28. The advantage of a multi- element linear array Is that it gives 

 phase measurements from many different sensor separations. Whereas some of 

 these separations may be too small or too large to use in Equation A9 , the 

 sinusoidal patterns in the Co and Quad plots show that all phase differences 

 from all sensor separations can be used. This avoids the aliasing problem for 

 short waves (as long as the minimum gage spacing is small enough) and allows 

 good resolution of longer waves (if the overall array is long enough). 

 Expected patterns in Co and Quad plots allow the fitting of model curves to Co 

 and Quad data. This improves resolution since multiple samples of the wave 

 directional pattern are realized in the Co and Quad data. 



Directional Spectra from Longshore Wave Number Estimates 



29. To this point, discussion has been about the contents of the Co and 

 Quad data for a single plane wave incident on the array. Nature does not work 

 like that; a real wave field contains a directional distribution of waves 

 incident on an array. The Co and Quad plots would then contain a super- 

 position of longshore wavelength signatures of all the incident waves, with 

 each signature representing a directional angle of incidence. To resolve 

 these directions, it is necessary to decompose the Co and Quad plots into a 

 variance distribution as a function of longshore wave number (or directional 

 angle) of the total wave field. 



30. This is the same problem encountered when a time series is decom- 

 posed into cosines and sines (Fourier components) in order to estimate the 

 frequency distribution of variance (or wave energy) . A reasonable approach 

 might be to decompose the Co and Quad data into Fourier components. However, 

 there are physical restrictions that make this approach untenable. 



31. For Fourier analysis of the Co and Quad data to work, the full 

 length of the array must be at least equal to the longest longshore wavelength 

 to be resolved. Everything would be in good shape if wind waves all traveled 

 parallel to the shore. For wind waves in the frequency range 0.05 to 0.33 Hz 

 and in a nominal water depth of 8 m, the largest wavelength to be resolved 

 would be 175 m. An array of this length can be constructed easily. However, 

 wind waves typically do not travel parallel to the shore so longshore wave- 

 lengths to be resolved are much larger. 



A12 



