74. The integrated direction spectrum of Figure 2d shows the net 

 directional distribution. Distinct peaks for sea and swell can be seen here 

 as well. The primary wind sea has energy spread over a range of approximately 

 90 deg with most energy (say, values above about half the primary peak) spread 

 over at least 40 deg. It appears that this can be approximated, more or less, 

 by the distribution model shown in Figure 2c. However, a detailed look at the 

 frequency-direction spectrum shows that the directional distribution is 

 different for each frequency. Distributions at some frequencies have more 

 than one peak. That is, real waves can be attacking a beach or coastal 

 structure simultaneously from many directions and frequencies. 



75. All examples shown in Figure 2 have the same H^^ , peak frequency, 

 and peak direction. It should be clear that an enormous variety of real sea 

 states is possible for fixed values of these parameters. This means that, 

 while these parameters are important in sea state description, they do not 

 define a sea completely. There are further characteristic properties that 

 must be resolved. 



76. The important point here is that the frequency-direction spectrum 

 is a compact form of bookkeeping which illustrates the energy distribution of 

 a wave field. It is a simple extension to one additional dimension of the 

 conventional way in which frequency spectra are considered. The frequency- 

 direction spectrum can be used to reconstruct a realistic sea in numerical and 

 physical models using the equations given; that is, there is an elemental 

 volume of the frequency-direction spectrum for each of the frequency-direction 

 grid intersection points. Using Equation 7, a wave amplitude can then be 

 assigned for each of the discretized frequencies and directions. If an 

 initial phase is chosen at random for each resulting wave train. Equation 5 

 along with Equation 2 can be used to simulate observed seas in models. 



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