It is assumed that the longshore transport rate, Q , is proportional 



to the angle of wave incidence, [a 



■) , and the Square of the rela- 



tive wave height. The variation of wave height with x is given by the 

 diffraction theory of Putnam and Arthur (1948) . The modification of 

 wave diffraction by wave refraction is neglected. 



A similar approach has been proposed by Price, Tomlinson, and Willis 



0.35 



(1972) , who assume that Q 



Y, 



E sin 2a , where E is the trans- 



mitted energy which is also a function of x as is a (and y is the 



submerged density of the beach material). Price, Tomlinson, and Willis 

 then obtain the one-line theory equation: 



0.55 



„ dE „„ „ da 



sm 2a -;— + 2E cos 2a -r- 



dx dx 



.b|I .o 



(45) 



which is solved numerically with 



-1 3y 

 a = a - tan ^r— 



(46) 



Laboratory experiments were performed with crushed coal by Price, 

 Tomlinson, and Willis (1972) . The theory giving the effect of wave 

 diffraction was verified by the experiments at the beginning of the 

 test. After a 3-hour test which may correspond to a prototype storm 

 duration, it is stated that the wave refraction pattern invalidates the 

 input wave data and a complex boundary condition developed at the up- 

 drift end of the wave basin. 



Bakker's (1970) consideration of wave diffraction has been included 

 in his two-line theory where. 



Qi = 



9yi 



- ^1 



(47) 



- q 



3y, 

 2 "3F 



(48) 



Neither the deepwater line, defined by y (x,t), nor q and Q , is 



affected by diffraction. Fig. 15 presents typical results obtained from 

 this theory for the case of beach evolution near a groin and between two 

 groins . 



40 



