420 



General Theory of Ocean Currents in a Homogeneous Sea 



depths. Since, however, due to the dependence of the frictional coefficient -q on the 

 depth, the stress T is somewhat too small it is of no great importance if e is put equal 

 to 1, especially for more intense winds. 



Most important, therefore, is the determination of /. This slope is made up of three 

 components: the first depends on the direct piling up of water by the wind, the second 

 is the static effect of the atmospheric pressure distribution, and the third is due to the 

 deep current produced in the enclosed basins by the wind (current effect). The atmos- 

 pheric pressure effect can be eliminated quite simply (pt. I, p. 7) ; the current effect 

 depends in the first place on the boundaries of the basin and on the stratification of 

 the water in it. In elongated seas with strong stratification (such as the Gulf of Finland) 

 it is rather large and acts at right angles to the main direction of the current. In an 

 oceanic area without any particular major axis the greatest piling up occurs exactly 

 in the direction of the wind (for example, in the Gulf of Bothnia). 



The equations (XIII.43-45) were first applied by Ekman (1905) for the case of a 

 storm in the southern Baltic (Colding, 1881) and gave 7=3-2 X lO^^v^ {w in 

 cm/sec). Inserting the density of the air, p' = 1-25 x 10-^ gives 



r=2-6 X 10-=^p'm'2. 



This relation applies for wind speeds of up to 20 m/sec. The magnitude of piling 

 up by the wind is given in Table 124. In more recent investigations Palmen has deter- 

 mined the dependence of the piling up by the wind on the strength of the wind and the 

 depth of the water for the Gulf of Bothnia from observations of the water level. He 

 found that, for the water depths in the area under investigation, the "Windstau" was 

 directly proportional to the wind intensity for lighter winds, while for strong winds 

 was rather proportional to the second power of the wind strength. Furthermore, the 

 tangential pressure of the wind according to equation (XIII.45) could usually be 

 expressed by the formula 



r= 0-14 X lO-V + 0-022 X 10-''vv'2. 



Table. 124. Piling up of water ''Wasserstau' by the wind for a depth of 50 m 



(according to Palmen) 



In a later investigation Palmen and Laurila (1938) found 



id =3-15 X 10-V2 



for rather intense winds during a storm in October 1936, which leads for a mean water 

 depth of 50 m and p' =--- 1-3 x 10-=^ to 



r= 2-4 x 10-3p'vf2. 



The values for the constant k agree well with this (see equation X.9). A more recent 

 determination in a similar way was made by Hela (1948), who found ^ = 1-9 X 10-^ 

 [^cm""^ sec"2]. 



