An Application of a Diffusive Reduced-Gravity Model to Deep Circulation above Various Forms of Bottom Topography

Abstract

A diffusive reduced-gravity model is applied to the deep circulation over a diversity of idealized bottom topography such as a basinwide uniform slope, a Gaussian sea mountain, or their complex. Although different circulations are generated by different forms or locations of bottom topography, a perturbation method with respect to the height of topography enables one to systematically interpret how these kinds of bottom topography modify the basic circulation on a flat bottom (the Stommel?Arons scheme). For instance, a slope deepening westward rotates a northeastward deep flow in the Stommel?Arons scheme eastward, whereas the opposite slope rotates the deep flow northward. Accordingly, it is the orientation of the slope that steers the deep flow rather than hypsometry. On the other hand, topography like a sea mountain forces a dipolar distribution of stretching along the basic flow without a sea mountain or a depression. This dipolar forcing turns out to induce two regimes of the circulation depending on how parallel or how perpendicular the direction of the basic flow is to contours of ambient potential vorticity above topography: the parallel regime causes low (high) pressure confined above a sea mountain (depression); the perpendicular regime generates low pressure extending westward along contours of ambient potential vorticity for both signs of the topography. The situation appears to be much more complicated above a region of a random ensemble of mountains and depressions. When averaged locally, however, the basin-scale circulation reduces to the Stommel?Arons scheme to the first order of approximation, leaving weak second-order low pressure above random topography accompanied by high pressure westward. These features of circulation over random topography are shown to agree well with that calculated from a dipole moment of topography-induced stretching. That is, no detailed information except the dipole moment of topography is necessary for understanding its effects on the basin-scale circulation.