674 The Stratospheric Circulation 



there where the major submarine ridges lie as transverse obstacles in the path of the 

 current. If the wind stress should be completely balanced by the frictional stresses 

 along the sea bottom, then the Antarctic Circumpolar Current must extend deep 

 enough to reach the sea bottom. It is certain from the vertical oceanic stratification in 

 these latitudes that the current reaches down to very large depths; this is clearly 

 indicated by the dynamic topographies of the individual isobaric surfaces. However, 

 the velocities decrease very rapidly with depth and at depths of more than 4000 m 

 the flow intensity of the Antarctic Circumpolar Current is extremely small. Corres- 

 pondingly, the frictional stresses at the sea bottom will also remain rather small. By 

 making the most favourable assumptions Munk and Palmen showed that the retarding 

 pressure of the submarine ridges against the deep current might still be able to balance 

 the wind stress on the surface. 



HiDAKA and Tsuchiya (1953) have recently taken up the problem again and 

 attempted to find a hydrodynamic solution. From the equations of motion and the 

 continuity equation with the corresponding boundary conditions they derived for 

 planar co-ordinates, a complete solution in the form of infinite series giving the total 

 mass transport, the surface slope and the vertical velocity distribution. Their calcula- 

 tions using some arbitrary numerical values of the lateral and vertical eddy viscosity 

 {Ah and y4„) give the same results as those of Munk and Palmen. For A„ = 2 x 10^ 

 and Ah = 10^" cm-^ g sec"^ they found a total mass transport of 9-3 x 10^^ g sec~\ 

 a surface slope of 3 m per 25° lat. and directions and strength of the currents in good 

 agreement with those observed. But also in this case choosing values of ^4^ less than 

 10^^ would give impossible conditions. In a more recent treatment of this problem 

 Takano (1955) introduces a special vertical and meridional density distribution corres- 

 ponding approximately to the observed ones. The rather complicated mathematical 

 solution led to the following conclusions: if the Ekman frictional layer is disregarded 

 then the geostrophic approximation can be safely applied for the small velocities near 

 the sea bottom. However, in order to obtain agreement with the observed values of 

 the surface velocity, of the surface slope, of the density diff'erences at the sea surface 

 and of the mass transport, it is necessary to take ^4^ = M x 10^". This is again the 

 same large value that was found to be a necessity in the investigations mentioned 

 before. 



There must thus be yet another source of energy dissipation in order to have a 

 complete balance in the sense put forward by Munk and Palmen between wind stress 

 and frictional stress. This can probably be obtained by taking into account the effect 

 of the boundary friction, not only at the sea bottom but rather along the extended 

 continental slope of the Antarctic continent which was previously neglected. An essen- 

 tially different explanation of the dynamics of the Antarctic Circumpolar Current has 

 been given recently by Stommel (1957). While Munk and Palmen and all others who 

 have treated the problem regarded the Antarctic Ocean as an example of an ocean 

 without meridional barriers for which a Sverdrup type solution could not be con- 

 structed, Stommel believed that while the circumpolar ocean was indeed a continuous 

 ring of water around the earth, it was so strongly narrowed at Drake's Passage between 

 Grahamland and the southern tip of South America that a pure zonal flow could 

 hardly develop in this section. On this basis the Antarctic Circumpolar Current is 

 amenable to treatment by the Sverdrup theory and is essentially frictionless except 



