356 



Tides and Tidal Currents in the Proximity of Land 



If there is no friction (F = 0, G = 0), these equations are reduced to 

 gH ~ = UoU-VfV) , gH~- - miaV+fU) , 



gH*~=> h (aU+fV) , s w% = n^v+fu) , 



ox ( ) 



aU+fV 

 tan;/' = 77— ^rr cotaiif 



tany/ 



oV+fU 

 cU+fV 



tane 



(XI. 34) 



oV+fU 



from the latter equation it follows that ip' = \n-\-y\ in the absence of friction, 

 the co-tidal lines and co-range lines are always perpendicular to each other. 



(a) 



(b). 



Mean- 

 level 



High, 

 water! 



High water 



Mean level 



High water after 

 peak of current 



High wafer before 

 peak of current 



Fjg. 147. , co-tidal lines; , co-range lines, (a) for a progressive tide wave (e = 0°), 



(b) for a standing tide wave (e = 90°), (c) when high water occurs -]- period after current 

 maximum < e < \n, (d) when high water occurs i period before current maximum 



— \ti < e < 0. 



If we take a progressive tide wave, then e 



»?2 



0, i.e. dH/dx = and 



dejdy = 0. Conditions will be as illustrated in Fig. 147a. The co-tidal lines 

 have the direction of the current at half tide, the co-range lines the direction 

 of the current at high and low water respectively. 



For a standing wave, s = 90° and n x = 0, i.e. dHjdy = and csjdx = 0, 

 and conditions are as in Fig. 1476. For this case also we find that the co- 

 tidal lines follow the direction of the current at half tide, the co-range lines 

 the direction of the current at high and low water respectively, so that this 

 rule applies in general. 



For an example, Proudman cites the distribution of the co-tidal and co- 

 range lines in the northern part of the Irish Sea (see p. 384). The minimum 

 velocity here is practically zero (V = 0) and high water occurs with slack 

 water. The co-tidal lines must follow the stream-lines, the co-range lines 

 must be perpendicular to these. This is, in fact, largely the case. 



For general conditions, we have mostly a > / and U > V, so that 

 (oU J r fV)/(oV J i-fU) is positive. If high water occurs within one quarter 

 period after the maximum in the current, we have < e < hn and \n <ip < tt, 

 < ip' < \n, i.e. the co-tidal lines make an obtuse angle, the co-range lines 



