MR. U. I. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 3 



In places where the bottom is uneven or weedy, BAZIN gives 1 7 as the value of y. 

 Under these circumstances 



K = 0-0013^1 + 



\ 



= O'OOIS ........ (5) 



It will be seen that large changes in the amount of roughness produce only" small 

 changes in the amount of friction on the bottom. On looking at BAZIN'S formula 

 it will be seen that this is due to the fact that the sea is deep. In order that the 

 roughness of the bottom may have a large effect in slowing down a stream, it is 

 necessary that r should be small. It seems, in fact, that the size of the projections 

 which constitute the roughness or inequality of the bed must be some definite fraction 

 of r in order that their effect may be felt on the stream as a whole. In other words, 

 the direct effect of the projections extends to a distance which is some multiple of 

 the linear dimension of the projections ; and if these are small enough compared with 

 the depth, very little difference is made to the total flow of the stream by changing 

 the amount of roughness on the bottom. 



This conclusion is important in the present application, because it means that by 

 adopting the values of K given above we shall be able to get a fairly accurate 

 estimate of the friction of the sea on the bottom without knowing the exact nature 

 of the bottom. We may under-estimate the friction, but we are certainly not likely 

 to over-estimate it ; for our estimate will not take account of unevennesses, such as 

 boulders and rocks, which are comparable with the depth of the sea, nor will it take 

 account of the increase in K in the shallow areas of estuaries and outlying banks. 



Friction of tit e W ind on the Groun d. It lias already been pointed out that the 

 friction of the sea on the sea-bottom is similar to the friction of the wind on the 

 ground. According to the principle of dynamical similarity the flow-patterns of the 

 sea and air will be the same, provided the scale of the projections which constitute 

 the roughness are the same, and provided 



where p a and p^, are the densities of air and sea-water respectively, /j. a and //. are 

 their viscosities, and v a and v m are their velocities. Using values obtained from 

 physical tables fj. w p a (n a p u .) will be found to be equal to T ' T . 



In a previous communication to the Koyal Society* the author has shown from 

 meteorological observations that the friction of the wind over the grass land of 

 Salisbury Plain may be expressed by means of the formula F = 0'002/3 a w a 2 over the 

 whole range of velocities tested, i.e., from 6 to 30 miles per hour. 



According to the principle of dynamical similarity therefore this same expression 

 may be expected to apply to tidal currents of -fa to f^ miles per hour, i.e., roughly 



* 'Roy. Soc. Proc,,' A, vol. 92, p. 196, 1916. 

 B 2 



