As an example, a family of wave spectra for fetch length X = 150 NM 

 (185 km) and for significant wave height of 4.0 m (13.1 ft) is shown in 

 Figure 9 . 



It is of interest to see a comparison of spectral shapes for three 

 different families. Since these families of wave spectra consist of 

 several members, it is not convenient to compare them by assembling all 

 members into one figure. Hence, a comparison will be made on three members 

 taken from each family. These three represent (i) the spectrum which is 

 most likely to occur, and (ii) the spectrum which has the smallest modal 

 frequency, and (iii) the one which has the largest modal frequency. 



Figure 10 shows a comparison made for a significant wave height of 

 8.2 m (26.9 ft) in the North Sea. The fetch length is 250 NM for the 

 JONSWAP family. As can be seen in the figure, the shapes of the JONSWAP 

 family are significantly different from those of the families for open 

 seas. That is, the range of modal frequencies is much smaller and the 

 shapes are much sharper for the JONSWAP family than those of the open sea. 

 This may cause a significant difference in the magnitude of responses of 

 mooring systems in a seaway; and therefore, serious consideration must be 

 given to this for the design of mooring systems located in fetch-limited 

 areas. 



EXTREME WAVE HEIGHT CRITICAL FOR THE SYSTEM 



It was stated in the Introduction that the concept of estimating 

 extreme wave height along with its associated period is highly desirable 

 for design consideration. This is because if the wave period is either 

 sufficiently long or short in comparison with the natural motion periods 

 of a mooring system, then the system may not be in danger even though the 

 wave height is large. Hence, for more rational design of a mooring system, 

 it is necessary to estimate extreme wave height for periods critical for 

 the system. These estimates can be achieved through the use of a joint 

 probability function of wave height and period. That is, we estimate the 

 extreme wave height under the condition that wave periods fall into a 

 certain range critical for the system's behavior in a seaway. 



Longuet-Higgins (1975) has derived the following probability density 

 function of wave height and period: 



99 



