62 



as was done in two dimensions in Section 2.1. 



MKFSBC = -g (KFSBC) + -^ (DFSBC) = 



— + g^, + 2{u- + v- + w-, 



^du dv dw (4.6) 



+ U -^- + UV-p- + UW^r- 



ox ox ox 



du 2 ^^ ^^ 



+ UV^r- + V-:r- + VW-^— 



oy oy oy 

 du dv o d 



w 



+ UW— 1- WV— h W -;r- = at 2 = 7? 



dz dz dz 



This form does not include the gradients of the water surface, and all the terms are 

 defined by the potential function. Applying both the modified kinematic free surface 

 boundary condition and the dynamic free surface boundary condition completes the 

 formulation without the need for knowledge of the gradients of the water surface. 



Observational Equations The field equation and the boundary conditions de- 

 scribe a free surface potential flow. In steady two dimensional wave theory, a wave 

 height and periodicity in space and time are specified to complete the formulation. 

 In the two dimensional LFI theory (Chapter 2), a form for the potential function is 

 chosen, with the parameters determined to fit the free surface boundary conditions 

 and the measured record in a small window in time. In three dimensions, the pro- 

 cess is essentially the same. A three dimensional form for the potential function will 

 be presented, with parameters that are found to fit the measured records and the 

 boundary conditions. 



In order to define a solution that fits the measured record, observational equations 

 are established. These equations are defined to make use of the particular quantities 

 that have been measured. In the case of an array of water surface measurements, they 

 are the free surface boundary conditions, applied at the measured elevations and hor- 

 izontal locations at a number of points in time throughout the window (Chapter 5). 

 In the case of an array of pressure measurements, they are the Bernoulli equation, 

 applied at the elevation and horizontal locations of the measurements, and also at 



