The cosine bell data window was applied to the simulated records; 

 therefore, it was sufficient to consider wave trains consisting of three 

 sinusoids with nearby periods spread over at most six adjacent spectral 

 periods. In general, the periods of waves in the ocean will differ from 

 the spectral periods. Thus, the sinusoids in each simulated observation 

 were specifically assigned periods differing slightly from the spectral 

 periods by use of equation (6) . Central periods of about 8 and 16 seconds 

 were chosen to simulate 8- and 16-second swells. Swells with periods in 

 this range are observed on the west coast. 



Each simulated wave record consisted of values of the wave profile 

 at the five gage locations computed at 0.25-second intervals for 17.07 

 minutes (1,024 seconds) , to simulate the sampling rate and record dura- 

 tion customarily used at CERC for field data. 



The three sinusoids were assigned specific directions and zero initial 

 phase at the origin of coordinates, and were propagated across the array 

 assuming a constant depth of 9.14 meters. Appendix C shows that the 

 Finite Fourier Transform gives the correct phases for three sinusoids 

 thus combined, provided the sinusoids are assigned the same direction, 

 nearly the same amplitudes, and the frequency difference of each com- 

 ponent to the nearest spectral frequency is the same. A frequency dif- 

 ference of 0.134/1,024 = 0.000120 hertz was chosen. 



Characteristics of the first eight simulated observations are given 

 in Table 3. Rough considerations of refraction using linear theory 

 (McClenan, 1975) yield 22° from the normal to the coastline as the maxi- 

 mum possible direction that waves with a 16-second period may have at 

 the depth of the array. Directions within 21° N. and 21° S. from the 

 normal were chosen for the first four simulated wave trains. Since waves 

 with an 8-second period may approach the coastline at the array site from 

 a much wider arc, directions up to 60° N. and 60° S. were used for the 

 directions of the fifth to eighth simulated trains. 



The computed spectra for these eight simulated observations are shown 

 in Appendix D (Figs. D- 1 to D-8) . In these figures the variance of the 

 record, proportional to the energy, at each spectral period is plotted 

 versus a linear frequency scale. No grouping of the variance at adjacent 

 spectral periods has been made. These ungrouped spectra are referred to 

 as high-resolution spectra. For spectra computed from 1,024-second records, 

 this high resolution is approximately 0.001 hertz. 



The program used to compute these spectra is the same program used at 

 CERC for the analysis of field data. Many spectra of field data computed 

 with this program and summarized by grouping 11 adjacent spectral periods 

 are given by Thompson (1974). 



The effect of spillover in the spectrum is shown in the figures of 

 Appendix D. Each spectrum resulted from combining only three sinusoids; 

 however, energy contributions appear at from five to nine adjacent spec- 

 tral periods. 



23 



