measurements; both give information about the broad outlines of the thermohaline circulation. The thermohaline circulation is characterized by extremely small velocities (especially vertical velocity), so direct measurement of the THC is impossible. Analytic and numerical models have therefore played a major role in our approach to understanding the THC. In particular, simple three-dimensional coarse-resolution sector models of the dynamics of the THC forced by steady mixed-boundary conditions (pioneered by F. Bryan, 1986a, 1986b) have begun to contribute a great deal to our understanding of the mean and variable THC.
Sector models contain the rudimentary dynamics needed to model the THC and its variability in a simplified context that allows many numerical experiments to be performed. On the other hand, the applicability of these simplified-model results to the real ocean will always be in question until they have been confirmed by experiments using more complex models with higher resolution, realistic geography and topography, and coupling to the cryosphere. Even then, the applicability of more complex forced ocean models to climate will be in doubt unless realistic, interactive coupling to the atmosphere can take place as well. (Fully coupled global atmosphere-ocean models are the ultimate tool for understanding the climate, but at present they are so expensive and complicated that they can be run only at a very small number of institutions.)
Coarse-resolution sector models have been used to investigate decadal and longer-term variability under steady mixed boundary conditions (see Weaver (1995), in this section, for a review and references). In sector models with two hemispheres, equatorially symmetric restoring boundary conditions on both temperature and salinity bring about a symmetric circulation with a sinking motion in the high latitudes of each hemisphere and a rising one at the equator. Upon a switch to mixed boundary conditions (restoring on temperature but with fluxes for fresh-water) asymmetric pole-to-pole circulations arise, with sinking in one hemisphere and rising in the other (F. Bryan, 1986b; Weaver and Sarachik, 1991a). With mixed boundary conditions (Weaver and Sarachik, 1991a), a transient chaotic state develops (in which symmetric circulations sometimes, though rarely, occur) that ultimately leads to a single asymmetric pole-to-pole steady-state circulation.
This paper presents a simplified model for investigating a more realistic geometry—one with a circumpolar current in one (the southern) hemisphere—in a sector context. Following a brief description of the model, the steady-state thermohaline circulations under restoring boundary conditions for both temperature and salinity are discussed, and then the variability of the model's physical quantities with a switch to mixed boundary conditions.
The model used in the experiments described below is the Modular Ocean Model (MOM), a modular form of the Cox (1984) version of the Bryan-Cox Ocean General Circulation Model. The latter is a full primitive-equation model (in spherical coordinates) described by Bryan (1979) and Bryan and Lewis (1979). The MOM employs the finite-difference scheme described by Bryan (1969) and Cox (1984), and the polynomial approximation to the UNESCO equation of state described by Bryan and Cox (1972). We use a coarse horizontal resolution of 4° in latitude by 3.75° in longitude. The basin extends from 72°S to 72°N and is bound by meridians separated by 56.25° of longitude. A single re-entrant channel extends longitudinally 3.75° and latitudinally from 64°S to 48°S, and from the surface to a sill at approximately 2500 m depth. The basin depth ramps down from the sill depth to its full depth of 5000 m in the three grid spaces surrounding the channel opening, both to the north and south and to the east and west, and is uniformly 5000 m elsewhere. Vertical resolution is in 20 levels, so that numerical problems involving spurious circulations are avoided (Weaver and Sarachik, 1991a).
Cyclic boundary conditions are applied to the meridional boundaries at the slot, creating the re-entrant channel. Coarse-resolution models present difficulties in representing straits and narrow and silled channels. The B-grid used in the Cox-Bryan model requires a channel width of at least two tracer grid points to define one velocity point within the channel. As discussed in Toggweiler et al. (1989), the horizontal viscosity required to define boundary currents prevents a realistic flow from occurring in a channel that contains only one velocity point. We therefore create a re-