Boundary mixing is implemented in an ocean general circulation model such that the vertical mixing coefficient ky is nonzero only near side boundaries and in convection regions. The model is used in a highly idealized configuration with no wind forcing and very nearly fixed surface density to investigate the three-dimensional dynamics of the thermohaline circulation. For ky 5 20 3 1024 m2 s21 and lower, the meridional overturning strength to great accuracy is proportional to ; meridional heat transport is proportional to . The circulation 2/3 1/2 kk y y patterns resemble those from runs with uniform vertical mixing, but vertical motion is entirely confined to the boundary regions. Near the western boundary, there is upwelling everywhere. Near the eastern boundary, there is a consistent pattern of downwelling above upwelling, with downwelling reaching deeper at high latitudes; this pattern is explained by convection and vertical advective‐diffusive balance underneath. For ky 5 30 3 1024 m2 s21 and higher, no steady solutions have been found; the meridional overturning oscillates on a timescale of about 25 years. A time-averaged thermally direct overturning cell is not supported dynamically because convection extends longitudinally across the entire basin, and upwelling near the western boundary does not lead to densities higher than at the eastern boundary. Assuming uniform upwelling in the west, level isopycnals near the equator, and level isopycnals along the eastern boundary south of the outcropping latitude permits the analytic determination of convection depth at the eastern wall and hence the density difference between the eastern and western walls. This difference is at most one-quarter the surface density difference between high and low latitudes, and agrees in magnitude and latitudinal dependence with the numerical experiments. Scaling arguments estimate overturning strength as of the order of 10 3 106 m3 s21 and confirm the 2/3 power dependence onky. The derivation also gives a dependence of overturning strength with latitude that agrees qualitatively with the numerical results. The scaling for the dependence of meridional heat transport on latitude agrees well with the model results; scaling for heat transport amplitude agrees less well but correctly predicts a weaker dependence on ky than maximum overturning.

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Boundary Mixing and the Dynamics of Three-Dimensional Thermohaline Circulations

The structure and dynamics of the large-scale circulation of a single-hemisphere, closed-basin ocean with small diapycnal diffusion are studied by numerical and analytical methods. The investigation is motivated in part by recent differing theoretical descriptions of the dynamics that control the stratification of the upper ocean, and in part by recent observational evidence that diapycnal diffusivities due to small-scale turbulence in the ocean thermocline are small (-0.1 cm2 s-i). Numerical solutions of a computationally efficient, three-dimensional, planetary geostrophic ocean circulation model are obtained in a square basin on a mid-latitude B-plane. The forcing consists of a zonal wind stress (imposed meridional Ekman flow) and a surface heat llux proportional to the difference between surface temperature and an imposed air temperature. For small diapycnal diffusivities (vertical:

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Large-scale circulation with small diapycnal diffusion: The two-thermocline limit

The combined effects of wind, geometry, and diffusion on the stratification and circulation of the ocean are explored by numerical and analytical methods. In particular, the production of deep stratification in a simply configured numerical model with small diffusivity is explored. In the ventilated thermocline of the subtropical gyre, the meridional temperature gradient is mapped continously to a corresponding vertical profile, essentially independently of (sufficiently small) diffusivity. Below this, as the vertical diffusivity tends to zero, the mapping becomes discontinuous and is concentrated in thin diffusive layers or internal thermoclines. It is shown that the way in which the thickness of the main internal thermocline (i.e., the diffusive lower part of the main thermocline), and the meridional overturning circulation, scales with diffusivity differs according to the presence or absence of a wind stress. For realistic parameter values, the ocean is in a scaling regime in which wind effects are important factors in the scaling of the thermohaline circulation, even for the single hemisphere, flat-bottomed case. It is shown that deep stratification may readily be produced by the combined effects of surface thermodynamic forcing and geometry. The form of the stratification, but not its existence, depends on the diffusivity. Such deep stratification is efficiently produced, even in single-basin, single-hemisphere simulations, in the presence of a partially topographically blocked channel at high latitudes, provided there is also a surface meridional temperature gradient across the channel. For sufficiently simple geometry and topography, the abyssal stratification is a maximum at the height of the topography. In the limit of small diffusivity, the stratification becomes concentrated in a thin diffusive layer, or front, whose thickness appears to scale as the one-third power of the diffusivity. Above and below this diffusive abyssal thermocline are thick, largely adiabatic and homogeneous water masses. In two hemisphere integrations, the water above the abyssal thermocline may be either ‘‘intermediate’’ water from the same hemisphere as the channel, or ‘‘deep’’ water from the opposing hemisphere, depending on whether the densest water from the opposing hemisphere is denser than the surface water at the equatorward edge of the channel. The zonal velocity in the channel is in thermal wind balance, thus determined more by the meridional temperature gradient across the channel than by the wind forcing. If the periodic channel extends equatorward past the latitude of zero wind-stress curl, the poleward extent of the ventilated thermocline, and the surface source of the mode water, both then lie at the equatorial boundary of the periodic circumpolar channel, rather than where the wind stress curl changes sign.

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Large-Scale Circulation and Production of Stratification: Effects of Wind, Geometry, and Diffusion

An idealized three-dimensional model of buoyancy-driven flow in a single hemisphere is used to investigate the relationship between the meridional overturning and the efficiency by which convective mixing eliminates static instability. In the “fast” limit (mixing timescale hours to weeks), the meridional overturning is not rate limited by the efficiency of convective mixing. If convective mixing is made less efficient, the model’s meridional overturning strength increases. Moreover, the dominant downwelling occurs not at the highest surface density;hence the deep ocean is relatively buoyant. The numerical results are explained by the different influences of convective mixing and downward advection on the deep-ocean heat budget; they underscore the fundamentally three-dimensional nature of the meridional overturning. In addition, the narrowness of deep downwelling is related to the geostrophic dynamics of deep temperature anomalies near the eastern wall. The model results presented here are in con...

/pdf/convective-mixing-and-the-thermohaline-circulation-4vq95pp1qo.pdf

Convective Mixing and the Thermohaline Circulation

The large-scale consequences of diapycnal mixing location are explored using an idealized three-dimensional model of buoyancy-forced flow in a single hemisphere. Diapycnal mixing is most effective in supporting a strong meridional overturning circulation (MOC) if mixing occurs in regions of strong stratification, that is, in the low-latitude thermocline where diffusion causes strong vertical buoyancy fluxes. Where stratification is weak, such as at high latitudes, diapycnal mixing plays little role in determining MOC strength, consistent with weak diffusive buoyancy fluxes at these latitudes. Boundary mixing is more efficient than interior mixing at driving the MOC; with interior mixing the planetary vorticity constraint inhibits the communication of interior water mass properties and the eastern boundary. Mixing below the thermocline affects the abyssal stratification and upwelling profile but does not contribute significantly to the meridional flow through the thermocline or the ocean's meridio...

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Sheng Zhang

Papers

A thermocline model for ocean-climate studies