where: 



p = Density of the cable 



S = Metallic cross -sectional area of cable 



E = Modulus of elasticity of cable 



K = Constant of friction on the cable by the surround- 

 ing water . It should be kept in mind that K may 

 not be actually a constant. 



In an actual operation, these waves can appear while the array is 

 being lowered at some rate, i.e., L in general changes with time . However, 

 if we assume that the rate of lowering is small as compared to the velocity of 

 the dynamic displacement due to the waves, then L can be considered constant 

 in time and the following dimensionless variables and parameters can be de- 

 fined: 



(5) 



X 



L ' 



t' 



tc 

 L 



E 

 Pc' 





 c 



KL 



p cS 

 c 



(6) 



where c is the "velocity of sound" in the cable. 

 Equation 4 then reduces to: 





In order to solve Equation 7, one needs two boundary conditions 

 (most likely one at each end of the cable) and, if transient solutions are sought, 

 initial conditions as well. One of the boundary conditions, which we will apply 

 here, is the specification of u at x' = for all times. Practically speaking, 

 we should specify the motion of the ocean surface for all times . But, then the 

 dynamics of the vessel and the way in which the cable is attached to the vessel 

 must be considered simultaneously with the dynamics of the cable and array, 

 which is a very complex problem. A discussion of the dynamics of the vessel 

 is presented in Section V; here we will assume that we know u at x' = for 

 all times . 



11 



Arthur m.littkjnc. 



S-7001-0307 



