so that 



i =(t^)(t^) tanh(^jj = (i.26)(26.45)(0.85) = 



28,33 feet = 28 feet, 



Note that equation (10) gives 



di = {(1.08)(5.7)[32. 25/5, 000(0. OOO33)]0-5} = 27.2 feet == 27 feet. 



With the same input parameters, the calculator program in the Appendix gives 

 the more precise results: 



d£ = 12.30 feet ^ 12 feet 



di = 28.32 feet - 28 feet. 



*************************************** 



These calculated results are to be considered in conjunction with other 

 possible indicators of the seaward limit to the wave-dominated profile. Everts 

 (1978) reported two geometric limit depths for Palm Beach near the center of 

 Galveston Island (29°12' N. , 94°57 ' W.). The limit depth to shore-parallel 

 bathymetry is 47 feet (14.3 meters), and the depth at the boundary between the 

 shoreface and ramp profile sectors is 59 feet (18.0 meters); both depths are 

 with respect to mean low water (MLW) . 



Sand-size variation along the profile can indicate a seaward limit to wave 

 effects (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 

 1977). For the Galveston area, Fisher, et al. (1972) charted the boundary be- 

 tween "shoreface sand and muddy sand" and "shelf mud and sand with shell" at 

 about 28 to 29 feet below mean sea level (MSL) . (MLW is about 1 foot below 

 MSL at this site.) 



Watson and Behrens (1976) presented six profiles surveyed to about 14 feet 

 below MSL in June and December 1974 and March 1976 near New Corpus Christi Pass, 

 Texas (28 41' N. , 97 11' W.). Five of these profiles superpose to within ±0.5 

 foot beyond a water depth of about 10 to 12 feet below MLW. Charted profile 

 geometry at this site is similar to that near Galveston (Everts, 1978), and wave 

 climate may be expected to be similar. 



The preceding information supports the calculated values of d^ and d^ for 

 this site. In this example, the shoal zone seems well-founded, while the two 

 geometric indicators derived by Everts (1978) are not supported by other evi- 

 dence on the limits to wave effects on the submarine profile. 



V . SUMMARY 



This report is a self-contained presentation of the calculation procedure 

 (Table 1) for locating a shoal zone along a sand beach profile. The water 

 depths bounding this shoal zone depend on sand characteristics (y', D) and sum- 

 mary statistics of annual wave climate (Hg , a, and Tg) . The shoal zone is de- 

 fined so that expected surface waves have only moderate effects on the sand 

 bottom in this zone throughout a typical year. The calculated shoal zone bounds 

 have applications in coastal engineering activities requiring an estimate of the 

 seaward limit to the wave-dominated nearshore region (see Sec. III). 



16 



