L > 2£[cos(a - 6)] (27) 



max 



which indicates that for the least adverse effects of spatial aliasing, the 

 gages should be alined parallel to the dominant orientation of the wave crests. 

 In the present case 5 = 86.8° and, in general, the waves approached within 

 approximately 40° of the shoreline. In the analysis, a variable aliasing fre- 

 quency limit depending on the wave directions for the lower frequencies was 

 developed for each record. Three frequency limits were considered, corre- 

 sponding to |a -3| values of A5° , 60°, and 75°, with the 75° value associated 

 with the highest frequency limit. Selection of the frequency limit required 

 that 90 percent of the wave energy in a frequency range c'a/2 ^° °A ^^y with- 

 in the associated wave direction range, where o^ is the frequency corre- • 

 sponding to the particular aliasing wave direction (eq. 27). For the water 

 depth at the site, the three directional limits of 45°, 60°, and 75° are associ- 

 ated with approximate wave periods of 5.3, 4.2, and 3.1 seconds, respectively. 

 The percentage of energy associated with periods shorter than 5.3 seconds was 

 substantial in the data, amounting to 25 to 30 percent. In later calculations 

 of Pj^g, an attempt was made to account for the energy above the aliasing fre- 

 quency by augmenting the calculated values, using 



Etot 



^Sis = P£s ~r (28) 



cm c 



in which the subscripts c and cm indicate calculated and calculated modified, 

 respectively. T^jqj and E represent the total wave energy values and the 

 energy below the spatial aliasing frequency. This modification is equivalent 

 to associating the effective direction as determined from the frequencies not 

 affected by the aliasing consideration or poorly conditioned data to all the 

 wave energy. 



b. Determination of Breaking Depth . At this stage, the wave energy and 

 wave direction in the vicinity of the gages are determined. These values are 

 then transformed to the breaker line, accounting for shoaling and refraction. 



To determine a breaking depth, a method was used in which the total onshore 

 flux of wave energy was equated at the gages and at the breaker line with the 

 requirement that the rms breaking wave height, Hj.ms> be related to the water 

 depth by 



Hrms = <db (29) 



in which k was taken as the usual spilling breaker value of 0.78. The total 

 onshore energy flux, Fr, at the reference (gage) location is 



N/2 

 Fr = 2y I [a2(n) + b^ (n) ] C , . cos a^ (30) 



n=l ^^^^ 



in which the subscript R denotes the reference location. Considering shallow- 

 water conditions for breaking C„(j^) = C = /gd, and cos a^ as 1.0, the onshore 

 energy flux at breaking is 



33 



