21. RIPPLES 



C. S. Cox 



Surface waves of sufficiently short length are controlled mainly by the ratio 

 of surface tension to density in water. The relation (Lamb, 1945, Art. 267) 

 between phase velocity c and wavelength A on still water in the absence of wind 

 is (Fig. 1) 



c2 = *c,„2(AA,„-i + A,„A-i). 



(1) 



Fig. 1. Phase velocity c and frequency/ as functions of wavelength A. 



The phase velocity reaches a minimum, Cm, at wavelength Am, where 



Cm'' = 2{l -s){\+s)-HgTy'K (2) 



Xm = 2n{Tlgy^; 



s is the ratio pi/p2 of air to water density, g is the acceleration due to gravity, 

 and T is the surface tension divided by pz — pi. 



According to Kelvin's definition, waves with lengths shorter than A^ are 

 ripples, longer waves are gravity waves. Numerical values appropriate to clean 

 sea-water are roughly 



s = 0.0012 



T = 14 cm3 sec~2 



Cm = 23 cm sec~i 



Xm = 1.7 cm 



fm = CmlXm = 13.5 c/s. 

 [MS received July, 1960] 720 



