wave setdown is identical to that given for perpendicular wave incidence, 

 equation (30). In terms of deepwater wave height H , and deepwater wave 

 angle a , this becomes 



K k ^,2 1 1. cosa 

 — _ _o _o coth"^ kh 



16 n sinh 2kh cosa (.3") 



Since the ratio n/h is very small outside the breakers, the Stillwater depth 

 d can replace h in equation (39) for ease in computation. 



b. Wave Setup . The solution for spilling- type breakers with y constant 

 across the surf zone follows closely to that outlined above with normal inci- 

 dence. All the same shallow-water assumptions are employed. The solution for 

 wave setup obtained by Jonsson and Jacobsen (1973) is 



dn ^ 1 dd , - 



dx 1 + 8/(3Y^cos^a) dx ^^^^ 



The setup slope is no longer a constant proportion to the beach slope as with 

 normal wave incidence. For a given set of deepwater conditions, H and T , 

 refraction will cause less setup at a given x due to the cos a term in equation 



(40) and the fact that waves break at a smaller water depth. 



The theoretical maximum setup n was also determined by Jonsson and 

 Jacobsen (1973) to be 



\= 16 n^i-TVi; ''"%^ ^^'^ 



and verified by Gourlay (1978) who put it in this form. Here the subscripts 

 b and o mean breaker point and deepwater conditions, respectively. Equation 



(41) was found by integrating equation (40) and use of the appropriate boundary 

 conditions and not the trigonometric manipulations for a plain beach as before 

 to obtain equation (37). Surprisingly, therefore, this model shows that maxi- 

 mum setup is independent of the bottom profile in the surf zone. The oblique 

 maximum setup is less than normal setup and equation (41) reduces to equption 

 (37) for a = 0. Further parameter study by Jonsson and Jacobsen (19/ j) showed 

 that wave steepness (H /L and y have much less influence than wave angle on 

 maximum setup which varied approximately as (cos a ) ^ . 



All the above are based on linear wave theory and regular waves . Wave 

 setdown and setup theories when nonlinear and irregular waves are present will 

 be reviewed in Section VI. 



3. Other Factors . 



A tilt of the MWL at the coast can also be due to the wind stress over a 

 long fetch distance inducing a wind setup. The horizontal distance involved 



77 



