3(j) 



u = A — — 

 dx 



v = A 



a* (4) 



dy 



where 



u,v = local horizontal velocity components 



x,y = horizontal coordinates 



Boundary conditions are specified in Regions A and B. At the solid boundary 

 dC, a reflection/absorption boundary condition is used similar to the impedance 

 condition in acoustics. The condition is specified as 



£"«♦-• (5, 



with 



1 + K r (6) 



where 



n = unit normal vector directed into the solid region 

 K r = reflection coefficient of the boundary 



Values of K r for wind waves and swell are normally chosen based on the 

 boundary material and shape. General guidelines for K r cw be assembled from 

 laboratory and field data (Thompson, Chen, and Hadley 1996). In wind wave 

 and swell studies, K r is generally chosen to be consistent with this guidance. 

 Effects such as slope, permeability, relative depth, wave period, breaking, and 

 overtopping can be considered in selecting values within these fairly wide 

 ranges. For long wave studies, K r is generally set equal to 1.0, representing full 

 reflection. 



The second boundary condition is imposed in the far region (Region B) at 

 infinity. It requires that the scattered wave, defined as the difference between the 

 total wave and incident wave, behave as a classical outgoing wave at infinity. 

 This radiation condition may be expressed as 



Chapter 4 Numerical Model 45 



