Figure shows 



slnh-l(i.25) = 1.05 = (2^d/L) and [1.05 tanha.05)] = 0.82 

 Equation (7) shows 



, ^ gpld^^^2^\-| (32.2) (0.82) 



(dmax)v = -^ ^;;2~^ — = ^2 = 2.7 ft (80.5 cm) as the 



maximum water depth for sand motion initiation. 



DISCUSSION : Since (d/L) = (1.05/2Tr) = 0.17, S = (H/2d) (L^/d^) = [ (0.5)/2(2.7) ] 

 (1/0.17)2 = 3.2 and (gHT^/d^) = [ (32.2) (0.5) (2)2/ (2.7)2] = g.g, all the limi- 

 tations on equation (1) as well as equations (8), (9), and (10) are satisfied, 

 A mean water depth less than 3 feet (0.91 meter), with a gentle offshore sand 

 slope and the given wave conditions, should be adequate to include the entire 

 wave-agitated bed . 



If artificial roughness is installed to provide a thoroughly mixed bottom 

 boundary layer in the incident wave, note that equation (2) gives 



(Cw)m = (8 Y'g 0)0-5 = [8(1.66) (32.2) (0.00066) ] -^ = 0.53 ft 

 (16.14 cm)/s 

 and that equations (6) and (7) then give 



(dn,ax)m = 3.2 ft (95.8 cm) 

 so that a larger mean water depth would be required. Note also that 

 (?w)^ dO-29 (0.53)(0.00066)°-29 



266.5 a)°-355 ^0.645 266.5(Tr) ° • ^55 (i.o8 x io-5)0.6'+5 



= 0.25 



so that roughness additional to that of a plane sand slope would definitely 

 be required to make the field criterion in equation (2) applicable. 



IV . SUMMARY 



This report presents a procedure for calculating peak oscillatory velocity 

 causing sand motion, and for converting this velocity into critical wave condi- 

 tions. Having specified the material characteristics (y', g, D, and v) and the 

 wave characteristics (T and either d or H) , the procedure provides the remaining 

 parameter — either the minimum wave height for sand motion in a given water depth, 

 or the maximum water depth for sand motion with a given wave height. This per- 

 mits estimating the seaward extent of bed activity in laboratory and field situ- 

 ations. Considering the assumptions and the factors ignored in developing this 

 procedure, in certain situations the present calculations must be regarded as a 

 minimum estimate of the extent of bed activity for the specific wave condition. 



