70 



for each window in time. At least 28 independent equations must be defined by 

 applying a combination of each of the free surface boundary conditions (Eq. 4.4 and 

 4.6) and the observational equations at a number of nodes throughout each window. 

 The specific combination of these equations will be determined by the layout of the 

 instruments. 



4.4.1 Kinematics 



In order to apply the free surface boundary conditions, the full kinematics must 

 be known. While the kinematics are completely specified by the potential function, 

 Eq. 4.18, some of the algebra may not be obvious. The full expressions are provided 

 here. 



u{x,y,z,t) = ^ = t/^ + ^A,-^(C(A;/i,A;2)cos(7i (4.22) 



2 = 1 



v{x,y,z,t) = -^ = Uy + ^A-p(C{Kih,K,z) cos a^ (4.23) 



w{x,y,zj) = -^ = J^AKiS3{K^hJxiz) cos a, (4.24) 



«=i 



^{x,y,z,t) = Y,A,^(£{K,h,K,z} cos a, (4.25) 



i=l 





