303] GENERATION OF WAVES BY WIND. 551 



that the forces above investigated, whether normal or tangential, 

 are on the whole urging the surface-particles in the directions in 

 which they are already moving. 



Owing to the irregular, eddying, character of a wind blowing 

 over a roughened surface, it is not easy to give more than a 

 general explanation of the manner in which it generates and 

 maintains waves. It is not difficult to see, however, that the 

 action of the wind will tend to produce surface forces of the 

 kinds above investigated. When the air is moving in the direction 

 in which the wave-form is travelling, but with a greater velocity, 

 there will evidently be an excess of pressure on the rear-slopes, as 

 well as a tangential drag on the exposed crests. The aggregate 

 effect of these forces will be a surface drift, and the residual 

 tractions, whether normal or tangential, will have on the whole 

 the distribution above postulated. Hence the tendency will be to 

 increase the amplitude of the waves to such a point that the 

 dissipation balances the work done by the surface forces. In like 

 manner waves travelling faster than the wind, or against the wind, 

 will have their amplitude continually reduced*. 



It has been shewn (Art. 246) that, under the joint influence 

 of gravity and capillarity, there is a minimum wave-velocity 

 of 23*2 cm. per sec., or 45 miles per hour. Hence a wind of 

 smaller velocity than this is incapable of reinforcing waves 

 accidentally started, which, if of short wave-length, must be 

 rapidly extinguished by viscosity f. This is in accordance with 

 the observations of Scott Russell J, from whose paper we make 

 the following interesting extract : 



&quot; Let [a spectator] begin his observations in a perfect calm, when the 

 surface of the water is smooth and reflects like a mirror the images of 

 surrounding objects. This appearance will not be affected by even a slight 

 motion of the air, and a velocity of less than half a mile an hour (8$ in. per sec.) 

 does not sensibly disturb the smoothness of the reflecting surface. A gentle 

 zephyr flitting along the surface from point to point, may be observed to 

 destroy the perfection of the mirror for a moment, and on departing, the 

 surface remains polished as before ; if the air have a velocity of about a mile 

 an hour, the surface of the water becomes less capable of distinct reflexion, and 



* Cf. Airy, &quot;Tides and Waves,&quot; Arts. 265272; Stokes, Camb. Trans., t. ix., 

 p. [62] ; Lord Eayleigh, 1. c. ante p. 526. 

 t Sir W. Thomson, 1. c. ante p. 446. 

 t I. c. ante p. 455. 



