Tides and Tidal Currents in the Proximity of Land 



355 



If e = or >] 2 = 0, the tide wave is a progressive wave; the maximum of 

 the flood occurs simultaneously with high water. If £ = 90° or rj x = 0, the 

 tide wave is a standing wave; the maximum flood occurs at half tide. Let 

 us designate the angles formed by the co-tidal lines (tan£ = const) and the 

 co-range lines (H = const) with the x-axis by ip and y' . 

 We find that 



Vi 



tany 



8x 



y* 



>n 



ill, 



<y 



'I: 



< >h 

 8x 



8y 



and tan^' 



Vl 8 x +% dx 



8in drjt 



Vl 8y +f}2 8y 



(XI. 29) 



The general equations of motion are 



8u r 



7, TV = —2 



8t J b 



"1 

 dx 



8v 

 8t 



+fu = 



F 



h' 

 G 



8r 1 _ 

 g 8y h 



(XI. 30) 



in which F and G are the components of the frictional force for the unit 

 surface of the ocean bottom. If at a locality the x-axis is put in the direction 

 of the maximal flood current and the time is counted from its start, then 

 eja is the time of high water relative to this time, and we can substitute 



(XI. 31) 



From the equations (XI. 39) results 



g 



8rh 

 8y 



(XI. 32) 



and 



tany> = 

 tany>' 



( qt/+/K)+Ftane 



(aV-\-fU)tane-G ' 



(or£/+/K)tane-F 



(oV+fU) + Gt<me' 



(XI. 33) 



23" 



