introduces a new time scale into the motion of the sea. The new, or modula- 

 tion, time scale is distinct from and substantially longer than the character- 

 istic time between waves. Modulation time scales can assume values which are 

 compatible with resonant behavior in many floating structures. They can also 

 lead to resonant oscillation of moored ships as well as to resonant oscilla- 

 tion in semienclosed harbors and bays. 



High wave groups seem to be a real characteristic of gravity waves as 

 observed in laboratory wind-wave flumes and in a wide variety of field con- 

 ditions. Evidence reviewed in Section III indicates that groups are more 

 common than would be expected if each wave height were randomly related to the 

 preceding and following wave heights. 



Unfortunately, wave grouping characteristics in field records sometimes 

 vary greatly over short time intervals (e.g., Burcharth, 1980). The varia- 

 tions, which are not consistent with present concepts about wave groups, 

 have made it difficult to describe grouping characteristics empirically. 

 It must be concluded that, despite its engineering significance and its 

 demonstrated presence in field records, the phenomenon of wave grouping is 

 poorly understood. 



It is often assumed that the sea surface represents a random Gaussian 

 process and that the Fourier transform of a time series of sea-surface eleva- 

 tions represents a continuous spectrum with an infinite number of independent 

 frequency components. Wave groups can be explained as modulations resulting 

 from linear superposition of high-energy components near the peak of a narrow 

 spectrum. This reasoning leads to the supposition that some measure of 

 spectral width may be related to wave grouping characteristics in the time 

 series. However, efforts to identify such a relationship in field data have 

 generally failed. 



An alternative approach which has received increasing attention during 

 the last 5 years treats wave groups as a nonlinear phenomenon and rejects the 

 assumption that all spectral components are independent. An obvious case in 

 which spectral components are not independent is a record of steep waves with 

 peaked crests and flat troughs. Wave profiles may be described as a summation 

 of a wave of the fundamental frequency and waves at frequencies which are 

 integral multiples of the fundamental, often called a Stokes wave. The spec- 

 trim has peaks at harmonics of the dominant frequency which are phase-bound to 

 the fundamental and are clearly not independent. 



Further evidence of nonindependence in the spectrum was published by 

 Benjamin and Feir (1967). Finding that the Stokes wave is unstable to small 

 perturbations in a certain range of frequencies, they showed in the laboratory 

 and in theory that bound spectral components can also be expected at discrete 

 frequencies very near the dominant frequency, much closer than the second 

 harmonic. The bound subharmonic components are evidenced in the time series 

 as strong modulations of the dominant wave. 



The Benjamin-Feir (BF) theory, as well as that of Longuet-Higgins (1980), 

 deals only with the growth of instability on an initially nearly uniform wave 

 train in relatively deep water. The theory does not follow the long-term 

 evolution of the wave condition. Also, it does not deal directly with the 

 problem of an actively growing sea state. Despite these restrictions, the BF 



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