the maximum setup line, in contrast to Collins (1972), Wave steepness effects 

 are shown in Figure 39(b). Battjes (1974a) used the breaking criterion of 

 Miche . (1951)^*^ which included wavelength effects so that decreasing steepness 

 (longer waves) made a wider surf zone to increase setup. In both these exam- 

 ples, Y = 0-8 



In Goda's (1975) model, the effect of wave steepness on setup is similar 

 to that obtained by Battjes (1974a). However, the magnitudes of both setdown 

 and setup are relatively greater and depend more on beach slope since y is 

 variable and increases as beach slope increases. This causes a greater maxi- 

 mum setup than the Battjes (1974a) model. 



The more sophisticated hydraulic jump model of the surf zone by Battjes 

 and Janssen (1978) produced the MWL variations shown as Figure 40. In all 

 cases the theoretical wave height variation across the surf zone is also 

 shown, The steep plane beach (Fig. 40, b) has less setup than the flatter pro- 

 file (Fig. 40, a). A smooth transition from setdown to setup is again evident. 

 The results for two bar-trough profiles are given in Figure 40 (c and d) . In 

 one case (Fig. 40, c) two wave setdown regions are apparent while in another 

 case (Fig. 40, d) a broad flat setup region is created. The crosses (x) in- 

 dicated laboratory measurements, and a detailed discussion of the comparison 

 is given in Chapter 4. 



Finally, based on extensive measurements in the field off the Isle of 

 Sylt (Germany) in the North Sea, Hansen (1978b) offered the following empi- 

 rical relations for the maximum wave setup due to irregular waves on a flat 

 plane beach 



n = 0.3 H 

 max o , s 



(125) 



n = 0.5 H, 

 max D , s 



where H^ g is the deepwater significant wave height and H^ is the same but 

 at the breakers. 



b. Longshore Current Profile . Collins (1972) and Battjes (1974a) were 

 primarily interested in the effect of irregular waves on longshore currents. 

 In a random sea the breaking line for regular waves becomes a zone for irre- 

 gular waves since the higher steeper waves break farther offshore than the 

 gentle waves which break near the beach. The stochastic description of a 

 real sea state (either spectral or probablistic) will find waves breaking in 

 different locations at slightly different angles and with a range of wave 

 heights and lengths. The net result is that irregular waves provide a de- 

 gree of lateral mixing to distribute the longshore currents and produce a 

 smooth profile across the surf zone similar to that found in the theory of 

 regular waves when the lateral turbulent mixing stress term is included (see 



'+&MICHE, R. , "Le Pouvoir Reflechissant Des Ouvrages Maritimes Exposes a 

 L' action De La Houle," Ann. des Fonts et Chaussees^ 121 e Annee, 1951, 

 pp. 285-319 (not in bibliography). 



139 



