**6. Conclusion**

158 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

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

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

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

process.

real ocean.

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

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heating and contracts at a low-pressure surface in polar regions because of cooling. Therefore, mechanical work outside (i.e. kinetic energy) is generated and the circulation is maintained. The results suggest that abyssal circulation can be regarded as a heat engine, which does not contradict Sandström's theorem.
