1.2 



1 



0.8 + 



>^'' 0.6 



0.4 -- 



0.2 -- 









0.02 



0.04 0.06 



iR"R 

 iR 



L = sphere lifting 

 R = sphere rolling 

 S = sphere stationary 



0.08 



0.1 



Figure 2.10. Incipient motion criterion (Equation 2.16 with v^ = 61.8 cm/s) versus wave 

 steepness 



Table 2.4 



Summary of incipient l\/lotion Experimental Results | 



Sphere 



depth 



cm 



Wave 



Height 



cm 



Wave 

 Period 



s 



Wave 

 Steep- 

 ness 



Velocity 



V 



cm/s 



v/Vj 1 



near free 



surface 



d,/d,= 0.16 



4.6 

 13.0 

 2.8 

 8.4 

 5.5 

 7.6 

 14.0 

 15.2 

 17.0 

 14.3 

 13.0 



1.0 

 1.0 

 2.0 

 2.0 

 3.0 

 3.0 

 1.0 

 1.5 

 1.5 

 2.0 

 2.0 



0.029 

 0.083 

 0.009 

 0.027 

 0.012 

 0.016 

 0.090 

 0.065 

 0.073 

 0.046 

 0.042 



28.3 

 41.8 

 11.0 

 29.6 

 20.2 

 17.2 

 42.5 

 67.8 

 64.9 

 63.8 

 59.8 



0.46 

 0.68 

 0.18 

 0.48 

 0.33 

 0.28 

 0.69 

 1.10 

 1.05 

 1.03 

 0.97 



one-third of 



depth 

 d,/d,= 0.38 



4.6 

 13.0 

 2.8 

 8.4 

 5.5 

 7.6 



1.0 

 1.0 

 2.0 

 2.0 

 3.0 

 3.0 



0.029 

 0.083 

 0.009 

 0.027 

 0.012 

 0.016 



8.8 

 31.3 

 7.5 

 22.9 

 14.9 

 12.3 



0.14 

 0.51 

 0.12 

 0.37 

 0.24 

 0.20 



31 



