APPENDIX 

 DERIVATION FOR LONGSHORE ENERGY FLUX FACTOR 

 Derivation of equation (1) for longshore energy flux factor: 

 (a) From Longuet-Higgins (1970) 



where 



V^ = longshore current at breaking zone 



3 = a mixing parameter 



d^j = breaking depth 



m = beach slope 



a^ = breaking wave angle 



K = ratio of breaking wave amplitude to water depth 



Hj, 



(b) Using relationship 2k = -~- equation (A-1) becomes 



d& 



Vi = i (§) (i)'" " W - sin 2aj tA-2) 



(c) Longshore velocity at any point within surf zone can be defined as 



where V is longshore current within surf zone and Vo is theoretical long- 

 shore velocity at breaking, no mixing. 



(d) From equation (58) of Longuet-Higgins (1970) 



^ = i (A-4) 



v^ e ^ -* 



(e) Using equations (A-4), (A-3) , and (A-2), longshore velocity is 



' ' (^) (S) (if) (27)' " ■" (8Hi) ' « Sin 2„, (A-5) 



(f) Using the SPM equation (4-28) 



I I 



