Since the shoal zone has a definite physical basis, the present calculation 

 procedure may reduce the need for detailed site-specific investigations of phys- 

 ical processes, and certainly aids in designing such investigations at localities 

 where wave climate is known. Nearshore measurements of wave climate along U.S. 

 coasts provide a basis for the example calculations given in Section IV. The 

 calculated shoal zone extent is to be considered in conjunction with other in- 

 formation pertinent to the seaward limit of the wave-dominated sand profile. 



II. BASIC EQUATIONS AND SOLUTION TECHNIQUES 



The water depths dg^ and di are calculated from relationships giving the 

 threshold flow energy for two distinct wave interactions with a sand bed. The 

 major assumptions involved are the accuracy of linear wave theory for calcula- 

 tions of near-bottom maximum flow velocity, and a modified exponential distri- 

 bution of nearshore wave heights. 



The landward bound to the shoal is determined from the relationship 



"iax(-dl^ Q_Q3 (^^ 



T'gd 



where 



u^ /JN = the maximum wave-induced horizontal fluid velocity near the bed 



y' = the ratio of the density difference between sand -and fluid to 

 the fluid density 



g = the acceleration due to gravity 



d = the mean water depth. 



Equation (1) describes a definite threshold of erosive sand-bed agitation by 

 steady wave action, and u^axC-d) will be taken as that due to an extreme wave 

 height exceeded 12 hours per year in determining d^ . The water depth then de- 

 fined by equation (1) agrees with field data on the maximum water depth for 

 significant profile changes (elevation excursions greater than ±0.5 foot or 

 ±0.15 meter) throughout a yearly cycle of wave climate. 



Linear wave theory gives 



""^^(-'^) = T {sinh'u.d/L)} ^2^ 



where H is the wave height, T the wave period, L the local wavelength at 

 d; and 



\tanh(2TTd/L) / o \ 2tt / 



where Lq is wavelength in deep water. 



The modified exponential distribution approximating typical measured near- 

 shore wave heights is shown in Figure 2. In terms of standard annual wave 



