122 



WIND CURRENTS AND WIND WAVES 



lower surfaces of the body of water are balanced by the component of 

 gravity acting on the entire body of water (fig. 29). 



This is the relation that Ekman used for determining the stress of 

 the wind. Studying sea levels recorded during a storm in 1872 at a 

 number of stations along the shores of the Baltic Sea, Colding found 

 that the lines of equal sea level were nearly perpendicular to the wind 

 direction, and that the relation between wind velocity, 

 K W, depth, d, and slope of the sea surface, i, could be 



^^ expressed by the equation 



id = 4.8 X lO-'W^, 



where depth is in centimeters and wind velocity in cen- 

 timeters per second. Ekman showed that the value 

 of Td probably lies between and }yi Ta. Assuming 



Td 



Vzr. 



I, he obtained 



Ta = 3.2 X 10-^^2, 

 or, introducing the density of the air, pc 



Ta = 2.6 X 10-'paW\ 



1.25 X 10- 



From observations during a storm in the Gulf of Bothnia 

 in 1936, Palmen and Laurila obtained similarly 



Ta = 2.4 X lO-'PaW, 



and they consider this formula valid at wind velocities 

 between 10 and 26 m/sec. These results are in very 

 good agreement with Rossby's formula (VII, 8). 



Changes in sea level due to the direct effect of the 

 stress of the wind are common in such shallow and 

 enclosed areas as the Baltic Sea and the Gulf of 

 Bothnia, and are often observed in shallow lakes. On 

 open coasts where shallow waters extend to appreciable 

 distances, similar piling up of water may take place 

 during violent storms, causing wide inundation of 

 For instance, this took place during the hurricane of 

 Galveston in 1900 and the hurricane of New England in 1938. 



The above equations are not applicable to conditions in the open 

 ocean, because there the density varies with depth and therefore the slopes 

 of the isobaric surfaces vary. When dealing with the open ocean, it is 

 more convenient to introduce the geopotential slope of the isobaric sur- 

 faces and write (VII, 13) in the form 



Fig. 29. Sche- 

 matic representa- 

 tion showing the 

 stresses acting at 

 the upper and lower 

 surfaces of a body 

 of water balanced 

 against the compo- 

 nent of gravity 

 acting on the en- 

 tire water body. 



low-lying areas. 



= - r 



JO 



dAD ^ 



(VII, 14) 



