dissipation for the 0.7-s waves, but significantly underpredicts dissipation for the 

 1.4-s waves. The correlation coefficient (r^ for the Resio formulation (both 

 periods) is 0.46. Likewise, the Komen et al. formulation (not shown) significantly 

 underpredicts the dissipation for all wave conditions (f = 0). Because these two 

 formulations are strongly dependent on wave steepness, it is expected that they 

 correlate poorly with the data set (see Figure 9). It is not surprising that these 

 white-capping expressions do not represent wave breaking on a current in shallow 

 water, because the formulations were developed to balance excess wind input in 

 saturated spectra without a current. The formulation of Battjes and Janssen is 

 plotted in Figure 13 with the laboratory measurements and gives the correct trend in 

 the data, but produces wide scatter (large deviation from the formulation), with a 

 correlation coefficient of 0.25. 



The poor performance of the dissipation formulations led to development of an 

 alternative relationship. Figure 10 showed good correlation of dissipation to wave 

 height, so a form consistent with dissipation in a bore was assumed, and the 

 following relationship was developed using linear regression: 



D = -0.002 





(Hl-H^) for H> H (18) 



where H^ is a critical wave height below which no dissipation occurs, 

 H^ = 0.08 L tanh(M) (19) 



The wavelength and wave number in Equation 19 include modification by a current. 

 Equation 18 was chosen to be of the form of Miche's criterion. Equation 18 is 

 plotted against the laboratory data in Figure 14 and shows reasonable agreement 

 (r^ = 0.78). 



Wave heights 



Applying the action balance equation (Equation 17) between the wave gauges, 

 together with the various dissipation models, gives a simple one-dimensional 

 shoaling and decay model. The Miche criterion also was applied as a dissipation 

 function by limiting the wave energy based on the maximum wave height given by 

 Equation 13. This transformation technique was used to calculate wave shoaling 

 and breaking through the gauge array for each of the 12 nms. Cases without current 

 had little or no wave height decay through the gauge array. Example cases with the 

 greatest dissipation are presented in Figures 15-17 (additional cases are given in 

 Appendix B). Note in the figures that the second point (x = 120 cm) is consistently 

 lower than the nearest points, probably due to a gauge calibration problem. This 

 gauge also accounts for some of the scatter in the dissipation calculations. 



Chapter 4 Results 23 



