Equation (2) is applicable for e > 1, 

 where 



266.5 cjO-355 ^0.645 



(3) 



describes the state of near -bed mixing due to sediment grain roughness. 



Available evidence indicates that equation (2) , which usually gives a lower 

 velocity than equation (1) , should always be applied in field situations due to 

 the prevalence of nonlaminar flow. Equation (1) is usually applicable in lab- 

 oratory situations with relatively high flow frequency and fine sand. In tran- 

 sitional laboratory situations where neither equation (1) nor equation (2) is 

 definitely appropriate, the transitional condition for sand motion is 



fe»'t ^TTT^ <« 



where one weighting factor is e given by equation (3) and the other is 



6 = 2- YXT' [^^'"^v i" ft/s] (5) 



2. Conversion to Critical Linear Wave Conditions . 



The threshold velocity given by equation (1) , (2) , or (4) can be converted 

 to more generally useful critical wave conditions for sand motion using rela- 

 tionships from linear wave theory. Peak near -bottom horizontal fluid velocity 

 induced by a linear surface wave is 



^ax(-d) = 5C0 = _ /2M\ (6) 



2 sxnh(^-Y-j 



where H is the surface wave height, d the local water depth, and L the 

 local wavelength determined by 



2^tanh(^) = ^ (7) 



The Figure provides graphs of (sinh x) and [x(tanh x)] as a function of x, 

 which are needed with equations (6) and (7) and the critical velocity from 

 equation (1) , (2) , or (4) to compute minimum wave height for sand motion in a 

 given water depth, or maximum water depth for sand motion with a given wave 

 height . 



For the minimum wave height computation, the calculated ((jo^ d/g) is used as 

 the ordinate of the [x(tanh x) ] curve in the Figure to yield the value of the 

 argument x = (27r d/L) and of sinh(2Trd/L) . Equation (6) then gives the minimum 

 wave height for sand motion, Hjj,£j^, to be [2(Cco) sinh(2ir d/L)/a)]. 



