"^ = -f/p n ds + /C^u lu I dl + /C a dl (2) 



■'•'^ •'Dn'n' ■'an ^ ' 



Note that the first term, v/hich is sometimes called the 

 Froude-Krylov force, was included with the added mass term in the 

 original Morison paper, and this is approximately correct for a 

 slender stationary cylinder. In the case considered here of a 

 moving body, however, the relative acceleration term includes 

 components due to both body motion and fluid motion while the 

 Froude-Krylov term is dependent upon fluid motion alone. 



The pressure, p, is determined from Bernoulli's equation and 

 the velocity potential appropriate for the wave motion. For 

 inf initisimal , deep water waves the potential function is given by 



<P = ~ e^^ sin(kx - tot) , (3) 



and the pressure by 



P = -pgn - pH + |p(*x' "^ ^y'^^^z'^ • ^^^ 



In a linearized motion analysis procedure, the last term in 

 the expression for the pressure is neglected since it involves the 

 square of the (small) wave-induced fluid velocity. 



The second term in equation (2) involves the square of the 

 relative velocity between fluid and member and is chosen by analogy 

 to the conventional representation of the fluid force on a body 

 immersed in a steadily flowing fluid. In order to obtain a linearized 

 formulation of the problem, this quadratic drag force is sometimes 

 replaced by an equivalent linear drag force, C^u . The equivalent 

 linear drag coefficient C" is chosen in such i way that the temporal 

 mean square error between the linear drag and the "exact" quadratic 

 drag is minimized. In regular waves, this results in 



*^D " 3¥ '^o'^nO (5) 



where u ^ = amplitude of the relative velocity. 

 nO "^ 



In random waves, 



where u = RMS value of the normal relative velocity, 

 n 



130 



