539 



itfr 



-o FETCH-I36m| 

 •• 100 |tOB4(I972I 



69 I 



KAWAI ttol II977I 



KUNISHI II963I 



MITSUYASU at ol (19711 



I.-0025 ub/o- 



irf: 



l(f 



■T" 



T" 



.*> 





/ 



10 



u.'/i-tr 



10" 



FIGURE 18. Data plots for the relationship (8) in a 

 dimensionless form. The same data with Figure 17 is 

 used. [Cited from Toba (1978b).] 



zg* = au^*/a* 



-/va, a 



0.025 



(8) 



is a better representation [Toba {1978b)]*. In 

 Figures 17 and 18 are shown plots of some available 

 data in tlie forms of (5) and (8) including wind-wave 

 tunnel experiments and field observations. It 

 should be said that the new formula is better at 

 least. It is seen from Figure 19 that the brealcing 

 of wind waves is also expressed as a function of 

 the parameter, u* /va, for data from the wind-wave 

 tunnel and the sea. The ordinate is the percentage 

 of the brea]cing crests among individual waves 

 travelling through a fixed point, and it was deter- 

 mined by the same procedure for both cases. The 

 breaking of wind waves occurs for the condition 

 u*2 va > 10^. 



Equation (8) corresponds to an elimination of g 

 from the form of (5) . In view of the recent 

 recognition since Munk (1955) that the waves of 

 high frequency components play a major role in the 

 transfer of momentum from the wind to the sea, it 

 seems rather unreasonable that Eq. (7) contains 

 information only of energy containing waves as o 

 in the denominator. However, since u* /v = i/y = 

 3u/vjri represents the magnitude of the average wind 

 stress, and a~^ a T is a measure of the integration 

 time associated with individual waves, u^^ /va is 

 interpreted as a measure of the accumulation of 

 the shearing stress or the concentration of the 

 vorticity at each crest of the individual waves, 

 conveying the horizontal momentum transferred from 

 the air into the interior of the water through 

 forced convection, whether or not the waves are 

 breaking, as stated in Section 3. As this effect 



*Toba, Y. (1978b). A formula of wind stress over 

 wind waves. To be published. 



increases, the total momentum transfer, as well as 

 the probability of the occurrence of the breaking 

 increases. 



The form of (8) may be transformed to 



^0 



!'"*Vg, 



i' = u c/u 



(9) 



which may be interpreted as an extension of Charnock's 

 formula (6) to include information of wind waves 

 in the form of the wave age, c/u^ , where c is the 

 phase speed of the dominant waves. Also, the drag 

 coefficient, C^,, may be expressed from (8) as 



k2/[ In (zioo/au )] ^ 



(10) 



where k is the von KarmSn constant and z^q the 

 reference height of 10 m. According to (10) , Cj, 

 is more sensitive to the wind waves than to the 

 wind speed. 



7. SHORT SUMMARY 



We may summarize the review paper as follows. First, 

 the initial wavelets are generated by an instability 

 of two-layer viscous shear flow of a type of insta- 

 bility that immediately transfers to three 

 dimensional turbulence. Second, the main phase of 

 the growth of wind waves is regarded as the conse- 

 quent, strongly nonlinear processes. Third, the 

 traditional component wave model is not necessarily 

 realistic, and the elementary physical substance 

 might better be treated by individual waves, 

 especially for younger stages as observed in wind- 

 wave tunnels. Fourth, the individual waves 

 represent a conspicuous and characteristic similarity 

 of structure, presumably as a result of the strong 

 nonlinearities , and this may be the basis for the 

 pure wind-wave field being represented by a single 

 dimensionless parameter. Finally, a new stress 

 formula over the wind-wave field is presented. 



40 



11130 



S20 



:io 



1 r 1 1 — r — I — r— r-| 



o FETCH • 13.6 ml 



d) 10,0 ^ TOBA (1972) 



e 6.9 J 



• TOBA at al (1971) 



-I 1 — I — 1 — i—r 



<s> o 



10' 



10' 

 U,«/Kr 



FIGURE 19. Percentage of breaking crests among indi- 

 vidual waves traveling through a fixed point, may be 

 expressed as a function of the same parameter with 

 Figure 18. Toba et al. (1971) data are from tower sta- 

 tion observations, which are common with data of Kawai 

 et al. (1977) used in Figure 18. [Cited from Toba 

 (197Bb).] 



