438 



General Theory of Ocean Currents in a Homogeneous Sea 



Here a is the angle of deflection of the ice drift from the wind direction and r is the 

 wind factor (relative drift velocity, p. 418). Both the angle of deflection and the wind 

 factor increase with decreasing ice resistance if the wind effect is constant. 



It can easily be shown that the end-points of the vectors of the wind factors must lie 

 on a circle with its centre on a straight line at right angles cum sole to the wind direc- 

 tion. Its radius is /? = c/2/. In Fig. 189 the vectors shown represent the drifts for 

 values k ^ Sf, 3/ and/. 



Fig. 



189. Relation between wind and ice drift for stationary wind conditions and for 

 diflFerent ice resistance (according to Sverdrup) 



A deep sea with a continuous vertical density increase. Here the equations of motion 

 are the same as for a pure drift current (XIII.23). The boundary conditions are, how- 

 ever, the following (wind along the positive >'-axis) : 



f(u)u^ and ~ -^ = — F(w)w +f{u)Uy 



forz = 0: 



dz 



P S^ P 



for z — co: Ux "= Uy = 0. 



The functions /(m) and F(h') are for the moment unknown. F(vv)vv is equal to the 

 wind stress T. With these boundary conditions a solution for the equations is thus 



Doj sin </> , u 



^r^^ and r = — 

 w 



tan a = 



F(vv)sina. (XIII.61) 



Doj sin 4> + 71'/(m) vv Doi sin ^ 



Also in this case the wind factor decreases with increasing ice resistance for otherwise 

 equal conditions, since the angle of deflection a decreases with increasing resistance. 

 As in the previous case, the end-points of the relative drift vectors drawn from the 

 starting point of the wind vector lie on a similar circle as before. The radius is, how- 

 ever, R = {ttF (w)]l{2Dco sin ^). The functions introduced here are not identical with 

 the coefficients k and c used in the previous case, but are in a way similar to them. 

 The function/(M) depends on the state of the ice while F (vv) is related to the turbulence 

 state of the wind blowing over the ice. 



The observations made during the ice drift allow the determination of both a and 

 r in both cases, and from these the coefficients k and c in the first case and the functions 

 /(«) and F{w) in the second can be determined. For a test of the relations only those 

 periods can be used, of course, in which a quasi-stationary state prevails. These 

 factors are grouped according to increasing wind factor and increasing deflection angle 

 and presented in Table 1 28 ; Fig, 1 90 shows these mean values in a graphical presentation 



