544 INMAN AND BAGNOLD [CHAP. 21 



from wliich the average discharge, q, becomes 4H~|^^/{^y^)T, where y = Hlh is 

 the relative depth of water, H and h are respectively the wave height and 

 depth of water, and T is the wave period. Substituting this value for the 

 discharge gives 



ui 



= 4 /^ -^1 *^i^ ^ ^^^ " cos "• (20b) 



C. Longshore Transport of Sand {Field and Laboratory) 



No satisfactory relationship has been developed between the rate of littoral 

 trans23ort and the waves and currents that cause it. The volume of littoral 

 transport along oceanic coasts is estimated from observed rates of erosion or 

 accretion, most commonly in the vicinity of coastal engineering structures such 

 as groins or jetties. Such observations indicate that the transport rates vary 

 from almost nothing to several million cubic metres per year, with average 

 values commonly falling between 100,000 and 1,000,000 m^ per year. In 

 general, these may be conservative estimates since the volume of sand moved 

 usually exceeds that indicated either by deposition or erosion. 



Laboratory studies of littoral drift (Saville, 1949; Johnson, 1953; Savage, 

 1959) show that rates of littoral transport in models vary with wave energy, 

 wave steepness, and the angle of wave approach. The maximum amount of 

 total transport was observed to occur for wave steepnesses of about 0.025 and 

 for angles of wave approach of about 30°. Also, the transport for waves of low 

 steef)ness ratio took place largely in the wave-swash zone on the beach face, 

 while the transj^ort for steeper waves occurred principally on the longshore 

 bar in the breaker zone. Marked changes in transport rate were observed as the 

 beaches adjust from one set of wave conditions to a new set. Since natural sand 

 beaches are in a continually transient state as the beach adjusts for changing 

 conditions of waves and tides, the application of model to the prototy^^e is 

 difficult. However, the general comparisons between model and prototype 

 appear to be consistent. 



It was suggested (Scripps, 1947) that the work performed by waves in the 

 nearshore zone might be a useful parameter for relating littoral transport 

 rates of sand to wave action, and wave- work factors were computed for that 

 purpose by wave period and direction. Caldwell (1956), observing the relation- 

 ship between wave power and longshore transport rates for actual field condi- 

 tions at Anaheim Bay, California, and South Lake Worth Inlet, Florida, 

 obtained the following approximation for the relationship of the combined 

 data from both locahties : 



S = 210[Psinacosa]0-8 = 2lOPi^^ 



where S is the longshore volume transport of sand in cubic yards per day, 

 Pf = Psinacosa is the longshore component of wave-energy transmission 

 (power) of the breaking waves in millions of ft-lb/day per ft of shoreline, and 

 pound is a unit of force. The factor sin a cos a converts P, the incident wave 



