320 Mr Taylor, Tides in the Bristol Channel 



Tides in the Bristol Channel. By G. I. Taylor, F.R.S. 

 [Read 24 January 1921.] 



It is well known that tidal waves coming from an open ocean 

 increase in amplitude as they reach the shallower water which 

 usually surrounds the land. This increase is specially marked when 

 the tidal wave enters a contracting channel. The cause of the 

 increase is well understood, and in certain simple cases its amount 

 has been discussed mathematically. 



Unfortunately it is very seldom that the nature of the bottom 

 or of the coast line of a channel permits us to apply these results 

 with any hope of getting even an approximate representation of 

 the actual state of affairs in any existing tidal basin. At any rate 

 I do not know of any case in which it has been attempted. 



One of the most striking examples of the effect of a contracting 

 channel in increasing the height of the tidal wave is that of the 

 Bristol Channel where there is one of the largest tides in the world. 

 On looking at a chart of that region, I was struck by the way in 

 which both the depth and the breadth of the channel at low water 

 appear to contract almost uniformly from the entrance to the head. 

 Under these circumstances it seemed worth while to work out 

 theoretically the increase in tide which might be expected in a 

 channel whose breadth and mean depth both decrease uniformly 

 from the open end to the head, and both vanish there. The results 

 might then be comparable with the observed tides in the Bristol 

 Channel. 



Theoretical Calculation. 



The differential equation which represents the variation in 

 amplitude of the tides in a channel as the mean depth and breadth 

 vary, is given in Lamb's Hydrodynamics"^ . It is 



fs(^^l) + "^ = o W' 



where tj represents the rise and fall of tide, h the breadth, and h the 

 mean depth of a section of the channel taken at a distance x from 

 the head. 277/cr is the period of the tidal oscillation and g is the 

 acceleration due to gravity. 



Two cases have been solved by Lamb, namely (1) A constant, 

 h proportional to x, and (2) h proportional to x, b constant. For 

 the Bristol Channel neither of these is suitable, we require both 

 b and h to be proportional to x. 



* P. 267, 4th edition. 



