Tides and Tidal Currents in the Proximity of Land 



321 



u = Vh* 



sin(o7— xx) , 



with 



c = - = \gh . 



(XI. 1) 



The tidal current, in the direction of propagation of the wave, is purely 

 alternating and attains its maximum velocity at high and low water. The 

 motion is uniform from the surface to the bottom. The velocity of pro- 

 pagation is c = | gh. 



If the canal has a rotating motion, these tide waves are changed into Kelvin 

 waves (p. 206, equation VI. 103). The only difference with conditions in 

 a non-rotating canal is that the amplitude of the vertical tide, and also that 

 of the alternating tidal currents varies across a section of the canal. The 

 amplitude decreases from right to left, referred to the direction in which the 

 wave progresses if the rotation is counter clockwise (contra solem) and from 

 left to right if clockwise (cum sole). These conditions are clearly illustrated 

 in Fig. 130, according to Sverdrup (1926). 



s--o 



Velocity 



-10 



_i i i 'i 



10 



<< < , 'i — > ■ >> 



Fig. 130. Tide wave in a rotating canal of uniform depth (without friction). A: vertical 



line of particles at different phases; B: current diagrams; C: wave form and distribution 



of the current in the direction of propatation of the wave (Sverdrup). 



The equations of tide waves on a rotating disk of infinite dimensions are 

 derived from the differential equations (VI. 100 and 101). Sverdrup showed 

 that progressive tide waves of a simple form are only possible if the period 

 of the tide is shorter than one-half pendulum day. These tide waves have 

 the form (/= 2cosin</>). 



21 



