PHILOSOPHICAL Til ANS ACTIONS. 



I. Tidal Friction in the Irish Sea. 

 By G. T. TAYLOR, M.A. 



Communicated by Sii- 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 method could be 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 1 criterion! 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 J 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 Tidal 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' 2 , 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. 



