MR. a I. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 
In places where the bottom is uneven or weedy, Bazin gives 17 as the value of y. 
Under these circumstances 
K = 0-0013 [l+= (V0018.. (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 1 ' 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 the Wind on the Ground .—It has 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 
_ f^wPa ( 6 ) 
PaPio 
where and are the densities of air and sea-water respectively, Ua Uw 
their viscosities, and and are their velocities. Using values obtained from 
physical tables {uaPi,) wid be found to be equal to yU- 
In a previous communication to the Royal 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 = 0'002pj^J 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 yV to U? miles per hour, i.e., roughly 
* ‘Roy. Soc. Proc,,’ A, yol. 92, p. 196, 1916. 
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