The techniques developed for spectral analysis and wave group analysis 

 were applied to the selected data samples. Results are presented in Section 

 V. In Section VI, the results are discussed and related to the six hypoth- 

 eses. Evidence from the field data samples supports the validity of each of 

 the six hypotheses. 



A summary of this study is given in Section VII. 



II. LITERATURE REVIEW 



1 . Spectra . 



Theories of ocean wave development have been based over the last 15 years 

 on one of two general concepts of a wave field. The first approach deals with 

 evolution of a continuous spectrum representing the superposition of an infi- 

 nite number of independent frequency components. The second approach deals 

 with evolution of an initially uniform train of steep waves. Both approaches 

 were first used in conjunction with deepwater waves, but more recent develop- 

 ments have included shallow-water waves as well. Relevant literature is 

 reviewed in this section, primarily as it relates to deepwater waves. 



a. Evolution of Continuous Spectra . Consideration of the spectrum of 

 ocean waves began to appear in the literature in the early 1950' s. Examples 

 given by Harris (1974) are Seiwell (1949), Ursell (1950), Pierson (1950), and 

 Neumann (1952). The spectrum is used to describe a sea surface which is 

 generally regarded to have Gaussian-distributed displacements. The Gaussian 

 assumption along with the assumptions of random phase and stationarity led to 

 application of computational procedures developed in other disciplines (e.g., 

 Taylor, 1938; Blackman and Tukey, 1959) to ocean waves. These assumptions 

 have formed the cornerstone of wave spectral analysis techniques, although 

 Harris ( 1974) pointed out that the development of the fast Fourier transform 

 algorithm (Cooley and Tukey, 1965) obviated the need for many of the restric- 

 tive assumptions . 



Nonlinear interactions between spectral components have increasingly come 

 to attention in recent years. Second-order interactions have been shown to be 

 of little significance. Third-order interactions, although initially small, 

 sometimes exhibit unbounded growth with time as discovered by Phillips 

 (1960). Subsequent theoretical explorations of this surprising third-order 

 resonant interaction between frequency components include Longuet-Higgins 

 (1962), Benney (1962), and Hasselmann (1962), 1963). 



The viability of third-order resonant interactions was demonstrated by 

 laboratory experiments in several special situations (Longuet-Higgins and 

 Smith, 1966; McGoldrick, et al., 1966) before finally being demonstrated for 

 growing wind waves in the laboratory by Mltsuyasu (1968) and later by Wu, Hsu, 

 and Street (1979). Field data showing that nonlinear energy transfer is an 

 important mechanism in explaining fetch-limited wave growth were presented 

 in considerable detail by Hasselmann, et al. (1973). Examples of nonlinear 

 transfer functions computed directly from the field spectra are shown to com- 

 pare favorably with transfer functions derived from theoretical expressions 

 for the third-order resonant interactions. 



14 



