APPENDIX A 

 DERIVATION OF EQUATION (9) FOR LONGSHORE ENERGY FLUX 

 a. From Longuet-Higgins (1970) 



Vb = if (■^)(8d|j)^''^(™ sin a^, cos a^) (A-1) 



where 



B = a mixing parameter (dimensionless) 



di, = breaking depth 



m = beach slope 



a^ = breaking wave angle 

 b. Using relationship 



db 

 equation (A-1) becomes 



Kb 

 K = T^ (A-2) 



u = ll ^tSA\ 1 (»^g^b " sin 2ab) 



^^ SzicJ/^ (A-3) 



c. Longshore velocity at any point within the surf zone can be defined as 



V - V, f ^V^\ (A-4) 



im 



where V is the longshore current within surf zone and Vq the theoretical 

 longshore velocity at breaking with no mixing. 



d. From equation (58) in Longuet-Higgins (1970) 



Vo _ 1 (A-5) 



Vb ^ B . 



e. Using equations (A-3), (A-4), and (A-5), longshore velocity is 



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