530 



FIGURE 1. Flow visualization 

 of the initial stage of the 

 generation of wind waves by 

 use of hydrogen bubble lines 

 produced by the electrolysis 

 of water. The photographs were 

 taken from a viewpoint slightly 

 below the air-water interface, 

 so images reflected at the in- 

 terface are seen in the upper 

 1/4 of each picture. The hydro- 

 gen bubble lines are produced 

 near the left end as pulses of 

 0.002-s width at 0.04-s inter- 

 vals in a very slow, uniform 

 flow of water which was pro- 

 duced before the start of 

 wind. The wind was 6.2 m/s 

 blowing from left to right of 

 each picture. The filmed time 

 of each picture from the start 

 of the wind is shown in sec- 

 onds. The out-of- focus areas 

 were caused by some fluctuation 

 of the mean flow, for very shal- 

 low depth of the focus. In (e) 

 are seen the initial wavelets, 

 and in (f) is seen the onset of 

 turbulent mode. [Cited from 

 Okuda et al. (1976).] 



(a) 040 sec 



(b) 140 



(c) 2.36 



(d) 329 



(e) 3 78 



(f) 4 20 



A resonance mechanism for the initial generation 

 proposed by Phillips (1957) and an instability 

 mechanism for further growth proposed first by Miles 

 (1957) have been referred to on every occasion. 

 Valenzuela (1976) showed that the growth rate of 

 waves in the gravity-capillary range, observed by 

 Larson and Wright (1957) at the initial stage of 

 the generation, agrees with the expected growth 

 rate by the instability theory applied to a coupled 

 shear flow of the air and the water. 



Kawai (1977 and 1978) of our laboratory has 

 arrived at the conclusion, by systematic experiments 

 together with theoretical analyses, that the mech- 

 anism of generation of the initial wavelets is the 

 instability in a two-layer shear flow of viscous 

 fluid of air and the water, as a selective amplifi- 

 cation of disturbances of the frequency at the 

 maximum growth rate. 



The experiments were carried out mainly by use 

 of a wind-wave tunnel of 20 m length, 60 cm x 120 cm 

 cross-section, containing water of 70 cm depth. 

 After the sudden starting of wind on the still 

 surface of water, a shear flow first develops in 

 the uppermost thin layer of water, and several 

 seconds later, regular, long-crested initial wavelets 

 appears [Figure 1(e)]. His theoretical analysis of 

 the shear flow instability of the two-layer viscous 

 fluids, using the actual profile of the shear flow 

 in water, shows that the system is unstable and 

 there exists a frequency at which the growth rate , 

 kCi, is maximum (Figure 2). The frequency of kCi- 

 maximum does not necessarily coincide with that of 

 Cr-minimum, or the minimum phase speed for the 

 gravity-capillary wave. Three properties of the 

 initial wavelets determined by the experiment, i.e., 

 the frequency, the growth rate, and the phase speed 

 are all virtually coincident with those of the 

 theoretically predicted waves of the maximum growth 

 rate as shown in the following. 



Figure 3 shows an evolution of the spectrum 

 calculated by the maximum entropy method, which may 

 be applicable to nonstationary processes. Each 

 spectrum represents an ensemble average of 8 runs . 



Wavelets of a constant frequency of about 15 Hz in 

 this case grow as shown in the figure with a smooth 

 spectrum. The peak then moves to a lower frequency 

 side showing the evolution to irregular wind waves 

 having the usual spectral form. In the stage of 

 constant frequency. Figure 4 shows the agreement of 

 the observed frequency of the initial wavelets with 

 the theoretical frequency for the kC-^ -maximum, as 

 a function of the friction velocity of the air, u* , 

 but independent of the fetch. The frequency for the 

 Cr-minimum is around 14 to 13 Hz, and does not 

 coincide with the observed initial wavelets. Figure 



5 shows the agreement in the phase speed, and Figure 



6 the growth rate between the observed initial 

 wavelets and the theoretical initial wavelets for 

 kCi-maximum. 



Thus, Kawai 's conclusion is that the generation 

 of wind waves, whose initial stage is called initial 

 wavelets, is caused by the selective amplification 

 of small perturbations which inevitably occur in 

 the flow by the instability of the two-layer viscous 

 shear flow. 



However, the duration of the exponential growth 

 of the initial wavelets was limited to from 1 to 8 

 seconds in the experiments. The transition from 

 the regular, long-crested initial wavelets to short- 

 crested, irregular wind waves takes place in a very 

 short time. The spectral peak, which has grown up 

 with an approximately constant frequency, starts 

 wandering at the transition, and then moves toward 

 the lower frequency side with the energy increased 

 in a general trend as seen in Figure 3 , and also 

 in Figure 7. The transition coincides with the 

 onset of turbulence at the water surface as revealed 

 in the next section. 



3. INTERNAL FLOW PATTERN OF WIND WAVES AN 



EXPERIMENTAL SUBSTANTIATION OF THE STRONGLY 

 NONLINEAR PROCESSES 



Irregularity is a character inherent in the wind 

 waves. This has been demonstrated by detailed 



