SECT. 3] BEACH AND NEAESHORE PROCESSES 547 



It is possible that the dimensionless quantity in brackets may tend to a 

 constant value for a given beach. If so, the spacing between rip currents, h, 

 would increase with the wave period T as it is found to do in nature. Aside 

 from the observation that h decreases with increasing wave activity, httle is 

 known regarding its dependence on the characteristics of the beach. 



In the above relations, y, j8 and depend respectively upon the type of 

 breaking wave, the slope of the beach, and the physical properties of the sand. 

 Collectively the factor 8 tan ^l\/{Sy) tan ^ has a unitless value ranging from 

 one-tenth to one for sandy beaches. The term {hEnjT) sin a cos^ a and its 

 equivalent {lilCT)Pi cos a are proportional to the total longshore component 

 of power available for transporting sand, and other factors being equal, give a 

 maximum in longshore power when the breaker angle a is about 35°. Larger 

 and smaller angles should result in a decrease in the rate of sediment transport. 



K is the ratio of the rate of the work done in transporting the sediment to 

 the total power available, and can be considered as an efficiency coefficient. 

 Approximate evaluation of K, using the laboratory data from SaviUe (1949, 

 run 11) in equation (22b), gives values of about 3% if it is assumed that h 

 is equal to the whole length of the model beach. An estimation of the value of 

 K for field conditions can be obtained by equating the coefficients of equation 

 (22c) with the numerical constant 2.0 x lO-i obtained for the empirical transport 

 relation of the previous section. Taking measured field data from Inman and 

 Quinn (1952, fig. 3), where Zi = 400 m, gives K equal to 17%. 



The theoretical relations expressed in equations (22a, b) refer to conditions 

 well above the threshold of bed movement and, therefore, to a constant maxi- 

 mum value to which K is supposed to rise. At the threshold of sediment move- 

 ment K is clearly equal to zero. If the field data leading to the empirical 

 transport rates include threshold and sub -threshold wave conditions, then the 

 calculated values of K will be lower than those for fuUy developed transport. 



E. Application 



An example of the possible appUcation of the above model to the develop- 

 ment of shorehne forms is given below and illustrated in Fig. 12. Imagine waves 

 approaching a straight shoreline having a single symmetrical bulge or headland. 

 The bulge could be caused by river deposition on an otherwise straight shore- 

 line. In the absence of the bulge the rate of longshore transport of sand would 

 be equal at aU sections along the beach for any given wave and angle of ap- 

 proach. Assume the coast to be exposed to waves having a period of 5 sec, a 

 deep -water-wave height Hd = Ql cm, and direction of approach a(i = 45°. Under 

 these conditions the transport rates will be approximately equal at beach 

 sections A, C and E, and appreciably less at sections B and D. 



The longshore transport rate given by equation (22b) can be expressed in 

 terms of deep-water-wave characteristics when the bottom contours are 

 straight and parallel by assuming that SneU's Law for ray optics apphes : CalC = 

 sin a al sin a ; and that energy is conserved between wave orthogonals : 



19— s. ra 



