where Re represents the real part of the function on the right side. The eventual 

 sea-surface distribution of pressure P'(X,Y,T) and flux Q'(X,Y,T) similarly are 

 assumed to be of the form 



P'(X,Y,T) = Re P(X,Y)exp[(a-ia))T] (2.2a) 



Q'(X,Y,T) = Re Q(X,Y)exp [ (a-ia))T] (2.2b) 



In this alternative approach, one is then faced with an initial-value problem, with 

 the obvious initial conditions $' = and B^'/BT = for T = ~°°. Use of Equations 

 (2.2) and (2.2a and b) in Equation (2.1) then yields the sea-surface boundary 

 condition 



[g9,-(a3-iU8 +ia)^]<l' = i(a)-iU8 +ia)P/p - gQ on Z = (2.3) 



for the "spatial component" <I>(X) of the actual potential $'(X,T). 



Nondimensional variables are defined in terms of 1/co as reference time, the 



ship length L as reference length, and the acceleration of gravity g as reference 



1/2 1/2 



acceleration, from which the reference velocity (gL) , potential (gL) L, and 



pressure pgL can be formed. The nondimensional variables 



t = a)T, J = X/L, 4) = $/(gL)^^^L, p = P/pgL, q = Q/igL)^^^ (2.4) 



are then defined. In terms of these nondimensional variables, the sea-surface 

 boundary condition (2.3) can be shown to take the form 



[S -(f-iF9 +ie)^](j) = i(f-iF8 +ie)p - q on z = (2.5) 



where f is the frequency parameter, F is the Froude number, and e is the time- 

 growth parameter defined as 



