73 



method for a point water surface record (Sobey 1992), but with the direction of the 

 wave determined. The varying directional trend of the sea state is accommodated 

 by determining the direction in each window separately, allowing for a fluctuation of 

 the wave direction with time, from window to window. In this case, the potential 

 function is Eq. 4.10 reduced to a single wave: 



4>{x,z,t) = Ua:X + Uyy + y^ Aj . ~ s'm j{k^x + kyp - cot + a) (5.1) 



^^^ coshjAn 



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 wave number in the x and y directions, 

 and K is the magnitude of the local wave number. 



When an array of water surface gauges is placed near a reflecting surface, such 

 as a sea wall, the resulting sea state is likely to contain simultaneous components in 

 diff'erent directions, such as in a standing wave or short crested sea. This effect can 

 not be captured with a potential function representing a single progressive wave. It is 

 possible, however, to capture this type of sea with a potential function representing 

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

 which is repeated here: 



20 



6{x, y, 2, t) = UxX + Uyy + ^ A' GC( A'iA, K^z) sin ai (5.2) 



i=l 



where: 



(CiKh Kz) = ^Q^^^^^'(^ + ^) T.' ^ /^^ , ^^ 



cosh Kih ' \l dx dy 



Si = {kx,ix + ky^iy - u!it + ai) 



^2 - {kx,2X + ky^2y - ^2t + Oi2) 



