VERTICAL CIRCULATION IN THE OCEAN 167 



the Antarctic water) receives its nutrient substances from the richer intermediate layer 

 of Atlantic origin ". Our sections show, on the other hand, that the nutrient substances 

 are carried back to the high southerly latitudes by the transversal circulation within the 

 Antarctic Zone, and that the low oxygen values of the intermediate layer are local and 

 must be due to processes within the transversal circulation. 



An estimate of the velocity of the north-south circulation gives at present uncertain 

 results, but a few numerical values may, nevertheless, be communicated. Let us suppose 

 that the average wind velocity is about 10 m./sec. and that the tangential stress of the 

 wind is T = V2 x 10-^ W 



n 



where PFis measured in cm. /sec. We then find T = 3-2, and in latitude 55° S the total 

 transport of water towards the north through a vertical surface which is i cm. wide will be 

 S = 2-7 X 10* cm.^ In summer the thickness of the upper homogeneous layerwhich moves 

 under the action of the wind appears to be 40-80 m. Introducing 60 m. as a probable 

 mean value we find an average velocity towards the north of the pure drift current of 

 about 4-5 cm. /sec. If half of the return flow to the south takes place within an interval of 

 depth of 300 m. the velocity of the southwards flow will be about 0-5 cm. /sec, and the 

 average speed of the transversal circulation within the upper layer about 2-5 cm. /sec. 



We have also other means of estimating the velocity within the intermediate return 

 current. If the temperature distribution within this current is stationary we must have 



where the :x;-axis is placed in north-south and where A is the coefficient of eddy con- 

 ductivity and t the temperature. From the observations we find 



-~2XI0-, g^~2XI0-B, ,~I, 



or Vx ~ o-i^. 



Our knowledge of the eddy conductivity in the sea is scanty, but at greater depths the 

 values of the coefficient appear to range between i and 20 (Helland-Hansen, 1930). 

 We, therefore, obtain o-i < ■y,. < 2-0. 



This estimate only shows the order of magnitude of the component, and the agreement 

 with our preceding value is, therefore, quite satisfactory. 



It is also of interest to examine the time which one water particle would need for a 

 complete transversal circulation in the upper layers. Within the Drake Passage and the 

 Scotia Sea the north-south extension of the transversal circulation appears to be about 

 300 km., and thus the total distance which a particle would travel is about 600 km. 

 Supposing the average speed to be 2-5 cm. /sec. and neglecting the time which is needed 

 during vertical displacements, we find that the particle returns to its most southern 

 position after 2-4 x 10' sec. or nearly 275 days. The time needed for vertical displace- 

 ments can also be estimated. Suppose that the volume of water which is transported to 

 the north through a vertical surface i cm. wide, 2-7 x 10* cm.^/sec, is replaced by water 

 which is drawn towards the surface within a belt, which is 100 km. wide. The velocity 



