The Stratospheric Circulation 673 



2-5 cm/sec. The time required to perform a single complete cycle in the upper vortex 

 with a horizontal axis in the area of Drake Strait thus amounts to at least a year when 

 the above mean velocity value is used. This transverse circulation is, however, undoubt- 

 edly stronger here than elsewhere in the Antarctic Circumpolar Ocean. 



South of the oceanic West Wind Drift the physical sea level and the isobaric surfaces 

 rise again towards the Antarctic continent. An indication of this rise in the Atlantic 

 Ocean can be seen also in Fig. 316. Near the continent easterly winds prevail, and the 

 currents flow towards west. In this flow along the continent there will thus occur a 

 vertical circulation similar to that appearing in the oceanic West Wind Drift except 

 that it performs a clockwise rotation when looking east. There are indications of such a 

 circulation found in the observations of many Antarctic expeditions. In this connection, 

 Sverdrup also drew attention to the transport of lighter water by the wind towards 

 the Antarctic shelf where it is strongly cooled. The wind thus has a tendency to pile 

 up the lighter surface water against the shelf and produces stronger and stronger 

 solenoidal fields, which are of no consequence, however, since the water simultaneously 

 is cooled there. Both effects thus work in opposite sense and prevent the development 

 of strong solenoid fields and also of stronger currents which would otherwise be 

 formed solely by the action of the wind. 



4. Dynamics of the Antarctic Circumpolar Current 



It is of interest to investigate the extent, in a broad current which encircles the whole 

 earth, to which the wind stresses acting on the sea surface are balanced by frictional 

 stresses against the outer boundaries of the ocean basins. For most oceanic currents 

 the computed transports diff'er as was shown by Munk (1950), by a factor of not more 

 than 2 from the observed transports. Munk and Palmen (1951) have made a similar 

 calculation for the Antarctic Circumpolar Current. They considered the Antarctic 

 Circumpolar Current as an eastward flow on a plane tangential to the earth at the 

 south pole. The flow is induced by the constant eastward winds and depends only on 

 the distance r of this plane from the pole. The balance between the wind stress T and 

 the lateral friction is expressed by the relation 



where A^ is the lateral kinematic viscosity and M is the eastward mass transport across 

 a normal vertical plane of unit width extending from the sea surface to the sea bottom. 

 For a solution in which M vanishes at the Antarctic continent {r = r^), and at some 

 other latitude (r = r^) the total mass transport of the flow will be 



18AV^ '« r, + ro'"/-oy 

 Putting r = 2 dyn cm-^, A^ = 10^ cm^ sec-^ and /"o = 70° S., r^ = 45° S. one obtains 

 M = 5 X 10^*^ g sec"^ whilj the observed transport is at least 1-5 x 10^* g sec"^. 

 This discrepancy is not materially altered on taking spherical co-ordinates or allowing 

 for the variation of the wind with latitude. The transport M is inversely proportional 

 to Ah and only values of 10^°t or more can give an agreemenwith the observed facts. 

 Values of Ah as large as this are. however, improbable. Munk and Palmen attempted 

 to reconcile the two values by taking into account the friction at the bottom especially 



2X 



M - I Mdr= ,^^ I ri^ - r^^ - :^^ In -| . (XIX.2) 



