Kaplan 



(1 +€,)cf); = V»4>03+Vo<|>J- Us (111) 



e; = V3' + U> (112) 



T 



which are a set of first order linear partial differential equations. 

 The boundary conditions for this set of equations is the next task of 

 importance. For a moored buoy in a combined current and seaway, 

 the current is felt acting on the buoy and also on the cable. How- 

 ever, the wave effects attenuate rapidly with depth, and hence the 

 wave forces act on the buoy along with no influence assumed on the 

 cable. In that case the buoy motions due to a regular sinusoidal 

 seaway (assumed for analytical simplification) are transmitted to 

 the cable at its attachment point, and the cable motions are then 

 sinusoidal in time at that point. 



The boundary conditions at the anchor point at the sea bottom 

 axe given by 



U=V = 0, s = (114) 



and at the buoy attachment point for the cable, s = i , the boundary 

 conditions are much more complicated. The velocities at the buoy 

 attachment point are given by 



u = X - Zj.e (115) 



V = z - ice (116) 



• • • 



where x, z and 9 are the wave-induced surge velocity, heave 



velocity, and pitch angular velocity, respectively, and Zc and ic 

 are the vertical and horizontal distances from the buoy CG to the 

 cable attachment point. The normal and tangential velocities are 

 defined by Eqs. (91) and (92), and considering the wave-induced 

 naotions to be of the same order as linearized perturbation terms, 

 the boundary condition relations for the perturbations are 



U' = (x - Zge)sin 4>o - (z -^c^) ^°^ "^0 (^^"^^ 



V' = (x - Zce)cos j^+ (z - i^e) sin <f>o (118) 



at s = i , where x, z and can be represented in the e form 

 for a sinusoidal wave input. The boundary conditions at s = are 



1066 



