An equation in the form of Equation 80 was developed for each seaward bar 

 angle by performing a regression analysis on Oj, as a function of H /L , 

 represented by the dashed line in Figure 39 (a-d) . Equations for the empiri- 

 cal parameters CC/^) and nC/^) were obtained by plotting these two param- 

 eters as a function of seaward bar angle, Figures 40 and 41, and fitting an 

 equation to the data by regression analysis. The resulting polynomial func- 

 tions were 



C(^) = 0.28 + 2.17tan0! - e.OOtan 2 ^ (81) 



and 



n^) =0.36 - l^tan^ + 4.85tan 2 ^ 1 (82) 



The coefficients of determination for C(/3 1 ) and n(/9 1 ) were 0.93 and 0.99, 

 respectively. The calculated values of Qj, using Equation 80 are shown as 

 the solid line in Figure 39 (a-d). The variation of breaker height index 

 calculated from the regression analysis of each /Spangle is presented in 

 Figure 42 as a function of wave steepness. Figure 43 shows a comparison of 

 fi b by seaward angle using Equation 80. 



140. Figure 42 shows that 0^, decreases for values of fi-y > 10 deg 

 for high wave steepnesses, whereas for low wave steepnesses U^ becomes 

 larger. Since the steeper bars are shorter, shoaling of the incident wave 

 prior to breaking occurs mainly on the 1/30 plane slope rather than the bar, 

 and fij, is approximately the same as the values predicted for the 1/30 slope 

 using Equation 61. Figure 43 shows ^-values for the 15-deg bar are higher 

 than those for the 10-deg bar at higher wave steepnesses, which differs from 

 Figure 42. This is simply due to the variability in the regression of the 

 coefficients C( / 9 1 ) and n(^ x ) . 



141. The higher values of fi b observed at low wave steepnesses may be 

 explained by the presence of a strong return flow visually observed in these 

 cases . A heuristic explanation can be given to describe the influence of 

 return velocity on wave height. The treatment is based on the depth inte- 

 grated energy equation of Phillips (1977) , which for the situation of the tank 

 becomes : 



93 



