This two-part paper considers the general circulation of the atmosphere (Part 1) and ocean (Part 2) within the deductive framework of our climate theory, which aims to derive the earth’s generic climate state from first principles. Because the planetary fluids are inherently turbulent, such state is a macroscopic manifestation of a nonequilibrium thermodynamic system, whose closure involves the maximum entropy production, a veritable generalization of the second fundamental law. The logical progression detailed in the preceding papers of the theory has reduced the planetary fluids to warm and cold thermal masses and determined their bulk properties, which provide the prior constraints for the present dynamical derivation. Consistent with the asymptotic thermal state, we assume the potential vorticity (PV) to be homogenized in thermal masses to derive the upper-bound general circulations. In Part 1, this upper bound is seen to resemble the prevailing wind, forsaking therefore discordant explanations of the easterly trades and the polar jet stream. In this Part 2, we show again that this upper-bound may reproduce the observed general ocean circulation, suggesting that the latter may be explained by PV mixing — in place of the laminar Sverdrup dynamics. Together with Part 1, we posit that the general planetary circulations are the maximum flow extractable by random eddy mixing when subjected to differential solar heating.