Miles 



of common knowledge (see, e.g., Franklin (10)), and both Keulegan (22) and Van 

 Dorn (23) found that the addition of detergent prevented the formation of sensible 

 waves by winds of at least 12 m/sec. There appears to be little doubt that the 

 primary effect of a surface film is to increase the dissipation, and hence the 

 energy that must be supplied by the wind, although associated changes in the 

 velocity profile of the wind also could be significant. (Dorrestein (14) suggested 

 that a surface film inhibits the transfer of energy from wind to waves through 

 tangential stresses, but it is now generally accepted that this transfer takes 

 place primarily through normal pressures.) 



We first assume that the aerodynamic energy transfer can be described by 

 the (equivalent) logarithmic decrement (24) 



-a^ = 77s(Ui/c)2/3, (36) 



where s - pJp^ is the air/water density ratio, c = a- /v. is the wave speed, Uj is 

 a reference wind speed, and /? is a dimensionless energy-transfer coefficient 

 that depends on c/Uj. Equating -a^ to a^'\ as given by Eq. (6), and solving for 

 u 1 as a function of c AJ j , we obtain 



u, . (gv/2s2)'/'(c/u, )'''/?- ''' (37a) 



= 150 (c/Ui) 1/3/3' ^/^ cm/sec , (37b) 



Where Eq. (37b) follows from Eq. (37a) after setting g = 980, v =10-2 ^^^ 

 s = 1.2x10"^ in cgs units. Invoking the theoretical model (24,25) for an equiva- 

 lent laminar profile of the form u = Uj log y + const., we find that the minimum 

 value of Uj predicted by Eq. (37b) is about 1 m/sec at cAJj ^ 3, corresponding 

 to a nominal wind speed of about 12 m/sec and a wavelength of about 6 m. The 

 predicted critical wind speed of 12 m/sec is at least consistent with the observa- 

 tions of Keulegan (22) and Van Dorn (23) and is roughly an order of magnitude 

 larger than that predicted by a similar calculation based on a^° ^ — namely, 

 Ui = 14-15 cm/sec for gravity waves of 20-30 cm (25). 



A rather different energy-transfer process, which depends on the existence 

 of a viscous sublayer for the wind structure very close to the water, may be ef- 

 fective for cAli < 3 (26). Hidy (27) has obtained qualitative confirmation of the 

 theoretical model, but found it necessary to postulate increased dissipation, 

 relative to that based on a.\^^ , in order to obtain approximate, quantitative 

 agreement. He commented that, "Although care was taken to minimize the 

 contamination of the water surface . . . , small amounts of oil may have been un- 

 avoidably present [and] could easily account for the systematic deviation be- 

 tween [the theoretical and experimental results] shown in the data." The origi- 

 nal theoretical predictions (26) were carried out for a wind profile that is linear 

 in the viscous sublayer and logarithmic above this layer with a free- surface 

 damping given by a^°>. Replacing a^° > by a^'> in these calculations, we find 

 that waves of roughly 4-10 cm in length should be generated by a wind with a 

 friction velocity u^ of 15 cm/sec, corresponding to a nominal wind speed of 

 roughly 4-5 m/sec. This prediction is consistent with the observations of Hidy, 

 but not with those of Keulegan (22). 



582 



