The Meridional Flow of Source-Driven Abyssal Currents in a Stratified Basin with Topography. Part I: Model Development and Dynamical Properties

Abstract

A numerical simulation is described for source-driven abyssal currents in a 3660 km ϫ 3660 km stratified Northern Hemisphere basin with zonally varying topography. The model is the two-layer quasigeostrophic equations, describing the overlying ocean, coupled to the finite-amplitude planetary geostrophic equations, describing the abyssal layer, on a midlatitude ␤ plane. The source region is a fixed 75 km ϫ 150 km area located in the northwestern sector of the basin with a steady downward volume transport of about 5.6 Sv (Sv ϵ 10 6 m 3 s Ϫ1) corresponding to an average downwelling velocity of about 0.05 cm s Ϫ1. The other parameter values are characteristic of the North Atlantic Ocean. It takes about 3.2 yr for the abyssal water mass to reach the southern boundary and about 25 yr for a statistical state to develop. Time-averaged and instantaneous fields at a late time are described. The time-averaged fields show an equatorward-flowing abyssal current with distinct up-and downslope groundings with decreasing height in the equatorward direction. The average equatorward abyssal transport is about 8 Sv, and the average abyssal current thickness is about 500 m and is about 400 km wide. The circulation in the upper layers is mostly cyclonic and is western intensified, with current speeds about 0.6 cm s Ϫ1. The upper layer cyclonic circulation intensifies in the source region with speeds about 4 cm s Ϫ1, and there is an anticyclonic circulation region immediately adjacent to the western boundary giving rise to a weak barotropic poleward current in the upper layers with a speed of about 0.6 cm s Ϫ1. The instantaneous fields are highly variable. Even though the source is steady, there is a pronounced spectral peak at the period of about 54 days. The frequency associated with the spectral peak is an increasing function of the downwelling volume flux. The periodicity is associated with the formation of transient cyclonic eddies in the overlying ocean in the source region and downslope propagating plumes and boluses in the abyssal water mass. The cyclonic eddies have a radii about 100-150 km and propagation speeds about 5-10 cm s Ϫ1. The eddies are formed initially because of stretching associated with the downwelling in the source region. Once detached from the source region, the cyclonic eddies are phase locked with the boluses or plumes that form on the downslope grounding of the abyssal current, which themselves form because of baroclinic instability. Eventually, the background vorticity gradients associated with ␤ and the sloping bottom arrest the downslope (eastward) motion, the abyssal boluses diminish in amplitude, the abyssal current flows preferentially equatorward, the upper layer eddies disperse and diminish in amplitude, and westward intensification develops.

Meridional flow of grounded abyssal currents on a sloping bottom in spherical geometry

“…We briefly describe the equilibrium solution to the model (8)- (10) in which h (λ, θ) will be determined by the steady-state quasi-linear hyperbolic equation…”

“…The formation of such a shock could result in mixing on the up slope flank of the abyssal water mass as it propagates equatorward. This would be a decidedly different "instability mechanism" than baroclinic destabilization, which preferentially occurs on the down slope or offshore side of grounded abyssal currents [7,8,10].…”

“…These currents form an important component in the deep "leg" of the meridional overturning circulation in the oceans. The mesoscale dynamics of these currents has been described in a series of papers [1][2][3][4][5][6][7][8][9][10][11]. All of these studies have implicitly assumed either an f or β-plane approximation in which the dynamics is modelled in a Cartesian coordinate system with the implicit assumption that the horizontal length scales are not too much larger than the internal deformation radius (on the order of about 10-100 km in the ocean).…”

Stability of meridionally-flowing grounded abyssal currents in the ocean

“…The model is a low frequency (sub-inertial) limit of the three-layer shallow-water equations on a β-plane with variable topography (for full details see Swaters [3]). In this limit, the primary dynamical variables are the geostrophic (leading order reduced) pressures in the upper two layers and the thickness of the bottom or abyssal layer (see Fig.…”

“…The three roots to the cubic dispersion relation (21) correspond to a barotropic and baroclinic topographic Rossby wave and to a planetary Rossby wave, respectively (Swaters [3]). The onset of instability corresponds to the coalescence of the barotropic and baroclinic topographic Rossby modes.…”