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Application of classical thermodynamic principles to the study of oceanic overturning circulation

Stationary deep-reaching overturning circulation in the ocean is studied by means of classical thermodynamic methods employing closed cycles in pV-space (p, pressure; V, volume). From observed (or computed) density fields, the pV-method may be used to infer the power required for driving a circulation with a given mass flux, or, if the available power is known, the resulting mass flux of the circulation may be assessed. Here, the circulation is assumed to be driven by diapycnal mixing caused by internal disturbances of meteorological and tidal origin and from transfer of geothermal heat through the ocean bottom. The analysis is developed on the basis that potential energy produced by any of these mechanisms is available for driving a circulation of the water masses above its level of generation. The method also takes into account secondary generated potential energy resulting from turbulence developed by the ensuing circulation. Models for different types of circulation are developed and applied to four types of hemispheric circulation with deepwater formation, convection and sinking in an idealized North Atlantic. Our calculations show that the energy input must exceed 15 J kg—1 for a cycle to the bottom to exist. An energy supply of 2 TW would in that case support a constant vertical mass flux of 3.2 G kg s—1 (3.1 Sv). Computed mass fluxes reaching the surface in the subtropics, corresponding to the same energy input, range between 2.3–5.2 G kg s—1, depending on the type of convection/sinking involved. Much higher flux values ensue with ascending water masses reaching the surface at higher geographical latitudes. The study reveals also that compressibility of sea water does not enhance the circulation. An incompressible system, operating within the same mass flux and temperature range, would require about 25% less energy supply, provided that the circulation comprises the same water masses. It is furthermore shown that the meridional distribution of surface salinity, with higher values in the tropics and lower values in regions of deep-water formation, actually enhances the circulation in comparison with one of a more uniform surface salinity. With a homohaline North Atlantic, operating within the same temperature range as presently observed, an increase of 66% of power supply would be required in order that the mass flux of the overturning circulation should remain the same.