( Vl/3 = h '° ^ (33) 



where nu, , the area under the curve of the wave spectrum, is the zero-moment of the 

 spectrum, 



a o = f s n (a v )da v 



The spectral bandwidth parameter and the broadness parameter are two methods of 

 depicting the broadness of the spectrum. The spectral bandwidth parameter, 



o m mo 

 v J 2 = -2-£ - i OU) 



o 2 



m l 



and the broadness parameter 



£ 2 = m o m k ~ m 2 ( 35 ) 



each depend on the moments of the spectrum, where n^ is the nth moment of the 

 spectral density 



% = r v^ "v 11 da v 



The average zero crossing period is defined as 



'.- (^ (36) 



nip 



If current effects, which will be discussed later, are brought into con- 

 sideration, the spectrum is modified. The Jacobian transformation associated 

 with current changes the spectral densities, while the frequency becomes 

 stationary rather than encountered. Only the frequencies and the spectral den- 

 sities have been changed, the other spectral components, the directions, and rms 

 spreading have not. If the current effects are accounted for, the frequency band- 

 widths no longer are necessarily constant. 



15 



