where D is the wave energy dissipation rate, Q^ is the percentage of waves break- 

 ing (function of the ratio of root-mean-square wave height to H^, and^ is the 

 mean frequency. 



Another class of breaking relationships with possible application to currents are 

 the whitecapping formulations used in spectra! wave generation models 

 (Hassehnann 1974). Two such relationships are: 



D = -a S^ Ui^j- E{ix>) (15) 



given by Komen, Hasselmann, and Hasselmann (1984) and Komen et al. (1994), 

 where a is a coefficient, S is an integrated relative steepness parameter, (o„ is the 

 mean angular frequency, ^ „ is the mean wave number, E is the energy density 

 spectrum, co is angular frequency; and 



D = -— ^^^-f- (16) 



tanh(^„^°^^ 



given by Resio (1987), where s is a coefficient and /is wave frequency. These 

 dissipation relationships were developed for waves in the absence of current, but 

 they are applied in this study of breaking on a current to give insight about the 

 processes. 



Spectra 



Selected spectra from two runs are shown in Figures 7 and 8 (additional spectra are 

 given in Appendix B). The peak periods for the runs were 0.7 and 1 .4 s, respectively, the 

 incident height for both cases was 5.5 cm, and the current was 24 cm/s. The curves are 

 labeled for gauges 0, 1,3, and 6; with gauge offshore (near the wave generator, average 

 of wave gauges 1-7 in Figure 3), gauge 1 approximately 3 m offshore of the jetty heads 

 (wave gauge 8 in Figure 3), gauge 3 near the jetty heads (wave gauge 10 in Figure 3), and 

 gauge 6 approximately 3 m inshore of the jetty heads. The spectra show interesting 

 trends. First, Figure 7 (Tj, = 0.7 s) shows a significant downshifting of the peak 

 frequency from the offshore (gauge 0) toward the inlet throat (gauge 6). The peak period 

 increased up to 16 percent for t/= 24 cm/s, 9 percent for f7= 14 cm/s, and varied by 0-6 

 percent for no current. Lai, Long, and Huang (1989) reported a similar trend which they 

 attribute to nonlinear side band instabilities. The energy dissipated through breaking was 

 extracted at the peak frequency and higher, with the slope of the high-frequency tail of 

 the spectra remaining fairly constant. This implies that dissipation is related to energy at 

 a given frequency or energy is nonlinearly redistributed to maintain the high-frequency 

 slope. The energy in the low-frequency end of the spectra increased, most noticeably in 

 the cases with longer peak periods (e.g.. Figure 8), with and vnthout current. 



18 Chapter 4 Results 



