4. Applicability of Regular Wave Coefficients to Irregular Wave Climates . 



Prototype wave conditions are, for the most part, strongly irregular. 

 Many design coefficients, however, have been developed in laboratory exper- 

 iments under regular monochromatic wave conditions. Hence, analysis of 

 prototype situations based on regular waves generated in wave tank tests may 

 be inadequate unless appropriate modifications are applied to the irregular 

 spectrum. The transmission coefficient, C t , for regular waves can be used 

 to calculate the corresponding coefficients in irregular waves, according to 

 Araki (1978). If the frequency of the incident wave is f, the transmission 

 coefficient of the regular wave field is C t (f). The frequency spectrum of 

 the transmitted wave, S t (f), is related to the frequency spectrum of the 

 incident wave, S^Cf), by 



S t (f) = [C t (f)] 2 x Si (f) (41) 



When the probability density function of the wave heights follows a Rayleigh 

 distribution, the significant wave height of the incident wave, (H*) / , is 



(H i ) l/3 = 4.0/ /"s ± (f) df (42) 



Hence, the significant wave height of the transmitted wave, (H ) / , is 



(H t ) l/3 = 4.0 // [C t (f)] 2 S i (f) df (43) 



The ratio of the significant transmitted wave height, (H t ) / , to the 

 significant incident wave height, ( H i^i/ 3 > is tne significant transmission 

 coefficient, (C t ) /. 



/nc t (f)] 2 S i (f) df 



(C t ) l/3 = /- ^ (44) 



/ / S.(f) df 



V 



This description of an ocean wave climate provides for the application of 

 experimental results from periodic wave tests to irregular wave conditions. 

 An objective in the design of mooring systems is to obtain a force spectrum 

 from which the various descriptors of the force (such as maximum probable 

 force) can be evaluated. A pertinent assumption is that if the wave heights 

 are distributed as a Rayleigh function, the mooring forces will be similarly 

 distributed. This assumption allows a researcher to obtain the maximum prob- 

 able force which can be used to indicate the probable degree of safety of a 

 mooring. When a force spectrum has been obtained from the wave spectrum in 

 the manner of Raichlen (1978), the maximum probable force can be expressed as 



50 



