55 



surface shear stress due to the wind associated with the storm. According 

 to Dean and Dalrymple (1984) the set-up, r; , for steady-state conditions is 

 given by 



fllxi= /l + 2B||_i (5.1) 



o / h 

 o 



where B includes the wind induced shear stress and hQ is the original water 

 depth. Note that at the shoreline (x = i) , the set-up increases with the 

 expanse of the shelf. Rearranging slightly and evaluating this expression 

 at the shoreline yields 



r){i) = (h ^ + 2B^)^/^ - h (5.2) 



' o o 



Taking the derivative with respect to hp, the dependence of rj( 2) on hQ can 

 be examined: 



^aili = [h (h^ + 2Bi)~-^/^ - 1] (5.3) 



ah ° ° 



dri(Jt) 



o (1 + 



2B1nV2 (5.4) 



2 ^ 



h 

 o 



Because Eq. 5.4 is always negative, r; decreases as hg increases. This 

 indicates that according to this simple model, as long-term sea level rises 

 (hg increases) the set-up induced by a given wind shear will decrease. 

 Consider the following situation: 



average depth hQ = 10 m 



shelf width 2 = 150 km 



average wind 



shear "head" B = 3.3 x 10"^ m (wind speed =12.5 m/s) 



