124 



presented in chapter 3, and for arrays of water surface measurements in chapter 5. 

 The formulation for arrays of subsurface pressure gauges is very similar to that for 

 arrays of water surface measurements, with the addition of the need to determine the 

 location of the water surface, as was done with the analysis of a subsurface pressure 

 trace. The following description includes the required information; greater detail has 

 been given in previous chapters. 



The flow is assumed to be irrotational and incompressible, with a potential func- 

 tion that represents either a single directional wave, or two separate intersecting 

 waves. The potential function locally representing a single wave is Eq. 4.10 reduced 

 to a single wave: 



J 



cosh jK{h + z) . 



<i){x,z,t) = UxX + Uyy + 7-4,- , ■..., sm j{kxX + ky-y - ut + a) (6.1^ 



■^^ cosh 7 A h 



K=. kl + kl 



where Ux and Uy are the components of the known depth uniform Eulerian current 

 in the x and y directions, h is the mean water depth, J is the truncation order of the 

 Fourier series, Aj are the Fourier coefficients, u is the local fundamental frequency, 

 kx and ky are the components of the local fundamental wave number in the x and y 

 directions, and K is the magnitude of the local wave number. 



The potential function for two intersecting waves to fourth order is Eq. 4.18, 

 repeated here: 



20 



(j)[x, y, z, t) = UxX + Uyy + 2_] ^i (C{Kih, Kiz) sin ai (6.2) 



where: 



rr(T^u T^ ^ coshKi{h + z) dai\ da,^ 



coshAjrt y ox oy 



Si = {kx,ix + ky^iy - ujit + Oi) 



S2 = {kx,2^ + ky^2y — ^2t + Q2) 



