Study on Wind Waves as a 

 Strongly Nonlinear Phenomenon 



Yoshiaki Toba 

 Tohoku University 

 Sendai, Japan 



ABSTRACT 



Recent studies on wind waves in our laboratory, 

 from a view point of strong nonlinearity of the 

 wind waves, are reviewed. The main items are as 

 follows. (1) It has been shown by experiments and 

 theoretical analyses that the mechanism of initial 

 generation of waves by the wind is the instability 

 of shear flows of two-layer viscous fluids, air and 

 water. It is a selective amplification of distur- 

 bances at the frequency of maximum growth rate. 

 However, the transition of the initial wavelets to 

 irregular wind waves including turbulence follows 

 within several seconds [Kawai (1977)]. (2) Flow 

 visualization studies of the internal flow pattern 

 of wind waves show that the shearing stress of the 

 wind is concentrated at the crest and windward face 

 of individual waves, and a special area is formed 

 where the surface wind drift, and consequently the 

 vorticity is concentrated, causing the forced con- 

 vection or the turbulent mode, which is the origin 

 of the irregularity of wind waves [e.g., Toba et al . 



(1975); Okuda et al . (1977)]. (3) Statistical 

 investigation of instantaneous individual waves in 

 a wind-wave tunnel shows clearly the existence of 

 similarity in the individual waves [Tokuda and Toba 



(1978)]. Namely, the energy spectrum, which is 

 newly defined for the individual waves, is virtually 

 equivalent to the traditional energy spectrum at 

 the frequency range from 0.7- to 1.5-times the 

 frequency of the energy maximiom. However, the energy 

 peaks which usually appear in the traditional spec- 

 trum at the higher harmonics of these dominant waves 

 completely disappear. The apparent phase speed of 

 individual waves, for each wind and fetch condition, 

 is inversely proportional to the square root of 

 their frequency, and is much larger than the phase 

 speed of linear water waves . For the individual 

 waves for each wind and fetch condition, there 

 exists statistically a conspicuous relationship of 

 the 3/2-power law [cf., Toba (1972, 1978a)] between 

 the normalized wave height and period. Consistently 



with this and the phase speed relationships, the 

 steepness of the individual waves is statistically 

 constant. (4) Discussion is presented as to the 

 possibility of approaching the above-mentioned 

 characteristics of the individual waves from the 

 similarity hypothesis and dimensional considerations. 

 Self-adjustment of the individual waves to the 

 local wind drift distribution is postulated to 

 explain the 3/2-power relationships, which may be 

 the basis of the possibility that the pure wind-wave 

 field is represented by a single dimensionless 

 parameter [Toba (1978a)]. (5) A new formulation 

 is presented for the roughness parameter or the 

 drag coefficient over the wind waves, incorporating 

 the single dimensionless parameter of the wind-wave 

 field. A physical interpretation of the form is 

 given from the internal flow pattern of individual 

 waves [Toba (1978b)]. 



1. INTRODUCTION 



In a traditional model, the wind waves are treated 

 as phenomena, expansible to component free water 

 waves having weakly nonlinear interactions among 

 waves of different wave numbers. However, detailed 

 experimental studies on the actual conditions of 

 wind waves produced in wind-wave tunnels, have 

 shown that wind waves are much more strongly non- 

 linear phenomena, especially in their younger stages. 

 This report presents a review of recent studies 

 made in our laboratory, giving much emphasis to 

 the strong nonlinearities which are inherent in 

 wind waves. 



2. INITIAL GENERATION OF WIND WAVES 



The first topic starts with an approach from the 

 process of the initial generation. The wind waves 

 have long been assumed to be generated from a still 

 water surface by the effect of pressure fluctuations. 



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