472 



Tides in Estuaries 



of the wave becomes almost vertical and the passage of this wall manifests 

 itself by an almost sudden variation of the water level. The raised water- 

 masses move rapidly onward, overtake and flood constantly the shallow 

 water-masses in front of this wall. The wave has adopted the form of the 

 breakers and, henceforth, is more like a travelling eddy with a horizontal 



Fig. 201. Profile of the water surface in Humber and in the River Trent during a complete 

 tidal period at springtide. Low water 1 at Grimsby, 2 at Hull, 3 at Bowes Staith, 4 at 

 Burton Stather, 5 at Flixborough, 6 at Keadby Bridge, 7 at Butterwick, 8 at East Ferry, 

 9 at Walkerith, 10 at Torskey, 11 at Dunham. 



axis than like a periodical variation of the water surface. The bore thus 

 becomes similar to the phenomenon which occurs when a water-mass is piled 

 up in a canal and suddenly freed and then moves down through the canal 

 in the form of a translation wave. Bazin (1865, p. 495) has been able, in 

 this way, to create experimentally a bore in a wave tank. It showed there 

 that those secondary waves which develop frequently behind the actual bore 

 in deeper water (les "eteules" in the Seine, the "whelpes" in the Trent) occur 

 also in the experiments and are, therefore, characteristic in the development 

 of this phenomenon. 



From a mathematical view, the bore can be treated as a discontinuity 

 wave. If there is a transition from one uniform level to another where the 

 heights of the water surface above the bottom at the deep and shallow side 

 of the wave are /z x and h 2 , and if the low water is at rest, we have for the 

 velocity of propagation of this discontinuity (bore) against the low water 



*-!/(**£? 



(XIII. 8) 



If h x is not very different from h 2 , this velocity is reduced to the velocity 

 of propagation of long waves \/(gh). If the process takes place in a river 

 with a velocity U directed downstream, them we have to add — U to the 

 right. 



