local wind-driven sea could occur from the same arc of direction as the 

 background swell such that there would exist a strong multimodal variation 

 with frequency in that range of directions. Low- frequency waves at later 

 stages of a locally wind- driven sea could occur at the same frequencies as 

 part of the background swell, creating multimodal directional distributions of 

 energy at these frequencies. Questions then arise as to (a) how often there 

 are distinct groupings of wave energy; (b) where groupings merge, how well the 

 complete spectrum can be related to the generation and radiation processes 

 that govern the wave field; (c) how important multiple peaks are to the 

 overall energy distribution; and (d) whether or not there is similarity in 

 energy distribution shapes. 



A Well-Developed Sea State 



130. Figure 7 shows the frequency- direction spectrum 21 hr after the 

 time of the spectrum shown in Figure 6. Considerable energy is present as 

 indicated by the H^g of about 3.1 m. The peak frequency in the frequency 

 spectrum has evolved from about 0.31 Hz in Figure 6 to 0.11 Hz in Figure 7. 

 Both the frequency- direction spectrum of Figure 7a and the contour plot of 

 Figure 7b show the peak direction to be near -20 deg. The integrated direc- 

 tion spectrum shows a maximum in total energy at about 10 deg. In all 

 distributions the total energy spread is rather large. Energy is spread over 

 a range of about 60 deg based on the 50 -percent contour line in Figure 7b. In 

 the integrated direction spectrum of Figure 7a, the spread is nearer to 90 deg 

 based on the arc subtended by the energy distribution at half the spectral 

 peak. 



131. This example has several interesting features. One is a sugges- 

 tion of refraction. Low- frequency waves in Figure 7 are more nearly shore- 

 normal (i.e., near deg) than are high-frequency waves. Compared to high- 

 frequency waves, low-frequency waves require a rather significant horizontal 

 space to evolve by wind forces. A wave train with a 10-sec period has a phase 

 speed of order 10 to 20 m/sec in water depths greater than 8 m. At these 

 speeds, a wave could cross the continental shelf (see Figure 1) in about 1 to 

 2 hr, a time scale comparable to the duration of one data collection in the 

 present experiment. Long waves also are affected by the bottom at greater 

 depths than are high-frequency waves and so would tend to be steered more by 



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