Inter‐hemispheric oceanic exchange

Abstract

SUMMARYThe exchange of water between hemispheres is examined theoretically by looking at the behaviour of continuous (double frontal) abyssal currents situated on the bottom of a (parabolic) meridional channel. We used a reduced-gravity (fluid) model with an active lower layer on the bottom of the channel, and a passive infinitely deep upper layer on the top. The topography is the agent responsible for forcing the current across the equator. We first examined analytically the nonlinear, steady, frictionless case and, as a second step, we considered a nonlinear numerical simulation (of the Bleck and Boudra type). We then compared the results of these two (fluid) models to each other and to the solid-balls model of Borisov and Nof which examined the migration of particles in the same cross-equatorial channel.All three models show that, in general, the current (or a 'cloud' of solid particles) advances gradually toward the equator without much change to its structure. Upon reaching the vicinity of the equator, the current width (or the distance between neighbouring balls) decreases dramatically. The current (or cloud) then turns eastward, flows rapidly downslope, and rises on the eastern side. The flow (or cloud) ultimately splits into two parts, one progressing northward and the other recirculating and advancing southward.Remarkably good agreement is found between the detailed solid-particles analysis and the new numerical fluid simulations, indicating that the inter-hemispheric exchange is primarily an inertial process that depends mainly on the channel geometry. It is shown that the partition of mass flux between the two hemispheres depends on the way that the solid particles, or the current-jet, impinge on the eastern flank of the channel. In contrast to the very good agreement between the solid balls and the fluid simulations, poor agreement was found between the detailed analytical prediction for the cross-equatorial transport and the numerical solution (even when the viscosity was as small as we could use for numerical stability). However, the analytical solution does give the correct prediction for the position of the resulting currents and their general behaviour. It is argued that the disagreement between the analytically calculated fluid mass transports (which, in contrast to the balls, is subject to a potential-vorticity constraint) and the numerical computations is due to the alteration of potential vorticity. Specifically, the friction alters the potential vorticity of the flow and prevents it from acting as a constraint to the crossing. Though crucial to the crossing, the role of friction is, therefore, passive. It merely allows the fluid to alter its potential vorticity in such a manner that the flow can adapt to the crossing pattern imposed by the geometry.It is suggested that the observed recirculation of Antarctic Bottom Water in the vicinity of the equatorial Atlantic may be a result of our splitting process.

Shallow water modeling of Antarctic Bottom Water crossing the equator

“…The important distinction between the two models is that the lack of inertial terms in the FG model severely restricts the motion of the fluid, whereas the shallow water model has inertial terms available when needed. This is entirely consistent with the conclusions of Nof andBorisov [1998] (andRodwell andHoskins [2001], for atmospheric equatorcrossing flows), who found that equator-crossing flow is primarily an inertial process, with the topography interacting strongly with the flow, but the presence of friction was necessary to modify potential vorticity as the fluid moved between hemispheres.…”

Modeling equator-crossing currents on the ocean bottom

“…Nof and Borisov [16] compared the numerical simulations of double frontal currents on a parabolic meridional channel using a reducedgravity shallow-water model to the solid particles of Borisov and Nof [16] and to the analytic solution of Nof and Olson [17]. Since the shallow-water simulations compared favorably with the dynamics of the solid particles, Nof and Borisov [16] concluded that the equatorcrossing process is an inertial one where the geometry of the bottom topography plays a crucial role.…”

“…Since the shallow-water simulations compared favorably with the dynamics of the solid particles, Nof and Borisov [16] concluded that the equatorcrossing process is an inertial one where the geometry of the bottom topography plays a crucial role. The differences between the inviscid analytic solutions of Nof and Olson [17], where potential vorticity is conserved, and the viscous shallow water simulations led them to conclude that the potential vorticity is modified by friction as the current proceeds, allowing the flow to propagate along the path prescribed by the bottom topography.…”

“…For simplicity, we will take r to be a prescribed constant in this study. [16], modified from DeMadron and Weatherly [4]..…”

The equatorial meandering of abyssal ocean currents

“…Thus, the theoretical question arises concerning the dynamical balances that govern the equatorial dynamics of these abyssal flows. The oceanographic data clearly shows that these flows cross the equator and circulate around the entire the globe [3].…”