Tides nad Tidal Currents in the Proximity of Land 



329 



(b) Frictionless current rotating to the right: r < s . In Fig. 134 the solid curve s must be moved 

 to the right according to s . In most cases there will then still be a point of intersection with the 

 dotted curve r. Above it the current rotates elliptically to the right, downwards elliptically to the 



02 



06 



10 



14 



Fig. 134. Current in the presence of tidal currents close to the bottom which rotate to 

 the right ( ) and to the left ( ). (4> = 54°N., M 2 -tide, according to Thorade). 



left. Only when s : r > D x : D 2 , the rotary motion to the right reaches down to the bottom, while 

 the current ellipse narrows gradually. 



(c) Frictionless current rotating to the left: r > s . The current ellipse remains an ellipse 

 rotating to the left down to the bottom, and the ratio of the axis increases constantly. 



The investigations made by Sverdrup and Fjeldstad deal particularly with 

 the dynamics of a free progressive tide wave. For a wide canal the solution 

 of the differential equations is: 



u =VH 



X 



Mcoscrfr— ~j-\+Nsma\t- 



C LP cos a / 



j + gsin<r(r 



e -nx-my ^ 



e -,ix-my ^ 



r] = Ccoso- [t— j \e-> ac - my 



(XL 13) 



M, N, P, Q are quantities depending in a complicated way upon the water 

 depth, the quantity s =f/<r, the damping of the wave //, the decrease m of 

 the wave amplitude transversely to the direction of propagation x, as well 



