(average of the highest one-third of the waves) . In this study it was desired 

 to compute the "true" wave energy flux; therefore, wave height was modified to 

 reflect the root-mean-square (rms) wave height in accordance with the statis- 

 tical wave train theory of Longuet-Higgins (1967) assuming a narrow-banded wave 

 energy spectrum. For this particular situation, which results in a Rayleigh 

 probability distribution for wave height, the relationship between significant 

 wave height and rms wave height is as follows: 



^s = (2)1/2 H^^ (8) 



where Hg is the significant wave height, and Hj-j^s the root-mean-square wave 

 height. 



The second method computes longshore energy flux, using breaker wave height 

 and longshore current as determined from LEO measurements, along with estimated 

 values of surf zone width, W, and distance from shoreline to injection point 

 of dye, X. The equation for determining longshore energy flux using this 

 second method is 



pg IL W V C. 



2.S 5iT 

 2 



(Vlh 



where V is the longshore velocity as measured in LEO program, Cf the friction 

 coefficient dependent on bottom, water particle excursion bottom roughness, and 

 (V/Vo)lH the theoretical dimensionless longshore velocity for Longuet-Higgins' 

 assumed mixing parameter, P = 0.4; (V/Vq)^^ is dependent on the parameter X/W 

 (see Longuet-Higgins, 1970). 



The derivation of equation (9) is given in Appendix A. The rms wave height 

 is used in equation (9) to calculate the longshore energy flux. Longshore 

 velocity is typically measured over a timespan on the order of the "modulated" 

 wave train period. 



In this part of the study, additional emphasis was placed on determining a 

 reasonable bottom friction coefficient, Cf , for use in equation (9). The fric- 

 tion coefficient was determined by minimizing the variance between computed 

 longshore currents (from LEO observation) and theoretical longshore currents 

 (from Longuet-Higgins' (197Q) formula with an assumed mixing coefficient 

 P = 0.4). LEO data from the two northernmost LEO stations (out of the zone of 

 breakwater influence) were chosen for the calculation. More than 2 years of 

 twice daily wave observations (4,464 observations) from the two stations was 

 used to compute the friction coefficient, Cf = 0.0056, which was used in equa- 

 tion (9) to calculate the longshore energy flux. 



In both methods, weighted averages of the longshore energy flux at breaking 

 are calculated which correspond to periods between volumetric surveys. Values 

 of Pjj,s are given for the three stations in Appendix B, Tables B-1 and B-2. In 

 most survey periods, the value of ?^^ computed from current data was higher 

 than the value of P£s calculated using wave angle information. In addition 

 to longshore energy flux, correlation coefficients R are also calculated for 

 the correspondence between calculated longshore currents (from Longuet-Higgins' 

 (1970) theoretical approach) and measured longshore currents. Correlation 

 coefficients ranged from -0.18 to 0.76 and are independent of assumed friction 

 factor. 



25 



