Modelling the dynamics of abyssal equator-crossing currents

The dynamical balance within abyssal equator-crossing flows is examined by studying simplified models of the flow in the equatorial region in the context of one- and two-layer shallow-water theory.; It is first demonstrated that, under reasonable assumptions, the shallow-water model is an appropriate model with which to study equatorial dynamics.; A simple model is then presented for one-layer cross-equatorial flow, where geostrophy is replaced at the equator by frictional flow down the pressure gradient. This model is compared via numerical simulations with the one-layer reduced gravity shallow-water model, first over idealized bottom topography, then over realistic equatorial Atlantic Ocean bottom topography. It is found that the frictional geostrophic model predicts certain aspects of the flow well, but neglects fluid inertia, which does affect the dynamics significantly.; Numerical simulations of the shallow-water equations over realistic Atlantic Ocean topography are described that show good agreement with the observed velocity fields of abyssal Antarctic Bottom Water as it crosses the equator. In particular, the observed southern-intensified flow within the equatorial channel at 36°W is reproduced. Additionally, our time-dependent simulations show that the large time variability observed in equatorial-crossing Antarctic Bottom Water can be reproduced by inducing relatively small temporal fluctuations in the current well before it reaches the equator.; The effects of baroclinicity are investigated by deriving a two-layer model of these currents. We first calculate the theoretical speed of a steadily-travelling, dense eddy on a slope, taking into account the effects of upper-layer pressure variations and bottom friction, where the height field of the eddy is assumed to have compact support and the f-plane approximation is assumed to apply. We then derive a two-layer model of cross-equatorial flow. The model is uniformly valid in the sense that it reduces, at leading order, to the appropriate equatorial model when expressed in equatorial scales, and to the correct mid-latitude model when in mid-latitude scales. The lower layer resembles the shallow-water equations, and the upper layer is similar to the Charney balance equations. The form of the model implies the two layers are partially decoupled at the equator.