CD 



(gY'D) 



where 



U, = the maximum wave-induced horizontal velocity near the bed 



g = the acceleration due to gravity 



D = the sediment diameter 



y' = the razio of the density difference between sediment and 

 fluid to the fluid density 



Equation (1) gives the peak near-bottom wave energy per unit sediment 

 grain volume, divided by the energy required to raise an immersed grain 

 against gravity a distance equal to half its diameter (Nayak, 1970). 

 Although the motion threshold cannot be described solely in terms of <l>^, 

 sediment generally begins to move when this number becomes larger than 

 one (Komar and Miller, 1973). Lofquist (1975) observed that $^ measured 

 the intensity of sand motion in his tests with a rippled bed; the motion 

 threshold was near $^ = 2.4, the ripple crests became less distinct for 

 $^ > 10, approximately, and, for larger $^, vortices of fluid and en- 

 trained sediment became increasingly evident, indicating more intense 

 bed agitation. These results show that % "^ 1 indicates the beginning 

 of sediment mobility by describing energetics in a thin layer near the 

 bed. 



After sediment grains begin to move, wavy bed features form. These 

 features are caused by grain flow, but liquid flow of high inertia can 

 scour these features from the bed (Bagnold, 1956). Because a plane 

 (intensely agitated) bed usually occurs in and near the surf zone (Inman 

 and Bagnold, 1963) , a criterion for the seaward limit to the active beach 

 might be based on a parameter measuring the energetics of intense bed 

 agitation. Available research results (reviewed briefly in App. A) indi- 

 cate that grain diameter has a weak influence in intense agitation of 

 fine sand beds, suggesting that another Froude number, like equation (1), 

 be used with a larger length scale replacing D. It is hypothesized that 

 intense bed agitation is described by the sediment entrainment parameter: 



U: 



'b' 



(egy'd) 



(2) 



where e is a number less than one and d is water depth. (The choice 

 of the length scale replacing D is discussed in App. A.) When $g 

 reaches one, the wave energy density is sufficient to raise a grain a 

 distance ed/2, taken to be appreciable fraction of the water depth and 

 much greater than D/2 for fine sands (D<0.4 millimeter). 



