75 



(5.3) 



surface boundary condition (f^)-, 



^ =aF + ^" + '<"¥ + " 97 + " ar' 

 2 du dv dw 



-\-U -^r- -\- UV—- + UW-— 



OX ox ox 



du 2 ^" 9w 



+ UV—- + V^r- + VW-— 



oy oy Oy 



du dv 2 ^^ 



+ UW— h WV— h W -;:— =0 at Z = T] 



dz dz dz 



and the dynamic free surface boundary condition (/■^), 



f^ = — + -{u^ + v'^ + w'^) + grj -'B = Q at z = -q (5.4) 



with the Bernoulli constant {B) defined as: 



1=1 ^ ■' 



The problem of determining the kinematics of irregular waves from a set of mea- 

 sured water surface traces is a mathematically better posed problem than interpreting 

 a subsurface record. The flow is governed by the elliptic Laplace equation (Eq. 4.2), 

 so that the solution is determined by the boundaries. While the complete boundaries 

 of the solution domain are not known, the boundary conditions and location of the 

 boundary are known at both the top and bottom of the solution domain. The bottom 

 boundary condition is well defined, and the location of the water surface is measured 

 at a few locations in space and many points in time, allowing the direct application of 

 the free surface boundary conditions. This is in contrast to working with subsurface 

 records, in which the location of the free surface must be determined in order to apply 

 the free surface boundary conditions. The need for horizontal boundary conditions is 

 eliminated by the assumed periodicity of the chosen potential function. However the 

 fundamental wavelength(s) and period(s) must be found as part of the solution. 



When working with a point measurement, the fundamental frequency is fairly well 

 defined by the time evolution in the window chosen, as long as the window is wide 

 enough. There is no direct information available about the spatial evolution of the 

 signal, however, so the wave number is determined only through the application of 



