**1.6 Principle of maximum entropy production and oceanic general circulation**

In this sub-section, we briefly explain another important thermodynamic postulate of stability of a nonlinear non-equilibrium system such as the oceanic general circulation, the principle of the maximum Entropy Production and consider the stability of oceanic general circulation from a global perspective because local processes of generation and dissipation of kinetic energy in a turbulent medium remain unknown.

The ocean system can be regarded as an open non-equilibrium system connected with surrounding systems mainly via heat and salt fluxes. The surrounding systems consist of the atmosphere, the Sun and space. Because of the curvature of the Earth's surface and the inclination of its rotation axis relative to the Sun, net gains of heat and salt are found in the equatorial region; net losses of heat and salt are apparent in polar regions. The heat and salt fluxes bring about an inhomogeneous distribution of temperature and salinity in the ocean system. This inhomogeneity produces the circulation, which in turn reduces the inhomogeneity. In this respect, the formation of the circulation can be regarded as a process leading to final equilibrium of the whole system: the ocean system and its surroundings. In this process, the rate of approach to equilibrium, i.e., the rate of entropy production by the oceanic circulation, is an important factor.

Related to the rate of entropy production in an open non-equilibrium system, Sawada (1981) reported that such a system tends to follow a path of evolution with a maximum rate of entropy production among manifold dynamically possible paths. This postulate has been called the principle of Maximum Entropy Production (MEP), which has been confirmed as valid for mean states of various nonlinear fluid systems, e.g., the global climate system of the Earth (Ozawa & Ohmura, 1997; Paltridge, 1975, 1978), those of other planets (Lorenz et al., 2001), the oceanic general circulation including both surface and abyssal circulations (Shimokawa, 2002; Shimokawa & Ozawa, 2001, 2002, 2007), and thermal convection and shear turbulence (Ozawa et al., 2001). Therefore, it would seem that MEP can stand for a

Thermodynamics of the Oceanic General Circulation –

Is the Abyssal Circulation a Heat Engine or a Mechanical Pump? 153

Fig. 3. (a) Model domain, and forcing fields of the model as functions of latitude, (b) forced

Fig. 4. The zonally integrated meridional stream function at years (a) 100, (b) 1000, (d) 2000, (e) 3000, (d) 4000, and (e) 5000 after starting the numerical calculations. The contour line interval is 2 SV (106 m3 s-1). The circulation pattern reached a statistically steady-state after

zonal wind stress (N m-2) defined as positive eastward, (c) prescribed sea surface

temperature (oC), and (d) prescribed sea surface salinity (‰).

year 4000.

universal principle for time evolution of non-equilibrium systems (see reviews of Kleidon and Lorenz, 2005; Lorenz, 2003; Martyushev & Seleznev, 2006; Ozawa et al., 2003; Whitfield, 2005). However, although some attempts have been made to seek a theoretical framework of MEP (e.g., Dewar, 2003, 2005), we remain uncertain about its physical meaning.
