140 DISCOVERY REPORTS 



the o and 600 surfaces relative to the 3000 surface, and if this should have a pronounced 

 slope of its own they cannot be regarded as measures of the absolute current. Under 

 the conditions of stationary equilibrium postulated in the specialized form of Bjerknes' 

 theorem the isobaths of the 3000 decibar surface will be approximately parallel to the 

 lines of equal specific volume anomaly at 3000 m. shown in Fig. 4, and the topography 

 of the surface must be very similar to those of the o and 600 surfaces but with much 

 gentler slopes. This being so, the charts showing the topographies of the o and 600 sur- 

 faces relative to the 3000 surface can be used without serious error as charts of the 

 absolute topographies, and their failure to give accurate representations of the surface 

 and deep current systems implies that the simple equation relating the current difference 

 between two levels to the solenoid field (equation (6), p. 13 1), developed from the special- 

 ized form of Bjerknes' theorem, is not strictly applicable to the conditions of the 

 Southern Ocean. 



THE PROBLEM OF THE MERIDIONAL WATER CIRCULATION 



IN THE SOUTHERN OCEAN 



The derivation of the specialized form of Bjerknes' theorem from the general equation 

 involves two main assumptions : that the current system is in stationary equilibrium so 

 that the circulation has no acceleration, and that the effect of friction is small enough to 

 be neglected. In many parts of the world the results obtained by the application of the 

 specialized theorem justify these assumptions, but the conditions in the Southern Ocean 

 seem to be definitely outstanding and the partial failure of the same methods seems to 

 coincide with conditions which cannot be regarded as stationary, and which are prob- 

 ably more than normally influenced by friction. 



On all sides of the Antarctic continent the isosteric surfaces slope downwards to the 

 north, and the fact that they retain this slope unaltered suggests that the principal 

 water movement is a stationary current, flowing horizontally and parallel to the surfaces, 

 towards the east. This is, however, not the only possible movement, since the steady 

 slope of the surfaces does not preclude the existence of the meridional currents sug- 

 gested by the temperature and salinity distributions— the sinking of the Antarctic sur- 

 face and the bottom currents towards the north and the climbing of the warm deep 

 current towards the south. Owing to the existence of such currents there will be screw- 

 ing movements in the main current towards the east, and the meridional circulation will 

 have accelerations that cannot be ignored. 



The further treatment of the problem and the evaluation of these accelerations presents 

 great difficulties and has so far not been attempted. Among the factors to be considered 

 is the apparent divergence of the surface and bottom currents from all sides of the 

 Antarctic continent, and the simultaneous convergence of the warm deep current. The 

 problem of a deep current converging from all sides to one point has been considered by 

 Ekman (1928, p. 313) and he points out that the movement in such a system cannot be 

 regarded as proportional to the angle of slope of the isobaric surfaces. Such an assump- 

 tion would require the existence of a continuous slope around the central region, so that 



