134 WIND CURRENTS AND WIND WAVES 



will be at a maximum when c = y^W. Therefore, unless 



^3 ^ 27vg{p- p'} ^ ^jj^ 24) 



there will be no values of c that satisfy condition (VII, 23). 



Equation (VII, 24) determines the velocity of the weakest wind 

 capable of raising waves, and this wind could be determined if the 

 sheltering coefficient were known. Jeffreys has not been able to make 

 independent determinations of this coefficient, but has, instead, con- 

 ducted wind measurements over ponds in order to determine the lowest 

 velocity at which small waves appear. He found that at wind velocities 

 of less than 1 m/sec no disturbance of the surface occurred, but that at a 

 velocity of about 1.1 m/sec distinct waves appeared. The corresponding 

 value of the sheltering coefficient, s, would be about 0.27. It should be 

 observed, however, that, because of the rapid change with height of wind 

 velocity near a boundary surface, this numerical value and the limiting 

 wind velocity both depend upon the height above the water at which the 

 wind velocity was measured. 



The velocity of the smallest possible waves should be one third of 

 the limiting wind velocity, or about 37 cm/sec, and according to the 

 theory (p. 135) the corresponding wave length must be 8.8 cm. Thus, 

 measurement of the smallest waves can be used for testing the correctness 

 of the theory, but measurement of such small wave lengths is very 

 difficult, and no exact observations have been made. The length of 

 the shortest waves observed by Jeffreys lies in the neighborhood of the 

 theoretical value, but the shortest waves measured by Scott Russell had 

 a length of 5 cm, and those measured by Cornish were only about 2.5 

 cm long. The problem of the generation of surface waves is therefore 

 not satisfactorily solved, but Jeffreys' approach is in better agreement 

 with observations than any made previously. 



It should be added that, if only the forces due to surface tension and 

 gravity are considered, waves should not be formed until the wind 

 velocity passes the limit of 6.7 m/sec and, if only the stress of the wind on 

 the surface and gravity are taken into account, the limiting wind velocity 

 would be about 4.3 m/sec. Experience shows that these values are 

 far too high, and the turbulent character of the wind must therefore 

 be of the greatest importance. 



Form and Characteristics of Wind Waves 



In physics the general picture of surface waves is that of sequences 

 of rhythmic rise and fall. Progressive waves appear to move along the 

 surface, and standing waves appear stationary. The actual appearance 

 of the surface of the open sea, however, is mostly in the sharpest contrast 

 to that of rhythmic regularity. If a wind blows, waves of many different 



