on 

 : |u orb| * = T sinh kh (31) 



where H is the local wave height, T is the wave period, and k is the 

 local wave number. The numerical model can be adapted easily in the future to 

 other formulations for friction such as nonlinear friction. 



28. As mentioned previously, the radiation stresses are of major impor- 

 tance since they furnish the "driving" forces for wave-induced currents and 

 setup. For monochromatic waves, they are defined by Equations 20, 21, and 22 

 in terms of the local wave climate variables H , k , and 9 which are 

 obtained from the wave propagation model described previously. 



29. In the numerical model, the coordinate scheme is chosen such that 



x is positive in the offshore direction and y is approximately in the 



alongshore direction (Figure 6). An eddy viscosity formulation is chosen for 



the lateral shear. The eddy viscosity is assumed to be anisotropic. Denoting 



e and e as the eddy viscosities in x and y directions, respectively, in 

 x y 



general, £ is assumed to be a constant and £ a function of x and 

 y x 



y . Accordingly, 



t = Pie |^+ e 4^1 



xy V y 9y x 9x 



For field applications, the eddy viscosity e is chosen according to the 

 following relation given by Jonsson et al. (1974): 



2 

 e = 5_|I cos 2 e (33) 



x 4ir h 



This represents twice the value used by Thornton (1970). It was believed that 

 for field situations Equation 33 represented the eddy viscosities more realis- 

 tically than the relation suggested by Longuet-Higgins (1970) for plane 

 beaches. The value of £ was in general taken to be equal to the value of 

 £ at the deepest part (usually near the offshore boundary) of the numerical 

 grid. The numerical model is flexible enough to permit other formulations for 

 eddy viscosity in the future, as our understanding improves. 



30. Using the variable grid formulation discussed previously, the 

 momentum equations become: 



23 



