Longuet-Higgins (1980) extended the analysis of subharmonic instabilities 

 to determine the frequency of the fastest growing instability as a function of 

 wave steepness. His results indicate slightly longer modulation periods than 

 predicted by the BF theory for wave steepness between and 0.3. Longuet- 

 Higgins (1980) showed that his results compare more favorably than the BF 

 results with the laboratory wind-wave data of Lake and Yuen (1978). 



An extensive review of the literature relevant to instabilities of deep- 

 water waves is given by Yuen and Lake (1980). 



The concept of a perturbed carrier wave train can be reconciled with a 

 broad spectrum of energy only if the assumption of independent spectral com- 

 ponents is abandoned. The nonpeak spectral components can be considered as 

 artifacts of the attempt to describe nonlinear waves with a set of linear 

 components. This interpretation has the direct consequences of well-defined 

 relationships between the carrier and other spectral components and a constant 

 phase speed for all components. Higher order harmonics of the carrier have 

 been generally considered to fit this description when wave steepness is high. 

 The most convincing evidence that spectral energy at nonharmonics may also be 

 a result of nonlinear wave shapes has been obtained by computing phase speed 

 for each spectral component between a spatially separated pair of gages. 



Early field evidence that the phase speed of spectral components can be 

 higher than expected from the linear dispersion relationship was obtained by 

 Burling (1959), Von Zweck (1969), and Yefimov, Solov'yev, and Khristoforov 

 (1972). Laboratory measurements by Ramamonjiarisoa and Coantic (1976) for 

 wind waves and by Lake and Yuen (1978) for mechanical and wind waves indicate 

 that phase speed for steep wave conditions is essentially constant for fre- 

 quencies higher than the peak spectral frequency. Additional evidence of 

 deviation from linear theory is given by Rlkiishi (1978), Mollo-Christensen 

 and Ramamonjiarisoa (1978), Ramamonjiarisoa and Giovanangeli (1978), and 

 Ramamonjiarisoa and Mollo-Christensen (1979). The latter reference includes 

 field measurements which led the authors to suggest that phase speed at fre- 

 quencies above the peak can range between the value from linear theory and the 

 phase speed of the peak frequency, depending on the degree of nonlinearity. 



The evidence is not conclusively in favor of interpretation of the 

 spectrum for steep waves as a system of bound components. Careful studies 

 indicating the efficacy of linear theory for describing phase speeds of com- 

 ponents in a wide frequency range around the peak (but terminating before the 

 second harmonic of the peak) have been reported by Mitsuyasu, Kuo, and Masuda 

 (1978, 1979); Kuo, Mitsuyasu, and Masuda (1979a, 1979b); and Komen (1980). 



Although the presence of bound frequency components has clear implications 

 for nonrandom-phase relationships between components, this important aspect of 

 a wave record has apparently never been examined explicitly. 



2. Wave Groups. 



Increasing recognition of the practical importance of a tendency for high 

 waves to occur in groups has led to numerous studies. Most of the studies 

 deal either with the serial variation in individual wave heights and periods 

 or with characteristics of an envelope of the individual waves. 



18 



