**5. Discussion – Sandström theorem and abyssal circulation**

As stated in section 1.5, Sandström suggested that a closed steady circulation can only be maintained in the ocean if the heating source is located at a higher pressure (i.e. a lower level) than that of the cooling source. Therefore, he suggested that the oceanic circulation is not a heat engine.

Huang (1999) showed using an idealized tube model and scaling analysis that when the heating source is at a level that is higher than the cooling source such as the real ocean, the circulation is mixing controlled, and in the contrary case, the circulation is frictioncontrolled. He also suggested that, within realistic parameter regimes, the circulation requires external sources of mechanical energy to support mixing to maintain basic stratification. Consequently, oceanic circulation is only a heat conveyer, not a heat engine.

Yamagata (1996) reported that the oceanic circulation can be driven steadily as a heat engine only with great difficulty, considering the fact that the efficiency as a heat engine of the

Thermodynamics of the Oceanic General Circulation –

(1996) might be right on target.

improvements of observational instruments.

**6. Conclusion** 

Is the Abyssal Circulation a Heat Engine or a Mechanical Pump? 159

overturning is feasibly a convective one. Therefore, they suggested that there might be no need to search for "missing mixing." As stated in section 1.4, the idea of the ocean as "mechanical pump" was the idea derived to solve the "missing mixing" problem: the "mechanical pump" was introduced as another new mechanism of diapycnal mixing to maintain abyssal circulation. If their conclusion is correct in the real ocean, then the assumption of a "mechanical pump" (i.e. "missing mixing") is not necessary. Small

It is possible that the idea of the ocean as a "heat engine" is not fully contradicted by the idea of the ocean as a "mechanical pump": it can be considered that a circulation driven as a "heat engine" is strengthened by a pump-up flow driven as a "mechanical pump". In a sense, the idea of a mixture of buoyancy processes and mechanical processes by Yamagata

As stated in section 1.3, although recent observations of turbulence show large diapycnal mixing, such observations are limited to a few locations. It is not clear how much is the value of diapycnal mixing averaged in the entire ocean. Although global mapping of diapycnal diffusivity based on expendable current profiler surveys has been tried (Hibiya et al., 2006), the observed places remain limited. To verify the thermodynamic structure of the oceanic general circulation suggested in this chapter, the entire structure of adiabatic heating and cooling should be resolved. Particularly, observations of the following are recommended: 1) the structure of turbulent heat transfer into the intermediate layer because of forced mixing by wind stress at the surface and the resultant adiabatic heating in the equatorial region, 2) the process of adiabatic cooling confined to the surface and the subsequent concentrated sinking in the polar regions. In addition, direct observations of sinking and upwelling, not inferred from other observations, are important because the inferred value might include the effects of assumptions and errors. The observation of sinking is difficult because of severe climates in polar winter, with the worst conditions occurring when the sinking occurs. Moreover, observation of the upwelling itself is extremely difficult because of the low velocity. Future challenges must include technical

This chapter presented discussion of the problem of whether the abyssal circulation is a heat engine or a mechanical pump. We also discussed how it is related to the Sandström theorem, referring to results of numerical simulations of the oceanic general circulation. The results obtained using our model show high-entropy production due to turbulent diapycnal diffusion down to 1000 m in the entire equatorial region (<30 deg). By contrast, diapycnal diffusion at high latitude is very small and is confined to the surface: the region of adiabatic heating at low latitudes extends into the deeper layer (i.e. a higher pressure), but the region of adiabatic cooling at high latitudes is confined to the surface (i.e. lower pressure). In this case, Sandström's theorem is not violated. In the equatorial region, the flow structure consisting of equatorial undercurrents and intermediate currents is organized such that forced mixing by wind stress at the surface accelerates turbulent heat transfer into the deeper layer. However, in polar regions, forced mixing by wind stress at the surface does not reach the deeper layer, and adiabatic cooling is confined to the surface. Consequently, seawater expands at a high-pressure intermediate layer in the equatorial region because of

"background" diapycnal mixing might be sufficient to maintain abyssal circulation.

oceanic circulation calculated heating and cooling sources at the sea surface is very low, in addition to a view of Sandström's theorem. He therefore concluded that the oceanic circulation might not be driven steadily as a heat engine, but that it shows closed circulation by transferral to mechanically driven (e.g. wind-driven) flow on the way: the oceanic circulation might be sustained with a mixture of the buoyancy process and mechanical process.

However, these arguments are based on the assumption that the heating source is located only at the sea surface. If a diabatic heating because of turbulent diffusion takes place in the ocean interior (and the cooling source is placed at the sea surface), then Sandström's theorem is not violated. The important quantity in this respect is diapycnal diffusion, as stated in section 1, which corresponds to *Az* in our model. As stated in section 4, *A*z in our model showed high entropy production attributable to turbulent diapycnal diffusion down to 1000 m in the whole equatorial region (<30 deg). By contrast, the diapycnal diffusion at high latitude is very small and is confined to the surface in Fig. 5(j). Although there also exists dissipation caused by convective adjustment in the polar region, it can be negligible as the regional average: the region of adiabatic heating at low latitudes extends into the deeper layer (i.e. a higher pressure), but the region of adiabatic cooling at high latitudes is confined to the surface (i.e. a lower pressure). These results support the inference described above. In addition, the real ocean is also affected by dynamic interaction among tides, topography, and the resultant diabatic heating, which has not been considered in our model.

Moreover, the inference is supported by some experimental studies that the circulation is possible if external heating and cooling are placed at the same level (Park & Whitehead, 1999), or even if external heating is placed at a higher level than external cooling (Coman et al. 2006). Coman et al. (2006) reported that heat diffusion (whether by molecular conduction or turbulent mixing) allows heat to enter and leave the fluid at the boundary and causes the heating to be distributed throughout at least the depth of the boundary layer. Warmed water ascends towards the surface after having warmed and expanded at higher pressures than the surface pressure. Positive work is available from the heating and cooling cycle, even when the heating source is above the cooling source. Therefore, they concluded that Sandström theorem cannot be used to discount the formation of a deep convective overturning in the oceans by the meridional gradient of surface temperature or buoyancy forcing suggested by Jeffreys (1925). In addition, the driving force of the circulation in these experiments is only internal diabatic heating by molecular conduction or turbulent diffusion: the real ocean includes stronger diabatic heating due to external forcing of wind and tide, as explained in sections 1.2 and 1.3. In the equatorial region, the flow structure consisting of equatorial undercurrents and intermediate currents is organized such that forced mixing by wind stress at the surface accelerates turbulent heat transfer into the deeper layer. However, in the polar regions, forced mixing by wind stress at the surface does not reach the deeper layer, and adiabatic cooling is confined to the surface. For that reason, seawater expands at the high-pressure intermediate layer in the equatorial region because of heating and contracts at the low-pressure surface in the polar regions because of cooling. Consequently, mechanical work outside (i.e. kinetic energy) is generated and the circulation is maintained. The above inference will be strengthened in consideration of the real ocean.

Using numerical simulations, Hughes & Griffiths (2006) showed that by including effects of turbulent entrainment into sinking regions, the model convective flow requires much less energy than Munk's prediction. Results obtained using their model indicate that the ocean overturning is feasibly a convective one. Therefore, they suggested that there might be no need to search for "missing mixing." As stated in section 1.4, the idea of the ocean as "mechanical pump" was the idea derived to solve the "missing mixing" problem: the "mechanical pump" was introduced as another new mechanism of diapycnal mixing to maintain abyssal circulation. If their conclusion is correct in the real ocean, then the assumption of a "mechanical pump" (i.e. "missing mixing") is not necessary. Small "background" diapycnal mixing might be sufficient to maintain abyssal circulation.

It is possible that the idea of the ocean as a "heat engine" is not fully contradicted by the idea of the ocean as a "mechanical pump": it can be considered that a circulation driven as a "heat engine" is strengthened by a pump-up flow driven as a "mechanical pump". In a sense, the idea of a mixture of buoyancy processes and mechanical processes by Yamagata (1996) might be right on target.

As stated in section 1.3, although recent observations of turbulence show large diapycnal mixing, such observations are limited to a few locations. It is not clear how much is the value of diapycnal mixing averaged in the entire ocean. Although global mapping of diapycnal diffusivity based on expendable current profiler surveys has been tried (Hibiya et al., 2006), the observed places remain limited. To verify the thermodynamic structure of the oceanic general circulation suggested in this chapter, the entire structure of adiabatic heating and cooling should be resolved. Particularly, observations of the following are recommended: 1) the structure of turbulent heat transfer into the intermediate layer because of forced mixing by wind stress at the surface and the resultant adiabatic heating in the equatorial region, 2) the process of adiabatic cooling confined to the surface and the subsequent concentrated sinking in the polar regions. In addition, direct observations of sinking and upwelling, not inferred from other observations, are important because the inferred value might include the effects of assumptions and errors. The observation of sinking is difficult because of severe climates in polar winter, with the worst conditions occurring when the sinking occurs. Moreover, observation of the upwelling itself is extremely difficult because of the low velocity. Future challenges must include technical improvements of observational instruments.
