measurements of Sawaragi and Iwata (1974) for regular wave dissipation 

 across a horizontal bed. Their results are repeated here as Figure 73(a). 

 Recent field measurements by Suhayda and Pettigrew (1977) presented some 

 confirmation of the fact that the y ratio varies with distance from the 

 breakpoint and ranged from 2.0 to 0.6 (Fig. 73, b). The theory of Sawaragi 

 and Iwata (1974) is also shown in Figure 73(b). It is based on a finite- 

 difference solution of a set of surf zone equations of motion and contin- 

 uity that includes excessive amounts of numerical information loss 

 (numerical viscosity). For this reason it has been omitted from this report. 

 Finally, the data of van Dorn (1976) are shown in Figure 74. This was 

 obtained as part of his wave setup results previously discussed. Steep 

 slopes (3 = 0.1) as employed in most laboratory studies of longshore current 

 profiles produced y ~ constant whereas it is again clearly shown that y 

 is not constant for flatter profiles. 



Use of constant y ratio in longshore current profile models introduces 

 a high sensitivity to bottofti profile variations that is unrealistic (Battjes, 

 1978). As seen in Figures 72, 73 and 74, a constant y is not applicable 

 for flat slopes, nor is it physically justifiable for bar-trough profiles. 

 Consequently, Battjes and Janssen (1978) developed an irregular wave model 

 for surf zone wave height decay as described in Chapter 3 and shown in 

 Figure 41 for examples with plane and bar-trough type beaches. It is based 

 on the conservation of energy equation (44) and not some semiempirical 

 y variation. A series of laboratory experiments was then conducted to 

 check the theory in a basin 45 meters long, 0.8 meters wide using SWL depths 

 about 0.7 meter. The free-surface fluctuations were measured by parallel- 

 wire resistance gages and data indicated by x on Figure 40. The theory 

 was found to give excellent results on a plane beach (tan 3 = 0.05) with 

 large wave steepness (Fig. 40, b) than the lower steepness (Fig. 40, a) where 

 only fair results are indicated. For bar-trough profiles, the theory was 

 considered quite good. It followed the visual observation of essentially 

 no wave breaking in the trough region (no energy dissipation) and also 

 produced a high dissipation rate just inside the bar. 



The theory shown in Figure 40 is based on only two closure parameters. 

 One is K in equation (124) which was expected to be about unity and K = 1 

 was in fact used in the theoretical calculation. The second is y^ taken 

 here as 0.8 for initial wave breaking only. The theory was found to 

 qualitatively and quantitatively predict wave height decay and MWL changes 

 on plane and bar- trough beach profiles. Use of the theory in combination 

 with longshore current calculations has yet to be attempted. 



Battjes and Jansen (1978) attribute the disparity between theory and 

 measurement for low steepness waves (~ 0.01) on plane beaches (Fig. 41,a) 

 to an enhancement effect. In other words, waves with low steepness have 

 time to shoal up to heights exceeding the deepwater wave height, before 

 the decay due to wave breaking sets in. 



194 



