|2 + M = ±q ( 3 ) 



ax 9t 



where q denotes the source or sink of sand per unit length of beach 



(m /m/sec) . The minus sign denotes a sink (loss of sand) , and the plus sign 



denotes a source. 



8. In order to solve Equation 2, it is necessary to specify an expres- 

 sion for the longshore sand transport rate. Longshore sand transport on an 

 open coast is believed to bear a close relation to the longshore current which 

 is generated by waves obliquely incident to the shoreline. A general expres- 

 sion for the longshore transport rate is 



Q = Q sin 2a, (4) 



where 



3 

 Q = amplitude of longshore sand transport rate (m /sec) 



a, = angle between breaking wave crests and shoreline 



b 



In the generally accepted formula for longshore current, the speed of the cur- 

 rent is proportional to sin 2a, (Longuet-Higgins 1970a, b) . 



9. The angle between the breaking wave crests and the shoreline 

 (Figure 2) may be expressed as 



a, = a - arc tan ( tt~ I (5) 



bo \9x/ 



in which 



a = angle of breaking wave crests relative to an axis set parallel 

 to the trend of the shoreline 



9y/9x = local shoreline orientation 



10. A wide range of expressions exists for the amplitude of the long- 

 shore sand transport rate, mainly based on empirical results. For example, 

 the Shore Protection Manual (SPM) (1984) gives the following equation: 



% - if H sb C H ur^rn (6) 



