**1.2 Energy sources of abyssal circulation**

Sustained abyssal circulation is a manifestation of conversion of potential energy to kinetic energy within the system. Production of potential energy is mainly the result of diapycnal mixing in the ocean interior, geothermal heating through the ocean floor, and the meridional distribution of precipitation, evaporation, and runoff (e.g., Gade & Gustafsson, 2004).

Diapycnal mixing results from turbulent diffusion by wind and tides. The most reasonable mechanism to transfer energy from the surface to the deeper layer is regarded as breaking and wave–wave interaction of internal waves generated by wind and tides (e.g., Muller & Briscoe, 2000). The wind and tidal dissipation quantities have been estimated respectively as about 1 TW (Wunsch, 1998) and 1 TW (Egbert & Ray, 2000). Using these estimates and *R*f = 0.15 (Osborn, 1980) as the flux Richardson number, γ= *R*f/(1-*R*f)=0.18 as the ratio of potential energy to available energy, and *S*=3.6 × 1014 m2 as the total surface area of the ocean, the production of potential energy caused by diapycnal mixing has been estimated as about 1.0 × 10-3 W m-2 (=2TW/(3.6 × 1014 m2) × 0.18).

Geothermal heating through the ocean floor causes a temperature increase and a thermal expansion in seawater, and generates potential energy. Production of potential energy caused by geothermal heating has been estimated as about 0.11 (Gade & Gustafsson, 2004) - 0.14 (Huang, 1999) × 10-3 W m-2.

Precipitation (evaporation) is a flux of mass to (from) the sea surface and consequently a flux of potential energy. On average, the warm (cold) tropics with high (low) sea level are regions of evaporation (precipitation). These therefore tend to reduce the potential energy. The value integrated for the entire ocean shows a net loss of potential energy. Loss of potential energy attributable to precipitation, evaporation, and runoff has been estimated as less than 0.02 (Gade & Gustafsson, 2004) – 0.03 (Huang, 1998) × 10-3 W m-2. These contributions can be negligible.

In addition, there can be work done on the ocean by surface heating and cooling. Heating (cooling) causes an expansion (contraction) with a net rise (fall) in the centre of mass and an increase (decrease) in potential energy. The exact estimate of the effect is difficult, but it will be small compared to the effect of the wind forcing. The best recent estimate of work done on the ocean by surface heating and cooling is zero (Wunsch & Ferrari, 2004).
