is much longer than wave setup which is a pure coastal phenomena. The direc- 

 tion, fetch distance, windspeed, and duration are all factors influencing the I 

 magnitude of wind setup. A quadratic wind-stress law is generally applied ' 

 where surface stress is proportional to the square of some reference windspeed. 

 The wind stress can be added to the momentum balance equations to theoretically 

 predict its influence on mean water surface gradients and nearshore currents 

 as discussed further in Section V. 



For normal wave incidence to the coast, wave breaking also induces a 

 vertical circulation current (about a horizontal axis) in the surf zone. This 

 is due to a vertical distribution of radiation stress which is greater near the 

 surface than near the bottom since it is proportional to orbital wave motion. ! 

 The result is schematized in Figure 22 (from Bijker and Visser, 1978)^'*, where i 

 it is theorized that a net shoreward force at the surface and a net seaward forcej 

 near the bottom results. The hypothetical circulation pattern resulting is | 

 also shown in Figure 22. There is no known theoretical attempt to solve this 

 wave-induced circulation problem using radiation stress principles. j 



IV. LONGSHORE CURRENTS 



As summarized at the end of Chapter 2, there are a large number of factors 

 influencing longshore currents. The complexity of the forcing field, geometry, 

 and fluid must be reduced to an idealized level to allow theoretical treatment 

 that permits analytic solution. The basic theory described in this section is 

 for the longshore current induced by simple waves striking an infinite, plane 



Resulting forces 

 and current 



Distribution of 

 Momentum Flux 



Distribution of excess 

 static pressure 

 'bottom pressure 

 distribution 



Figure 22. Circulation current in breaker zone (not to scale) (from Bijker and 

 Visser, 1978). 



2^* BIJKER, E. W. , and VISSER, P. J. , "Wave Set-Up, "Coastal Engineering," W.Wl 

 Massie, ed.. Vol. II, Harbor and Beach Problems, Department of Civil Engineer- 

 ing, Delft University of Technology, The Netherlands, 1979 (not in bibliogra- | 

 phy). 



78 



