V. THE DYNAMICS OF THE VESSEL AND SPECTRAL 

 CHARACTERISTICS OF A REALISTIC SEA 



It has been already pointed out that, in calculating the dynamic stres- 

 ses induced in the cable by a disturbed sea, the dynamics of the vessel and the 

 way in which the cable is attached to it must be considered simultaneously with 

 the dynamics of the cable and array. Besides the elastic force exerted by the 

 cable, other forces acting on the vessel are mertia, dynamic buoyancy due to 

 the waves of the sea, viscous damping, and damping due to the "radiation" of 

 surface waves by the vessel. Then, in an analysis of the entire system, simi- 

 lar to the analysis carried out in Section IV for the system without the vessel, 

 at least three additional parameters must be introduced. This will be a very 

 complicated problem. 



We will assume that the dynamic loading of the vessel by the cable 

 and array is negligible and, therefore, the motions of the vessel during the 

 operation will not be influenced by the cable and array. Because of the relative 

 dynamic masses of the vessel and the cable and array, this condition is well 

 satisfied in practice, except possibly when the array is lowered through a long 

 boom from the side of a vessel which is rather unstable in rolling. 



In Section IV, we have shown that near resonant frequencies, which 

 can be as small as 1.5 rad/sec, the amplitude of the input to the cable should 

 be about 2 feet or less. This definitely shows that the vessel must be very 

 stable at such frequencies, and it limits the variety of ways in which the cable 

 can be attached to the vessel. 



Let us first examine the spectral characteristics of a realistic sea 

 where such an operation will be carried out. A realistic sea has a continuous 

 probabilistic distribution of all possible amplitudes and frequencies. Depend- 

 ing on the weather conditions (mostly the speed of the wind) and the degree of 

 development of the sea (duration of the wind and extent of the fetch), amplitudes 

 above a certain value and frequencies outside a certain range are not very prob- 

 able, while amplitudes and frequencies within a certain range are most probable . 

 It appears that separate probability data for amplitude or frequency exist in 

 available literature, but data for the joint probability for a specified amplitude 

 and frequency do not exist; i.e. , we do not really know what is the probability 

 for the occurrence of a certain amplitude with a certain frequency in a given sea 

 state. Tables I and II show some important characteristics of a fully arisen sea 

 (infinite fetch and wind duration) at various wind speeds. These data have been 

 obtained from "Observing and Forecasting Ocean Waves," H.O. Pub. No. 603, 

 U.S. Navy Hydrographic Office. The significant range of frequencies is defined 

 as the range outside which it is highly improbable to find a frequency at the indi- 

 cated wind speed. 



25 



Arthur B.lLittU3M. 



S-7001-0307 



