418 



General Theory of Ocean Currents in a Homogeneous Sea 



Table 123. Currents for different wind directions at the lightship ''Finngrundet" (mean 



value at 2-7 Beaufort) 



The directional turn between and 20 m depth is 19° cum sole and at the same time 

 the velocity falls by about a quarter of the surface value. This turn of the current 

 is in good agreement with the theory; the decrease in velocity is, however, much too 

 small to be explained by a constant frictlonal coefficient ; for a water depth of 23 m 

 and for a 77 about 200-300, it must be about 0-12 instead of 0-81. Only an assumption 

 of a variable r] with depth approximately in the sense of the discussion given on p. 405 

 could explain such a small decrease. 



The relationship of wind strength to current strength. According to the theory the 

 surface velocity Vq is given by the relation 



Ko = ..^ ^ . ,. . (XIII.4]) 



From this it follows that for constant 77 and p the surface velocity Vq is proportional 

 to the wind velocity w and is inversely proportional to the square root of sin ^: 



Vq = —-^ w (XIII.42) 



V(sm (p) 



A is a universal constant. The quantity VqJw is denoted as the "wind factor". Numerous 

 investigations have been made of this relationship (see especially Thorade, 1914); 

 the following values have been found for A, when Vq and h' are expressed in cm/sec: 



Mohn 

 00103 



Dinklage 

 C-0127 



Witting 

 00100 



Thorade 

 00126 



Pal men 

 00114 



Nansen 

 00190 



Sverdrup Brennecke 

 00177 00269 



The first of these values are in good agreement. For the ice drift, on the other hand, 

 considerably higher values were obtained (Nansen, 1902; Sverdrup, 1928; 

 Brennecke, 1921). See p. 437 concerning these. Usually an almost linear relationship 

 has been found between the wind velocity and the velocity of the surface current. 

 Witting and Thorade, however, arrived at a different result : for a wind force of up 

 to 3 Beaufort a better fit to the observations was obtained by a quadratic relation. 

 Palmen believed, however, that this was due to the uncertainty of the conversion of 

 wind strength from the Beaufort scale into m/sec. For the magnitude of 77 it seems to 

 be also of importance, on what height the wind measurements are based; a better 

 agreement could probably be obtained if also this was taken into account (Exner, 

 1912; Durst, 1924). 



