Typically, each box represents a rectangular volume several hundred kil- 

 ometers in each horizontal dimension and a few hundred meters in the 

 vertical. An average velocity vector is calculated for each box from the 

 equations of motion. No calculations are made for scales of motion less 

 than the basic cell size. The interaction of smaller scale motion with larger 

 scales is represented by Reynolds' stresses in terms of the larger scale 

 flow pattern. 



At present there is not enough empirical information on the meso- 

 scale velocity structure of the ocean to specify an optimal closure scheme. 

 MODE-I, described elsewhere in this report, should contribute to just 

 this sort of information for a typical open ocean location. As an in- 

 terim solution to this problem, closure for the world ocean model is 

 made by an eddy viscosity formulation, and numerical tests are being 

 carried out to determine the sensitivity of the results to the exact level 

 of eddy viscosity used. 



The change of temperature and salinity for each cell is computed for 

 conservation equations which have a parallel form to the Reynolds aver- 

 aged equations of motion. A detailed equation of state is used to relate 

 density to the local value of temperature and salinity. The effect of small- 

 scale motions is taken into account by an eddy diffusion of temperature and 

 salinity. If the velocity, temperature, and salinity fields are known, the mo- 

 mentum, temperature, and salinity equations determine the time change 

 of all the major variables in each cell. This allows a numerical integration 

 to be carried out to calculate the time-dependent response over the entire 

 44 ocean basin to a given set of surface boundary conditions. 



Because of the complexity of the model, its development has proceeded 

 in a step-by-step fashion. The first calculation carried out assumed that 

 the world ocean has a uniform density and the only driving force is the 

 surface wind stress. The homogeneous case provides a good test for the 

 behavior of the model, since it allows a comparison with familiar analytic 

 results from the theory of wind-driven currents. If the model is further 

 simplified by making the depth uniform, there are also several published 

 numerical calculations available for comparison, based on quite different 

 numerical methods than the present study, thus allowing an independent 

 check. 



The wind-stress field used as an upper boundary condition is shown 

 in Figure 21. The pattern of mass transport for the homogeneous case 

 with uniform depth is shown in Figure 22. The direction of flow is indi- 

 cated by small arrows. The pattern shown does not represent a complete 

 equilibrium. While the flow was steady elsewhere, the transport through 

 the Drake Passage was still increasing above the very high value of 600x 

 10" m^/sec shown. Observations indicate that the strength of the sub- 

 tropical gyres is too low and the Circumpolar Current is too high. 



In Figure 23 one sees the effect of bottom topography on the homo- 

 geneous, wind-driven world ocean. The Northern Hemisphere subtropical 

 gyres are only slightly changed. The most drastic effects are in the South- 

 ern Hemisphere, notably in the East Australian and Circumpolar Currents. 

 In contrast to the previous case, the Circumpolar Current is very weak, only 

 about 30x10" m^/sec. The Circumpolar Current is much narrower and 

 highly controlled by bottom topography. The northward excursion of the 



