344 



Tides and Tidal Currents in the Proximity of Land 



(XI. 18) 



I = ^cosoY + ^sincr/ , | 

 f) = rjicosot+rjismat j 



and replacing the differential quotients by difference quotients, one obtains the system of 

 equations 



Arjy = a(t!-^ 2 ), 



Arj 2 = a(£ 2 +6f 2 ) , 



(XI. 19) 



1 r 



fi = — — | nMx 



■ji " 



| 2 = i] % bdx 



Si J 



By means of this system we can compute step wise the quantities li,!*, and >h> ? ?2, and their 

 combination in (XI. 18) gives the tidal motion within the bay. The equation for Arj 1} is similar to 

 the one without friction, except that another term is added which contains the coefficient for 

 friction. Generally, it is small and acquires some importance only there, where f 2 is large, i.e. at 

 the nodal lines. 



An example is given in Table 39. It concerns the co-oscillating tide of the Gulf of Bristol with 

 the external tide in the Irish Channel, as given by Defant (1920, p. 253). The computation was 

 started at the cross-section with the boundary values & = £ 2 = and the arbitrary values 2% = 

 + 100 and 2?? 2 = +20 cm. The table gives the correlated values of 2t]i, and 2/; 2 for all eight cross- 

 sections. According to the observations, the range at the open end is 7-6 m, the phase 5-5 h. We 

 then have for y = 1 the equation 



3416cos —(/-<?)- 46-01 sin — (t-e) 

 T T 



In 



pcos — (t— 5-5 h) 



This gives e = 7- 3h and l//> = 0174, and the co-oscillating tide at the various cross-sections; 

 in the next column are the observed values of establishment and range at coastal localities. The 

 agreement is very good. 



Table 39. Co-oscillating tide in gulf of Bristol 



Cross- 

 section 



2m 



+ 100 — 

 95-8 

 88-8 

 76-2 

 61-4 

 51-5 

 43-2 

 3416 



2r) 2 



+ 200 



+ 4-5 

 - 7-9 

 -22-4 

 -34-1 

 -400 

 -43-4 

 -460 



2rj 

 (min) 



13-6 



12-8 



11-9 



10-6 



9-4 



8-7 



8-2 



7-6 



Phase 

 lunar 

 hours 



7-64 



7-4 



7-1 



6-7 



6-3 



60 



5-8 



5-5 



The development of the co-oscillating tide into a standing wave requires 

 that the incoming wave is totally reflected at the inner end of the bay. If this 

 is not the case, the reflected wave is not exactly like the incoming one and 



