548 



INMAN AND BAGNOLD 



[chap. 21 



E(iCdndSd = ECns, where the sub.scrii)t d refers to deep-water-wave conditions 

 and s is the spacing between wave orthogonals (Fig. 11), 



// = 



\ {Sy) tan0 



tan ^ EaMd . 



All rr, Sni Ud COS ttrf COS a. 



(22d) 



This equation iin])Hes that for a given deep-water-wave condition, the 

 dynamic transjwrt rate. //, should be ])roportional to sin a^^ cos a<i cos a = 

 ^ sin 'lad cos a. For these wave conditions the sin-cos function has a value of 



INITIAL 

 SHORELINE 



SUBSEQUENT 

 SHORELINE 



Fig. 12. Hypothetical wave and shoreline conditions, and the postulated subsequent 

 modification of the shoreline. The waves in deep water approach the coast at an 

 angle of 45° and have a height of Hd — 61 cm and a period of 5 sec. 



0.48 at sections A, C, E and 0.25 and 0.23 respectively at sections B and 1).^ 

 As a working api)roximation it would have been adequate to assume that 

 cos a is unity and the transjiort rate is proportional to | sin 2ad. This function 

 has values of I, | and \ respectively for the tlu'ee beach conditions. 



The relationshi]) imjilies that the transport rate is two times greater at beach 

 sections A, C and E than at the inchned sections B and D. If tliis is the case, 



1 It is assumed that the bottom contours are straight and parallel off the beach sections 

 in question, and that the wave refraction can be obtained from SnelTs Law, assuming a 

 wave velocity at the breaking point oi C = ^^/{2.2SgH), where // = 0.3lWrf[l/rfS(^/ff(is]!3 

 (Munk, 1949a). 



