**1.1 Outline of oceanic general circulation**

Oceanic general circulation is the largest current in the world ocean, making a circuit from the surface to the bottom over a few thousand years. The present oceanic general circulation, briefly speaking, is a series of flows, in which seawater sinks from restricted surface regions in high latitudes of the Atlantic Ocean to the deep bottom ocean. It later comes to broad surface regions of the Pacific Ocean, and returns to the Atlantic Ocean through the surface of the Indian Ocean (see Fig. 1). The atmosphere affects the daily weather, whereas the ocean affects the long-term climate because of its larger heat capacity. Therefore, it is important for our life to elucidate the oceanic general circulation.

The causes generating the oceanic general circulation are momentum flux by wind stress at the sea surface and density flux by heating, cooling, precipitation, and evaporation through the sea surface, except for tides. In general, the oceanic general circulation is explained as consisting of surface (wind-driven) circulation attributable to the momentum flux and abyssal (thermohaline) circulation caused by the density flux. However, the distinction between them is not simple because diapycnal mixing, which is important for abyssal circulation, depends largely on wind, as described in the next sub-section. Moreover, diapycnal mixing depends also on tides.

Thermodynamics of the Oceanic General Circulation –

deep water estimated by observations in the sinking area.

**1.4 Abyssal circulation as a heat engine or a mechanical pump** 

designated as the "missing mixing" problem.

Lorenz (1955).

**1.3 "Missing mixing" problem** 

Is the Abyssal Circulation a Heat Engine or a Mechanical Pump? 149

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

Munk (1966) estimated that the magnitude of diapycnal mixing to drive and maintain abyssal circulation is about K≈10-4 m2 s-1. He reached that figure by fitting of vertical profiles of tracers with one-dimensional vertical balance equation of advection and diffusion as

where *K* is a diapycnal mixing coefficient, *T* denotes a tracer variable such as temperature, salinity and radioactive tracers, *z* signifies a vertical coordinate, and *w* represents the upwelling velocity. The estimated value has been regarded as reasonable because the total upwelling of deep water estimated using the above *K* is consistent with the total sinking of

However, some direct observations of turbulence (Gregg, 1989) and dye diffusion (Ledwell et al., 1993) in the deep ocean indicate a diapycnal mixing of only *K*≈10-5 m2 s-1. Moreover, this is consistent with mixing estimated from the energy cascade in an internal wave spectrum (called "background") (McComas & Mullar, 1981). This difference of *K* is

On the other hand, recent observations of turbulence show larger diapycnal mixing of *K*≥10-4 m2 s-1 (Ledwell et al., 2000; Polizin et al., 1997), although such observations are limited to areas near places with large topographic changes such as seamounts (called "hot spots"), where internal waves are strongly generated as sources of diapycnal mixing. Munk & Wunsch (1998) reported that the value averaged over the entire ocean including "background" and "hot spots" can be about *K*≈10-4 m2 s-1, which remains controversial.

Traditionally, the abyssal circulation has been treated as a heat engine (or a buoyancy process) driven by an equatorial hot source and polar cold sources. Broecker & Denton (1990) reported that abrupt changes in the ocean's overturning causes the ocean's heat loss, which might engender large swings in high-latitude climate, such as that occurring during the ice age. They also suggested a descriptive image of abyssal circulation: a conveyor-belt (see Fig. 1). Peixoto & Oort (1992) investigated the atmosphere–ocean system as a heat engine using the concept of available potential energy developed by

Toggweiler (1994 ) reported that the abyssal formation in the North Atlantic is induced by upwelling because of strong surface wind stress in the Antarctic circumpolar current (a mechanical pump or a mechanical process). This mechanism is inferred from the "missing mixing" problem, as stated in section 1.3. If "background" diapycnal mixing for maintaining abyssal circulation is weaker than Munk's estimate, then another new mechanism to pump

*<sup>z</sup> <sup>z</sup>* , (1)

2 2 d d d d *T T K w*

on the ocean by surface heating and cooling is zero (Wunsch & Ferrari, 2004).

Fig. 1. Illustration of oceanic general circulation (Broecker, 1987).
