to move from the first gage to the second gives information about the direc- 

 tion the wave propagates. By harmonic analysis, these time series also give 

 the wave frequency and, by the dispersion relation (Equation 2) , an estimate 

 of the wave number, the inverse of which yields the wavelength. The frac- 

 tional part of the wave period measured by the time difference is proportional 

 to the fractional part of the wavelength by which the crest lags in passing 

 from one gage to the other. 



86. With this information it is a matter of simple geometry to estimate 

 wave direction. A crest in a wave train propagating perpendicular to the line 

 between the two gages will reach both gages simultaneously so no time dif- 

 ference is observed. As angle of attack increases, the time difference grows 

 (either positive or negative, depending on the sense of attack angle). 

 Maximum time difference occurs when a wave train propagates along the line 

 between the two gages. In this case the time difference equals the time for 

 the wave to propagate (at its phase speed) the distance between the two gages. 

 A more detailed description of this principle is given in Appendix A. 



87. A direct extension of this principle is that, with a very large 

 number of gages, the spatial equivalent of a discrete time series could be 

 obtained. Then, high-resolution directional information could be found from a 

 Fourier wave number transformation, in analogy with frequency transformation. 

 This direct method is highly impractical, requiring hundreds, if not thou- 

 sands, of gages; consequently, an indirect method has been developed. 

 Theoretical considerations by various investigators, referenced below, 

 indicate that reliable high-resolution directional estimation can also be done 

 with a sparse array of gages, generally 4 to 10, which is much more practical. 



88. The FRF array consists of nine pressure gages mounted 0.7 ra off the 

 bottom along the 8-m isobath to the north of the pier as shown in Figure 3. A 

 tenth gage, located 5 m seaward of the array, exists to create a colocated Sxy 

 gage. Since the main array is along a straight line, it is called a linear 

 array. Its location offshore was determined by satisfying three constraints. 

 First, it had to be outside the surf zone so that linear wave theory would be 

 applicable. Inside the surf zone, bottom- induced steepening and breaking 

 reduce the validity of linear theory. Second, it had to be in water shallow 

 enough that pressure signals could be converted to surface displacement 

 signals without excessive introduction of noise. High-frequency waves are 

 most affected by this. The depth was chosen so that waves with frequency 



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