Wave Induaed Forces and Motions of Tubular Stratures 



in the direction of propagation of the waves, r| is directed upward, 

 and t, is defined so as to form a right-handed coordinate system. 



Wave Forces 



In order to be consistent with our assumption of small plat- 

 form motions, an assumption of small incident waves must also be 

 made. The velocity potential for regular infinitesimal gravity waves 

 moving in the direction of the positive |-axis is 



<p{i,r\,i,t) = Ml S2^lL^^ sin (ki - cot). (8) 



■r\=.»i»s»/ j^ coshkd ' 



The pressure is given by 



P = - pgTl - P -gf , (9) 



and the linearized velocities and accelerations in the ^- and r|- 

 directions by 



d(p dip 



au • av 



^ = ar ^ = 87 



(10) 



We shall first compute the Froude-Krylov force which is 

 given by the first term in (7). This integral, which is to be evaluated 

 over the entire immersed surface of the body in order to obtain the 

 total force, may be replaced by the following volume integral through 

 the application of Gauss' theorem 



The corresponding integral expressed for the moment referred to the 

 4'n£,-axes is 



-II 



p( r X n ) ds 

 Note that in defining these integrals for a member which projects 



1091 



