APPENDIX A 



-PREDICTION CAPABILITY OF METHOD 



Because the method presented in this CETA is significantly different from 

 the procedures in the SPM, summarized data are presented here to illustrate 

 the method's prediction capability. Irregular wave conditions with a spectral 

 shape similar to wind sea spectra were mechanically generated in a wave tank 

 at CERC. The waves were allowed to propagate up a 1 on 30 slope and break. 

 Wave staffs located along the tank were used to measure the waves. Wave 

 spectra and the wave height H = 4o = 4(E) 1 / 2 were calculated. Figure A-l 

 provides an example showing measured H (H obtained using this CETA) and the 

 value of H projected by linear shoaling theory, H 1 = K S H Q . The SPM methods 

 would predict the value H 1 . The method in this CETA appears to be a better 

 estimate of the quantity H. 



Figure A- 2 provides data from a storm of 25 October 1980 at the Field 

 Research Facility (FRF) in Duck, North Carolina. The measured values of 

 H = 4o are plotted against the square root of water depth, (h) 1 ' 2 . Also 

 plotted are (1) the upper limit for H for the maximum a and f condition 

 observed, and (2) a monochromatic determined breaker height which considers 

 the shore steepness, water depth, and wave period. In most cases H^ is 

 greater than H. A suggested approximation of H = 0.5h is also plotted. This 

 relationship is adequate at the deeper end of the pier but is an underestimate 

 at the shallower depths. 



The bathymetry under the pier is somewhat distorted (Fig. A-3,a). A 

 refraction and shoaling analysis of a 12-second wave approaching from the 

 primary direction of waves of the October storm was performed and the joint 

 refraction-shoaling coefficient, K R K. g , is shown in Figure A-3(b). Refrac- 

 tion and shoaling create regions of higher waves to either side of the pier. 

 However, shoaling predominates and even under the pier, K R K g is greater than 

 1.1. During the part of the October storm plotted in Figure A-2, waves off- 

 shore were in excess of 4.2 meters, and waves along the pier would be expected 

 to reach the monochromatic breaking limit unless some other process is acting. 



Figure A-4 provides plots of spectra at 36-, 8-, 7-, 4- and 2-meter depths 

 during a storm at the FRF in December 1980. The expected upper bound on 

 spectral density for the 7-, 4-, and 2-meter depths are plotted also. The 

 figure indicates the degree and location of energy loss in the spectrum and 

 the degree of approximation of the theory used in development of this CETA. 



The method in this CETA represents a simple approximation of estimating 

 depth-controlled wave energy. The method does not consider any of a number of 

 mechanisms important to predicting precisely the shape of the wave spectrum 

 but still provides what appears to be a useful approximation to the quantity 

 H = 4o = 4(E) 1/2 . 



15 



