u T 

 ™^ i-d) _ (0.1365) (8) 



.H 2 



0.546 



Interpolating between curves in the inset of Figure 4-29 yields 



d = 40 meters (130 feet) 



This is the required maximum water depth for sand motion because at greater 

 depths the wave-induced velocity for the given H and T will be less than 

 the threshold velocity. 



(c) Solution (a) and Figure 4-29 indicate that wave periods greater than 10 

 seconds will certainly cause sand motion with H = 1 meter and d = 20 

 meters . Estimating T = 7.5 seconds , Figure 4-29 shows for d = 20 meters 

 (65.6 feet) 



u T 



max , J, 

 (-a) 



H 

 and 



= 1.35 



u „ =0.18 meter/second 

 ™^ (-d) 

 which is somewhat larger than the threshold velocity. For T = 5 seconds , 

 Figure 4-29 shows ^ 



wax , 7, 



and 



u „ = 0.05 meter/ second 



™^ i-d) 



which is much less than the required threshold. Refining the estimate to T 

 =6.5 seconds , interpolation in Figure 4-29 yields 



^ ^ ^0.85 



H 



so that 



(0.85) (1) n 1-3 . / A 



u = -^ -. — r^ — = 0.13 meter/ second 



mx ^_^^ 6.5 



or slightly less than the threshold velocity. Thus, T = 6.6 seconds is a 

 reasonable approximate solution. 



*************************************** 



c. Seaward Limit of Significant Transport . Example problem 2, together 

 with available measurements of usual nearshore wave conditions (Table 4-4), 

 indicate that waves can set in motion occasionally each year fine sands over 

 most of the continental shelf to water depths on the order of 50 to 100 meters 

 (Silvester and Mogridge, 1970). An important question is this: what is the 

 maximum water depth at which sand transport occurs at rates significant in 

 coastal engineering? Such a seaward limit figures as a critical parameter in 



4-70 



