Modelling the ocean thermohaline circulation in the laboratory
Ross W. Griffiths 1 , Graham O. Hughes 1 , Melissa A. Coman 1 , Julia C. Mullarney 2
1 Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia
2 Department of Oceanography, Dalhousie University , Halifax , NS ?????, Canada
We have developed a new theoretical model for the ocean overturning circulation and shown that the theory works well when tested against laboratory experiments. We have also examined the nature of circulation changes that may occur when heat and freshwater fluxes across the ocean surface change, as expected owing to global warming. The global meridional overturning circulation of the oceans (otherwise known as the thermohaline circulation) is forced by density differences owing to heat and water fluxes at the sea surface, wind stress on the surface and injections of energy into turbulent mixing from the winds and tides. In our approach we examine the extent to which the density differences and interior turbulent mixing together, but in the absence of large-scale wind stresses, could force the overturning.
As outlined in a key paper last year (Hughes and Griffiths 2005) our calculations show that, after taking account of the behaviour of cold, dense currents sinking from localized surface regions to large depths in the oceans along gentle bottom slopes under the influence of Coriolis forces, the buoyancy-forced flow can account for a number of key features of the observed circulation: using the estimated poleward heat transport and the measured average interior vertical mixing rate we successfully predicted the top to bottom density difference, the dilution of dense currents by a factor of around three as they sink, the rate of formation of Antarctic Bottom Water (AABW) and North Atlantic Deep Water (NADW), and the thickness of the subtropical thermocline. Thus a simple model can provide powerful insights into the dynamics of the oceans. We concluded that substantially less energy than previously proposed for turbulent mixing is required for a convective circulation to be of the observed magnitude, partially as a result of turbulent entrainment into the dense sinking currents. This year we have modified the theory to describe laboratory experiments with this form of convective circulation (often termed “horizontal convection” by virtue of the forcing at only the horizontal sea surface). A detailed comparison of our own laboratory data from previous years with this theory has been outstandingly successful and provides a new explanation for the heat flux-Rayleigh number relationship, boundary layer thickness and overturning rate in terms of inviscid dynamics of the sinking currents and interior flow (Hughes et al . 2006).
One remaining difficulty is that the model in its simplest form predicts an abyssal ocean density gradient much smaller than measured. A PhD student, Ms Coman, has used further experiments to examine the possibility that dual sinking regions, one in either hemisphere and generating waters of different density (the AABW and NADW) may produce a larger abyssal gradient (figure 3). This notion is born out by the results, but the effect is apparently not large enough to explain the ocean stratification and other factors will be explored in the coming year.
In other experiments the convective circulation was brought to its equilibrium (steady) state and then the surface boundary conditions were changed, so as to mimick climate changes such as a warming or increased freshwater inflow in high latitude oceans, or a change in the radiative heat input in the subtropics. These changes disturb the balance within the circulation. For example, a cooling in the subtropical ocean leads to a temporary strengthening of the overturning, more vigorous sinking of colder water and an exponential adjustment to a new equilibrium much the same as the initial state (figure 4). The measured exponential timescale is easily predicted from a simple theory. On the other hand, a surface warming can lead to a shutdown of the deep sinking and the circulation quickly becomes confined to a shallow upper ocean layer around twice the thickness of the thermocline (figure 5). This state of shallow overturning is temporary. After a long period (several times the exponential timescale mentioned above) the circulation evolves through a period of large oscillations in the depth of convection, to the initial state of full-depth overturning.
All of this work examines the fundamental dynamics of convective overturning, and ultimately examines the role of such convection in the global circulation. An important role for convection has not always been accepted, in part because it was ruled out by Sandstrom's theorem, a postulate drawn from experiments carried out at the beginning of the twentieth century and still referred to today. However, this theorem is in conflict with modern experiments. We therefore re-created those early experiments (Coman et al . 2006) and concluded that Sandstrom's report, hence the theorem, are incorrect: heating and cooling sources on the same geopotential surface do drive a persistent recirculation. Most of our experiments have been carried out in non-rotating tanks. However, the role of Coriolis accelerations is being studied in a series of runs in which the carefully designed convection apparatus sits on a precision rotating platform. The flow with rotation is far more complicated and three-dimensional, and is rich in wave and vortex motions, but is less readily scaled to ocean conditions.
Figure 3. A photograph of dye in the convective overturning when a larger heat flux is applied to the left hand side of the base of a box, a weaker heat flux is applied to the right hand side of the base, and the central section of the base is cooled such that there is no net heat input. I this example the right hand plume drives a shallow cell, and its water (blue) is eventually entrained into the stronger plume at left and cycled throughout the box.
Figure 4. Overturning driven by heating the left half of the base of a box and cooling the right half of the base. The photograph was taken shortly after the temperature of the heating base was increased by a small amount.
Figure 5. Photographs of the evolution of overturning as in figure 2, but after the temperature of the base at the right was decreased. The flow evolves through a period of shallow convection before returning to a state of full-depth overturning.
References: Hughes, G.O. and Griffiths, R.W. (2005) A simple convective model of the global overturning circulation, including effects of entrainment into sinking regions. Ocean Modelling 12 , 46-79 (doi:10.1016/j.ocemod.2005.04.001).
Hughes, G.O. Griffiths, R.W., Mullarney, J.C. and Peterson, W.H. (2006) A theoretical model for horizontal convection at large Rayleigh number. J. Fluid Mech ., in press, accepted July 2006.
Coman, M.A., Griffiths, R.W. and Hughes, G.O. Sandstrom's experiments revisited. (2006) J.Marine Res ., in press, accepted October 2006.