22 



.du dw 



-\-U -r- -\- UW^— 



OX OX 



du 2 ^^' 

 + uw— — I- w -7— = at z — n 



oz dz 



(3.2) 



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



86 I ^ \ 



f^ = — + -u^ + ^w^ + gr]-B = at z = rj (3.3) 



and the unsteady Bernoulli equation (/ 



B^ 



f^ = ^ + \{u^ + w') + P^-B^O (3.4) 



with the Bernoulli constant defined as: 



The unknown parameter, 2;, appears in the potential function only when coupled 

 with the parameter, k. It is convenient to solve for the non-dimensional parameter, 

 kx, essentially a phase parameter in the potential function. 



The action of waves is greatest near the surface, so that the fluid velocities and 

 accelerations are largest near the surface and decay rapidly with depth, particularly 

 in deep water. In addition, for pressure sensors placed at or near the bottom, the 

 vertical component of the velocity is damped out completely, as expressed by the 

 bottom boundary condition. The problem, then, is to extrapolate the motion of the 

 fluid up to the surface, where the motion is greatest, using only data extracted from 

 the subsurface, where the motion is much less. 



