Mixing and energetics of the oceanic thermohaline circulation

Using an idealized tube model and scaling analysis, the physics supporting the oceanic thermohaline circulation is examined. Thermal circulation in the tube model can be classified into two categories. When the cooling source is at a level higher than that of the heating source, the thermal circulation is friction-controlled; thus, mixing is not important in determining the circulation rate. When the cooling source is at a level lower than that of the heating source, the circulation is mixing controlled; thus, weak (strong) mixing will lead to weak (strong) thermal circulation. Within realistic parameter regimes the thermohaline circulation requires external sources of mechanical energy to support mixing in order to maintain the basic stratification. Thus, the oceanic circulation is only a heat conveyor belt, not a heat engine. Simple scaling shows that the meridional mass and heat fluxes are linearly proportional to the energy supplied to mixing. The rate of tidal dissipation in the open oceans (excluding the shallow marginal seas) is about 0.9-1.3 (X10(12) W); the rate of potential energy generated by geothermal heating is estimated to be 0.5 X 10(12) W. Accordingly, the global-mean rate of mixing inferred from oceanic climatological data is about 0.22 X 10(-4) m(2) s(-1). Using a primitive equation model, numerical experiments based on a fixed energy source for mixing have been carried out in order to test the scaling law. In comparison with models under fixed rate of mixing, a model under a fixed energy for mixing is less sensitive to changes in the forcing conditions due to climatic changes. Under a surface relaxation condition for temperature and standard parameters, the model is well within the region of Hopf bifurcation, so decadal variability is expected.