398 MISCELLANEOUS STUDIES 



Ekman (1905) also used the general equations of the motion of a 

 viscous fluid, but included the deflecting force due to the earth's 

 rotation, and used in place of the coefficient of viscosity a constant 

 whose value was estimated by applying his formal solution of the 

 equations to field data. That is, he used a virtual value of the co- 

 efficient of viscosity in order to take into account the effect of the 

 irregular vortex motion which greatly increases the magnitude of the 

 mutual reaction between the adjacent water layers. 



On the simple assumption that the depth of the region considered 

 is large and the coast is at a sufficiently great distance Ekman (1905, 

 p. 7) deduced the effect of a wind, constant in magnitude and direc- 

 tion, over the whole region. His results for the northern hemisphere 

 are, for the velocity of the water, perpendicular and parallel respec- 

 tively to that of the wind, 



U' = V e- cos (~ ay\ (172) 



V = V Q e-y sin fc ay\ (173) 



Where V is the absolute velocity of the water at the surface y is the 

 depth below the surface and a is a constant. The value of a (Ekman. 



1905, p. 6) is n = v* sm <fr where w is the angular velocity 



" 



of the earth, <f> is the latitude, p. 2 is the virtual coefficient of viscosity, 

 and q is the density of the water. From equations (172) and (173) 

 it follows that the surface water velocity (where y equals zero) makes 

 an angle of 45 degrees to the right of the wind velocity, and the angle 

 increases as y increases. "When y has such a value (denoted by D) 

 that the water velocity has the opposite direction to that of the sur- 

 face, that is, when 



f 



(174) 



the magnitude of the velocity is e~ v or .043 times its surface value. 

 D is called the "depth of frictional influence," since the water velocity 

 below that depth produced by a wind over the open ocean is but a 

 small fractoin of that at the surface. From an estimate of the relation 

 between the wind velocity and its tangential pressure and the corre- 



