Linear Theories — Viscous 



93 



The height contours computed from this example are shown in fig. 59. To 

 extend the results of this study to the Southern Hemisphere, the reader will 

 notice that since /? is unaffected by crossing the equator and F simply 

 changes sign, all the diagrams may be transformed to below the equator by 

 simple reflection across the cc-axis. The crowding of streamlines is therefore 

 toward the western border of each ocean, irrespective of hemisphere. 



The artificial nature of this theoretical model should be emphasized, 

 particularly the form of the dissipative term. 



Fig. 59. Contours of surface height which are associated with flow shown in 

 fig. 58 (Stommel, 1948, fig. 6). 



MUNK S THEORY OF THE WIND-DRIVEN 

 OCEAN CIRCULATION 



By far the most distinguished theoretical investigation into the wind-driven 

 ocean circulation is that conducted by Munk (1950), who has succeeded in 

 deducing many features of the mean ocean circulation from the wind stress 

 alone. In the preceding section of this chapter we have discussed quaUta- 

 tively the reason for the great intensification of western currents; in this 

 section we shall follow Munk's quantitative development of the theory. 



Let us suppose the ocean surface to be a plane surface at rest : x is eastward, 

 y is northward, and z is upward. The plane 2 = Ues at the mean surface; the 

 actual surface is at 2 = z^. 



The equations of steady motion in the horizontal plane are: 



-pfv = 

 pju = 



dp /8^ 8^ 



dx \8x^ 8y^ 



l-'+K^^- 



8p (8^ 8^\ 8 I 8v 



~8y^^^\8^-^8y^]''^dz\^'Fz 



(17) 

 (18) 



