Dynamics of nonlinear cross-equatorial flow in the deep ocean

Abstract

The transformation of potential vorticity within and stability of nonlinear deep western boundary currents in an idealized tropical ocean are studied using a shallowwater model. Observational evidence indicates that the potential vorticity of fluid parcels in deep western boundary currents must change sign as they cross the equator, but this evidence is otherwise unable to clarify the process. A series of numerical experiments investigate this transformation in a rectangular basin straddling the equator. A mass source located in the northwestern corner feeds fluid into the domain where it is constrained to cross the equator to reach a distributed mass sink. Dissipation is included as momentum diffusion. The Reynolds number, defined as the ratio of the mass source per unit depth to the viscosity, determines the nature of the flow, and a critical value, Rec, divides its possible behavior into two regimes. For Re < Rec, the flow is laminar and well described by linear theory. For Re just above the critical value, the flow is time-dependent, with cyclonic eddies forming in the western boundary current near the equator. For still larger Reynolds number, eddies of both signs emerge and form a complicated, interacting network that extends into the basin several deformation radii from the western boundary, as well as north and south of the equator. The eddy field is established as the mechanism for potential vorticity transformation in nonlinear cross-equatorial flow. The analysis of vorticity fluxes follows from the flux-conservative form of the absolute vorticity equation. It is shown that the zonally integrated meridional flux of vorticity across the equator using no slip boundary conditions is virtually zero even in the strongly nonlinear limit suggesting that the eddies are extremely efficient vorticity transfer agents. A decomposition of the vorticity fluxes into components due to mean advection, eddy transport, and friction, 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 sub-layer where modification is straightforward. A linear stability analysis of the shallow-water system in the tropical ocean examines the initial formation of the eddy field. The formulation assumes that the basic state is purely meridional and on a local f-plane. Realistic western boundary current profiles undergo a horizontal shear instability that is partially stabilized by viscosity. Calculations at several latitudes indicate that the instability is enhanced in the tropics where the internal deformation radius is a maximum. The linear stability analysis predicts a length scale of the disturbance, a location for its origin, and a critical Reynolds number that agree well with numerical results.