Wave-Induced Current and Setup Model 



22. When waves break, they generate currents (e.g., littoral and rip 

 currents) and changes in the mean water level (setup and setdown). Since 

 these currents are the main transport mechanism for sediment on a coastline, 

 they must be simulated in detail in order to model coastal processes. The 

 theory of the generation of wave-induced currents was developed by Bowen 

 (1969), Thornton (1970), and Longuet-Higgins (1970). Numerical models have 

 been developed to determine wave-induced currents (Noda 1974, Birkemeier and 

 Dalrymple 1975, Liu and Lennon 1978). These models typically either consider 

 only simple and idealized situations, such as plane beaches and periodic 

 bathymetries , or neglect terms of the governing equations involving unstead- 

 iness, advection, and/or lateral mixing. 



23. In recent years, Ebersole and Dalrymple (1980) developed a wave- 

 induced current model that solves equations that include terms for unsteady 

 flow, advection, and lateral mixing. The model was applied to fairly small 

 problems with relatively simple bathymetries. It used a simple explicit fi- 

 nite difference computational scheme and grid cells of uniform size. Sta- 

 bility was obtained by Ebersole and Dalrymple by using a time-step such that 

 the Courant number was less than 1.0. 



24. Since the Oregon Inlet region that required modeling was relatively 

 large, it was important to develop a model that had a variable grid and was 

 extremely efficient computationally. One solution technique that is extremely 

 efficient is the alternating direction implicit (ADD finite-difference 

 method. ADI schemes are not limited (as are explicit schemes) to a Courant 

 number less than 1 to maintain stability. Courant numbers of 5 to 10 or 

 higher are typically used. In view of the similarity between the equations 

 that govern wave-induced currents and currents produced by long waves (e.g., 

 tides) , a wave-induced current model was developed in this study by modifying 

 an existing, well tested Waterways Experiment Station (WES) long-wave 

 numerical model known as WIFM (WES Implicit Flooding Model) (Butler 1980). 

 WIFM is a finite-difference numerical model that employs an ADI computational 

 scheme and in addition uses grid cells of variable sizes. 



25. WIFM was modified to calculate wave-induced currents and setup by 

 adding radiation stress terms that are the driving mechanism for wave-induced 

 currents. In addition, the friction and mixing terms used in WIFM were 



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