Bryan, K., 1969: Climate and the ocean circulation climate and the ocean circulation III. The ocean model. Monthly Weather Review, 97 (11), 806-827.

Abstract: The ocean model used in a calculation of the earth's climate is described in detail. Compared with earlier numerical models used in ocean circulation studies, the present model includes several new features. Temperature and salinity are treated separately. Density is calculated with an accurate equation of state for sea water. The model also includes a method for calculating the growth and movement of sea ice.
Due to the very slow adjustment of the deep water in the ocean model, a numerical integration extending over the equivalent of a century fails to reach a climatic equilibrium. At the termination of the run, the surface layers of the ocean show little change with respect to time, but the average heating rate for the ocean as a whole is 2 degrees per century. The salinity patterns at the termination of the run are highly realistic compared to observations. A halocline forms in the Arctic Zone and a surface salinity maximum is present in the subtropics. A weak salinity minimum at a depth of 1 km indicates an extensive water mass very similar to the Antarctic intermediate water of the Southern Hemisphere. Poleward heat transport is found to be closely related to the intensity of the thermohaline circulation. A vertical mixing coefficient, k, of 1.5 cm² sec^-1 leads to a very reasonable heat exchange with the atmosphere based on estimates of the heat balance of the North Atlantic.
The calculation indicates that the thermal "relaxation" time of the ocean is too long for a numerical integration of the time-dependent equations to be a practical method of finding an equilibrium solution, and new methods should be sought for future calculations of this type.