Ocean Currents in a Non-homogeneous Ocean 



503 



In the method presented by Jacobsen and Jensen, further assumptions are 

 added to those used before which simpHfy matters even more. A and B (Fig. 232) 

 are two stations at which observations are available down to the bottom. The depth at 

 B is greater than at A and the difference in the physical sea level between A and B has 

 to be found. Aq and Bq are the points on the sea bottom at the stations A and B and 



Fig. 232. 



A 0^1 shall be a level line ("Niveaulinie")- The dynamic height difference BqB^ is denoted 

 by h and the specific volumes at .4o and B^ by aA,o and aB,i. Provided that: 



(1) the sea bottom AqBq is linear in the vertical section and 



(2) within the triangular section A o^o^i the mass field is linear and the isosteres are 

 therefore straight, equidistant and parallel lines and 



(3) the pressure gradient vanishes at the bottom. 



Then a simple integration method enables the required level difference to be cal- 

 culated by first calculating the difference in sea level between A and B, on the assump- 

 tion that the pressures at ^q and B^ are the same, and then adding the correction term 

 hK^Ba — oiA,o)- Ekman (1939) has shown that the method of Helland-Hansen leads 

 to exactly the same correction term. Both methods require that not only the current 

 velocity but also the horizontal pressure gradient should vanish at the sea bottom. 

 The first condition is satisfied because of the bottom friction, but the second is in 

 many cases a rather doubtful assumption, since considerable density differences 

 sometimes appear in both vertical and horizontal directions, at the shelf bottom. 

 Before applying the method it is thus first necessary to ascertain whether the pre- 

 sumptions are approximately satisfied or not. The method of Jacobsen and Jensen is 

 simpler for use and less time consuming than that of Helland-Hansen and requires also 

 less complete data. 



A third method has been suggested by Sverdrup and co-workers (1942, p. 451). 

 They postulate below the sea bottom an imaginary water body in which the specific 

 volume a (or its anomaly S) and the slope of the isosteres is given at each depth by the 

 corresponding value on the continental slope. It is easily shown that the slope of an 

 isobaric surface pi relative to that of pa can be computed approximately from the 

 simple equation ip = — is(8i — So), where is is the mean slope of the S-lines between 

 Pi and p.2: Sj and S., are the specific volume anomalies at points 1 and 2. The mass 

 distribution in the imaginary water body then gives the pressure distribution, and the 



