Meridional dynamics of grounded abyssal water masses on a sloping bottom in a mid-latitude -plane

Observations, numerical simulations and theoretical scaling arguments suggest that in mid-latitudes, away from the source regions and the equator, the meridional transport of abyssal water masses along a continental slope corresponds to planetary geostrophic flows that are gravity- or density-driven and topographically steered. We investigate these dynamics using a nonlinear reduced-gravity model that can describe grounded abyssal meridional flow over sloping topography that crosses the planetary vorticity gradient. Exact nonlinear steady and time-dependent solutions are obtained. The general steady theory is illustrated for a non-parallel equatorward flow that possesses a single along-slope grounding along the upslope flank of the current (complementing previous work). Four specific nonlinear time-dependent solutions are described. Two initial-value problems are solved exactly. The first initial configuration corresponds to an equatorward abyssal flow that has no cross-slope shear in the along-slope velocity and possesses a single grounding along the upslope flank of the current. The nonlinear time-dependent evolution of this initial current into a non-parallel shear flow is described. The second initial condition corresponds to an isolated radially symmetric grounded abyssal pool or dome. The nonlinear time-dependent evolution of this abyssal dome, which propagates equatorward with unsteady along- and cross-slope velocities while deforming into an elliptically shaped abyssal dome with $\unicode[STIX]{x1D6FD}$-induced diminishing height, is described. Finally, the nonlinear time-dependent boundary-value problem can be solved exactly in which the in-flow boundary condition on the poleward boundary of the mid-latitude domain corresponds to a time-dependent abyssal current with both an upslope and downslope grounding. Two specific time-dependent boundary conditions are examined. The first corresponds to a time-limited surge in the equatorward volume transport in the abyssal current along the poleward boundary. The second configuration corresponds to the nonlinear evolution of a finite-amplitude downslope plume or loop that forms in the abyssal current that is reminiscent of those seen in baroclinic instability simulations.

The Meridional Flow of Source-Driven Abyssal Currents in a Stratified Basin with Topography. Part II: Numerical Simulation

A numerical simulation is described for source-driven abyssal currents in a 3660 km × 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 β plane. The source region is a fixed 75 km × 150 km area located in the northwestern sector of the basin with a steady downward volume transport of about 5.6 Sv (Sv ≡ 106 m3 s−1) corresponding to an average downwelling velocity of about 0.05 cm s−1. 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−1. The upper layer cyclonic circulation intensifies in the source region with speeds about 4 cm s−1, 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−1. 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−1. 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 β 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.

Finite-Amplitude Baroclinic Instability of Time-Varying Abyssal Currents

The weakly nonlinear baroclinic instability characteristics of time-varying grounded abyssal flow on sloping topography with dissipation are described. Specifically, the finite-amplitude evolution of marginally unstable or stable abyssal flow both at and removed from the point of marginal stability (i.e., the minimum shear required for instability) is determined. The equations governing the evolution of time-varying dissipative abyssal flow not at the point of marginal stability are identical to those previously obtained for the Phillips model for zonal flow on a β plane. The stability problem at the point of marginally stability is fully nonlinear at leading order. A wave packet model is introduced to examine the role of dissipation and time variability in the background abyssal current. This model is a generalization of one introduced for the baroclinic instability of zonal flow on a β plane. A spectral decomposition and truncation leads, in the absence of time variability in the background flow and dissipation, to the sine–Gordon solitary wave equation that has grounded abyssal soliton solutions. The modulation characteristics of the soliton are determined when the underlying abyssal current is marginally stable or unstable and possesses time variability and/or dissipation. The theory is illustrated with examples.