PHILOSOPHICAL TRANSACTIONS. 
I. Tidal Friction in the Irish Sea. 
By G. T. Taylor, M.A. 
Communicated hy Sir Napier Shaw, F.R.S. 
Received December 4, 1918,—Read March 20, 1919. 
The dissipation of energy in the tides has recently formed the subject of a paper by 
Mr. R. O. Street.* In that paper it is assumed that the energy is dissipated by the 
viscous drag of layers of water which move parallel to the bottom of the sea. The 
assumption that tidal currents move in laminar motion is so opposed to ordinary 
observation of the surface of the sea in a tideway that I felt certain, on reading the 
paper, that if some other mathod could he found, which did not depend on any special 
assumptions as to the nature of the motion, it would be found that Mr. Street’s 
estimate of the dissipation is very much too small. 
This view is strengthened by the consideration that Reynolds’ criteriont of 
stability would lead us to expect that eddies would form in any stream of sea-water 
flowing at a speed of 1 knot or more, when the depth is greater than some quantity 
of the order of magnitude of 1 or 2 cm. Since the mean depth of the Irish Sea is 
over 40 fathoms, mathematical considerations alone would lead us to suspect the 
existence of the eddies, which can in fact be seen marking the surface of the sea in 
places where the current runs exceptionally strongly, or over a particularly uneven 
bottom. Several of these places are marked as “ripples” on the chart of the Irish 
Sea, the sheet of water to which Mr. Street applied his calculations. 
Dissipation of Energy in Tided Currents. 
The mechanism by means of which energy is dissipated in a tidal current by 
friction on the bottom must be similar to the mechanism by which the energy of a 
river is dissipated by friction on its bed, and also to the mechanism by which the 
energy of the wind is dissipated by friction on the ground. The amount of friction 
in both these cases is known. It can in both cases be expressed by a term of the 
form F, the skin-friction per square centimetre, which is equal to KpV^, where p is 
‘Roy. Soc. Proc.,’ A, vol. 93, 1917, p. 349. 
t See Osborne Reynolds, “On the Dynamic Theory of Incompressible Viscous Fluid and the 
Determination of the Criterion,” ‘ Phil. Trans.,’ A, 1894, p. 123. 
VOL. CCXX.-A 571. 
B 
[Published November 29, 1919. 
