1.0 



0.8 



0,6 ■ 



'(-») 



O.i 



0.2 



0.0 



No Lateral Mixing 





"•'J^ 



P=0 





X y^ 





/ 



/y'^ 

 y ^y' 



A 



y 



/"' 



/^ 



y 





/y ^^ 





_^„*-' 



yVy^ 



^^ 



-'as' 



/x^^ " 







J^^ 



"*■ 



45" 



yT 





■ 



0.0 0.2 O.A 0.6 0.8 1-0 



X 



Figure 28. Dimenslonless theoretical current profile Inside the breaker 

 line as a function of Incident breaker wave angle, neglecting 

 lateral mixing (from Kraus and Sasaki, 1979). Solution Includes 

 refraction and angle-dependent bottom friction force. (au = 

 means angle correction to zero-order solution is zero.) 



SO that the solution form is consistent with the original model (eq. 65). 

 However, the coefficient expressions and definitions are quite lengthy and 

 involved, so they are included as Appendix D. The key dimensionless parameter 

 P* for this derivation is defined as 



P* =^, 



tang 



C^2 1+3y2/8 



(95) I 



where T is the closure coefficient for the kinematic eddy viscosity. P* is 

 slightly different than that defined by Longuet-Higgins (eq. 73); however, 

 this distinction is not fundamental and will be disregarded in the discussion. 

 The factor y must now be specified along with P* to obtain a solution. 



Dimensionless profiles with mixing parameter P* = 0.5, 0.1 and 0.05 (y= 

 1.0) and various incident breaker angles (o<a,<30°) are shown in Figure 29 

 (after Kraus and Sasaki, 1979). The dashline (L-H) is the original theory 

 of Longuet-Higgins (1970) corrected for normal wave setup. Earlier Figure 24 

 showed how increasing the lateral turbulent mixing (larger P values) flattened 



104 



