Abyssal gyres

The flow of Antarctic Bottom Water in the western part of the Atlantic Ocean is modeled in terms of an annulus consisting of a coupled frontal current (i.e., a cold filament) moving along the internal surface of a cone. Namely, the interface bounding the (reduced-gravity) cyclonic current from above intersects the bottom along two curves, one on its right hand side and the other on its left (looking downstream); the cone represents the ocean floor which rises on the north, west and south due to the presence of the continents and on the east due to the Mid-Atlantic Ridge. The inertial current is nonlinear in the sense that both its amplitude and its Rossby number are of order unity. Its response to the presence of β, a varying bottom slope and a cyclonic flow above that varies seasonally is examined in detail. This is done analytically using a perturbation scheme applicable to narrow gyres where the ratio of the filament width to its distance from the center R is small. It is found that the variation of the Coriolis parameter with latitude causes the cyclonic gyre to intensify on its southern side. This is analogous to the familiar (linear) intensification of the so-called Fofonoff flow. However, in our problem the role of bottom topography is not analogous to that of β; an increased bottom slope along the northern and western parts of the basin causes a significant intensification there. A peculiar aspect of the gyre is that when the parameter β R/f 0 (where f 0 is the Coriolis parameter at the center) is above a "critical" value, the filament cannot negotiate the low latitude portion of the cone and, as a result, it plunges into the abyss and approaches the apex of the cone. This may occur even if the southern edge of the gyre is many deformation radii away from the equator. It is also found that an increase (decrease) of a cyclonic flow above the filament causes the entire gyre to contract (expand) and shift its position down (up) the slope. It is suggested that (i) the observed westward intensification of the filament is due to the sloping bottom, and (ii) the observed seasonal shift in the gyre's position might be caused by the seasonality of the flow above. Furthermore, it is speculated that the inability of various investigators to locate the western filament (i.e., the filament on the western flanks of the basin) at low latitudes (despite extensive searches for it) might be related to the plunging process.