Av 

 0.105£ b (97) 



for 0.31 < £ b < 1.06 . Equations 96 and 97 give good estimates of vortex 

 area for spilling and plunging waves. For larger values of the surf similar- 

 ity parameter, Equation 95 can be used to estimate Ay . 



Wave Height Decay 



153. Wave height measurements were made for all tests, and the data 

 should be of value for surf zone wave model development. Figure 57 (a— e) shows 

 wave height at each gage normalized by H as a function of distance for five 

 cases. Comparison of measured wave height with predictions of wave decay 

 models is left for future work. Because beach profiles were irregular, 

 numerical models (e.g., Svendsen (1984, 1985); Dally (1980); and Dally, Dean, 

 and Dalrymple (1985a, 1985b)) will need to be applied. Average wave heights 

 for 12 to 15 waves at each gage for all tests are included in Appendix C. 



Wave Runup 



154. Wave runup measurements were made for all tests. Figure 58 shows 

 R/H plotted as a function of seaward bar angle fl x , and, for the plane - 

 slope data, beach slope angle (m = 1/30, i.e., fi 1 = 1.91 deg) . Except for 

 the plane-slope points, each data point represents the average R/H — value 

 for the four shoreward bar angles associated with the seaward bar angle for 

 the particular wave steepness. Basically, the seaward bar angle has no in- 

 fluence on runup. Runup also shows no dependence on £ , as shown in Fig- 

 ure 59. Runup was plotted versus the surf similarity parameter using the 1/30 

 slope as the primary angle. The data show increasing R/H with increasing 

 values of £ . The line drawn in Figure 60 represents the average value of 

 (R/H )/£ , which was 0.76, whereas Equation 52 (Battjes 1975) predicts this 

 ratio to be 1.0. Figure 61 shows runup for the plane slope cases versus the 

 surf similarity parameter. All measured values are overpredicted by Equa- 

 tion 52, shown as the solid line. The cause of the difference in runup deter- 

 mined in this experiment and by Battjes is not known; additional measurements 

 are clearly warranted. 



109 



