H = 4o (3-13) 



m 

 o 



Experimental results and calculations based on the Rayleigh distribution 

 function show that when wave shapes are not severely deformed by shallow-water 

 depth or high wave steepness, the following approximation can be used 



(3-14) 



(3-15) 



(3-16) 



These approximations may be poor when waves are breaking or near breaking (see 

 Chapter 3, Section 11,5, Comparability of Wave Height Parameters). 



The variation of a.^ with frequency can be used to estimate the distri- 

 bution of wave energy as a function of frequency. This distribution is called 

 the energy spectrum, often expressed as 



2 

 a . 



Eim.) iLui). = -J- (3-17) 



where E(a).) is the energy density in the 2 component of the energy 



spectrum and (Ao)). is the frequency bandwidth (difference between successive 



0) .) . 

 3 



J 



Equation (3-17) can be combined with equation (3-12) and N made to approach 

 infinity to give 



/ 



a2 = / E (oj) do) (3-18) 



o 



where E(a)) is the continuous energy spectrum. 



The spectrum E(a)) or E(a).) permits specific parts of the total wave 

 energy to be assigned to specific frequency intervals. Frequencies associated 

 with large values of E( oj) are dominant frequencies (periodicities) in a wave 

 field. Frequencies associated with small values of E(a)) are usually unim- 

 portant. It is common for ocean wave spectra to show two or more dominant 

 frequencies, indicating the presence of two or more wave trains (see Figure 

 3-6) . The spectrum allows easy identification of all prominent frequencies 

 present and an assessment of their relative importance. Thus it also permits 

 a first approximation in the calculation of velocities and accelerations from 



3-12 



