n /H, is strongly influenced by d/(gT^) for a given value of wave steepness 

 for d/(gT^) > 0.05. The breaking limit, H^, given in this figure is from 

 Goda (1975): 



0.17 Lo (l.O - exp (-4.712 |- [l.O + 15m j j\ (5) 



1 . 3 3 3] \ 1 



Figure 12 presents n^/H for constant values of the ratio of wave height 

 to breaker height, H/H^j. The figure shows that in relatively deep water, 

 rip/H only deviates from the Airy condition of ri(./H = 0.5 when the wave 

 height becomes a significant fraction of the breaking wave height. Relatively 

 shallower vjater causes a wave to become more nonlinear, even when the wave 

 height is small compared to the maximum possible breaker height. For example, 

 Hc/H = 0.75 at d/(gT2) = 0.0015 for n/\ = 0.1 (Fig. 12). 



The parameter n /d is presented in Figure 13 for constant values of H/d 

 at various values of d/(gT^). This figure shows the combined influence of 

 wave steepness and water depth on crest elevation. ri(,/d reaches a minimum 

 for constant values of H/d at d/(gT^) in the neighborhood of 0.03. At 

 values of d/(gT2) larger than 0.03 the increasing wave steepness causes r\^/d 

 to increase until the breaking point is reached. For smaller values of 

 d/(gT^) the decreased depth or increased period produces greater wave non- 

 linearity and increased rip/d. 



3. Relative Crest Duration for Monochromatic Waves . 



As waves become increasingly nonlinear the duration of the crest, T^, 

 decreases to less than half of the wave period. Values of relative crest 

 duration, T /T, predicted by stream-function theory (Dean, 1974) can be 

 approximated by the empirical relation: 



T 



—^ = C 1 tanh 



C2 In |C3 - 



(6) 



where C^, C2, and C3 are empirical coefficients with C^ = 0.5 for waves on a 

 flat bottom (m = 0.0). Values of C2 and C3 are given in Figure 14 and 

 Table 4. Good correlation is found between equation (6) and experimental data 

 for small beach slopes as shown in Table 5. However, the equation does not 

 apply to beach slopes steeper than 1 on 20 (m = 0.05). 



Figure 15 presents predicted values of T^-ZT as functions of d/(gT^) 

 and H/(gT2). Note that the duration of the wave trough, T^ is given by 



f=1.0-^ (7) 



V. TEST RESULTS AND PREDICTION TECHNIQUES FOR IRREGULAR WAVES 



Irregular wave crest elevations and durations are more variable than mono- 

 chromatic wave conditions because wave energy is distributed over a range of 

 frequencies. This energy distribution produces waves with a variety of heights 

 and periods, which have varying amounts of nonlinearity . Larger waves are of 



24 



