The present procedure presumes that the stated requirements of equations (9) 

 and (10) and of a gentle slope are satisfied. 



e. Wave Spectrum . There is no simple alternative to the customary engi- 

 neering assumption that an irregular surface wave field may be represented by 



a single wave height and period. However, there is no direct evidence that the 

 significant wave condition is an adequate representation in considering sand 

 motion initiation by waves having a spectrum of height, frequency, or direction. 



f. Superimposed Steady Flow . Some evidence indicates that the present 

 criterion for sand motion remains appropriate with a small current superimposed 

 on an oscillatory flow, provided that the current speed is less than (O.lgio). 

 Hammond and Collins (1979) provide the first data on sand motion initiation with 

 steady and oscillatory flows in the same direction. These results indicate that 

 the threshold peak velocity in combinations of waves and currents is fairly 

 close to that with waves alone. Thus, in a situation with a known steady flow, 

 this velocity can be subtracted from the calculated threshold peak near -bottom 

 fluid velocity and then the wave conditions required for sand motion can be 

 determined by the procedure in Section 11,2. 



An alternative is to ignore the steady-flow velocity, and regard calculated 

 results as indicating the minimum extent of bed activity due to waves. In 

 situations with significant astronomical tides, water depth should be considered 

 as being with respect to mean low water (MLW) datum. 



III. EXAMPLE CALCULATIONS OF CRITICAL CONDITIONS 



The following example problems demonstrate the use of the present procedure 

 in calculating critical conditions for sand motion initiation by waves. 



*************** EXAMPLE PROBLEM 1*************** 



GIVEN ; At Point Mugu, California (34°07' N. , 119°09' W.), the average yearly 

 wave period is 11 seconds, according to records from a near -bottom pressure 

 wave gage in a 31-foot (9.4 meters) mean water depth (Thompson, 1977). Also, 

 y' is 1.59 (quartz sand in saltwater), v is 1.28 x 10~^ square feet 

 (0.0119 square centim.eter) per second (15° Celsius mean water temperature; 

 National Ocean Survey, 1970), and the typical offshore sediment median diam- . 

 eter D is Q.Q0033 foot CO.Ql centimeter). 



FIND ; The minimum wave height required for sand motion in a water depth of 60 

 feet (18.3 meters) with a wave of the average frequency (o) = 2tv/11.0 = 0.571 

 radian per second) for this site. 



SOLUTION : Equation (2) gives 



(Caj)j^ = (8 Y'g D)°-5 = [8(1.59) (32. 2)(0.00033)]°'5 = 0.37 ft (11.17 cm)/s 



and equation (3) gives 



(^0))^, dO-29 (Q.37)(0.QG033)°-29 



266.5 to°-355 ^0.645 266.5 C0.571)°-355 (i.28 x lo-5)0.6i+5 



12 



= 0.24 



