56 



and using Eq. 5.2, the wind- Induced set-up at the shoreline is calculated: 

 ri(2) = 0.49 m. For the same shear and shelf width, but including aim 

 rise in sea level yields »?(i) = 0.45 m. There is 4 cm less set-up with sea 

 level rise, but of course the total water level would be 96 cm higher than 

 without the 1 m rise in sea level. It is noted that the conditions in this 

 example correspond to a shallow shelf, such as the Gulf of Mexico. The 

 storm surge on deeper shelves would respond even less to an increase in sea 

 level . 



Another relevant idealized geometry for the continental shelf and 

 nearshore region is that of a uniformly sloping bottom, as shown in 

 Fig. 5.3b. Dean and Dalrymple (1984) present an implicit solution for 

 wind- induced set-up 



= [1 - ^^] _ 



B^ 



in 



h + r? 

 h 



Bi 



"^r 



(5.5) 



where 



h = h^ (1 - |) = h^(l - M*) 



o 



(5.6) 



where m is the shelf slope. If we attempt to follow the same procedure as 

 before, »?(i) is given by the transcendental expression 



= n{2) + 2 in i ^f^P - "? ) 

 m h — B 



m 



Taking the derivative of Eq. 5.7 with respect to la^ yields 



(5.7) 



dv(£) = 



ah 



1 - 



B 



mn(Jl) 



h m 



-O- - 1 

 B 



(5.8) 



