlinear cross-equatorial flow.