ing as in the preceding formulas, and M(l) is the value of the eddy 

 viscosity coefficient in the case where p = 1 in (37). By putting 

 p = ^* in (37) it follows M(p^*) = M as given by (36) for the fiaiy 

 developed state. 



The formula (38) is not applicable to the very earliest stages 

 of wave development, but it seems to be sufficiently accurate for 

 P>0,1. It has already been mentioned in connection with (I8) that 

 these earliest stages of turbulent wave generation are so rapid that 

 the exact form of the relationship is of very little consequence to 

 the later development of the sea. It is to be expected that the 

 change from ordinary viscosity to turbulent eddy viscosity does not 

 occur continuously. This change to turbulent wave motion probably 

 will take place when the maximum steepness of the "ripples" is at- 

 tained with the ratio H/a = l/7» that is at a wind velocity of 

 about 123 cm/sec [14]. At a wind velocity of v = 125 cm/sec, for- 

 mula (36) would result in a value of M = 3.2 [cm" g sec" ] for the 

 "coefficient of turbulence" (eddy viscosity) in the uppermost layers 

 of the sea where wave motion takes place. The wave length of the 

 ripples at this wind velocity is 11-12 cm, and these wavelets are 

 already breaking up at the crests. Below this limit of about v = 

 123 cm/sec the initial waves have a steepness less than I/7. They 

 are stable, and the dissipation takes place only by ordinary viscosity. 



In the case of fully developed (not breaking) initial waves it 

 follows from the condition A = D, according to (21) and (32), that 



p'v^p ^ (1 - p)2 = 2^Tr^g6^ , (39) 



where A- is the coefficient of ordinary viscosity, substituted in 

 (32) for M(p), and where in (21) 



70 



