330 



Tides and Tidal Currents in the Proximity of Land 



as upon the coefficient of friction v. The vector diagram of the current is an 

 ellipse, the ratio of the small axis to the large axis is smaller than in the case 

 of an infinite ocean, where the ratio is exactly equal to s. The effect of the 

 Coriolis force is partly compensated by the slope of the wave crest transversely 

 to the direction of propagation. Under these circumstances, such a wave 

 cannot travel without changing its form; however, the solution will remain 

 valid for a relatively long distance. The velocity of propagation is no longer 

 as it was in (XI. 2), but will be 



c =n\ gh 



X \-s 2 ' 



in which the factor n depends in a complicated way upon the depth h, the 

 frequency a and/. The factor n is the ratio of c/c , when c = \/gh \/\j(\ — s 2 ) 

 or the velocity of the wave in absence of turbulence. Sverdrup has given 

 the following Table 36 for n. 



Table 36. The ratio c/c as function 

 of h \/a/2v and s 



The last line gives the values without friction (v = 0). It is apparent that 

 the friction retards the waves, and much more so at the pole (s = 09) than 

 at lower latitudes. But the velocity of propagation also depends very much 

 upon the frequency a of the waves, so that for long distances there must be 

 a dispersion of the waves. 



The motion at a depth h can be fully described by the following four 

 quantities (Fig. 135). 



(1) V = the scalar value of the maximum velocity in the direction of the 

 main axis of the current ellipse. 



(2) aV = the minimum velocity in the direction of the small axis; a is the 

 ratio between the scalar values of minimum and maximum velocity. 



