Equation (2) and a coupled pair of quantitative assumptions perniit 

 calculating a maximum water depth for intense bed agitation by shoaling 

 waves. Taking ^^ = 1 and using linear wave theory, equation (2) may be 

 written as 



/2ud3\ /2^dA /2^d3\ u2 rH-|2 



(3) 



where H is wave height, L is wavelength, and dg is the limit depth. 

 To assist selecting a reasonable magnitude for e, the case of maximum 

 wave steepness (eq. 100 in Madsen, 1976) is examined: 



(lI 



0.14 tanh (^) 



(4) 



Table 1 lists the dg/L solving equations (3) and (4) for four values of 

 e with y' = 1-6 (quartz sand in freshwater or saltwater). For the 

 present purpose, e = 0.03 seems the proper magnitude. The limit depth 

 then remains well beyond the breaker depth for a steep wave, and the 

 limit to the active profile generally lies seaward of the breakers. This 

 e is also large enough that the previous assumption of ed>>D can be 

 easily satisfied for fine sands. Based on these considerations, "t^ = 1 



with e = 0.03 

 agitation. 



is taken to indicate the limit depth of intense bed 



Table 1. Dimensionless water depth, dg/L, solving 

 equations (3) and (4) for four values of 



e 



dg/L 



H/L 



H/dg 



0.10 



0.0610 



0.0512 



0.839^ 



0.06 



0.1211 



0.0898 



0.7422 



0.03 



0.1790 



0.1133 



0.633 



0.01 



0.2579 



0.1296 



0.503 



^Calculated using Table C-2 in U.S. Army, Corps 

 of Engineers, Coastal Engineering Research 

 Center (1975) . 



^Breaking wave, if bed slope is small (see eq. 

 102 in Madsen, 1976). 



With these assumptions, equation (3) can be rewritten as 



K sinh2 5 tanh^ , (l . _^^) = 205.6 (^) (5) 



