As the clearance is increased to 1/16 inch, the maximum upward 

 forces decrease in magnitude, and also occur slightly later in the wave 

 cycle. At the same time, the downward forces increase, reaching their 

 maximum values at approximately 90° and 270°. 



Further increases in the bottom clearance produce a continuous shift 

 of the positions of both the maximum upward and maximum downward forces 

 later in the wave cycle. Simultaneously, the forces become downward 

 rather than upward for a larger part of the cycle. At the same time, 

 the vertical components of the wave force under the crests and troughs 

 become negative and increase in the downward direction, while the negative 

 forces at 90° and 270° gradually decrease to zero. 



At a 1-inch clearance, the resultant force acts downward throughout 

 almost the complete wave cycle, with maximum downward forces occurring 

 under the crests and troughs of the passing waves. The vertical forces 

 are zero at 90° and 270°, the positions of the maximum horizontal iner- 

 tial forces. However, the lift effect is not very large for the 1-inch 

 clearance. The resultant force plot for the 2-inch clearance shows that 

 the lift effect is still present, but is relatively small, even in com- 

 parison to the small vertical inertial forces. 



At a slightly larger clearance, the lift effect will disappear, and 

 the vertical forces will be due almost entirely to the inertial forces, 

 since the vertical drag forces are negligible near the bottom. At this 

 clearance, the inertial force will act upward under the trough and down- 

 ward under the crest, so the resultant force plot will take the form of 

 an approximately sym.metrical ellipse. This condition is shown in 

 Figure 34 for a smaller wave period (1.23 seconds), with a 1-inch bottom 

 clearance. The ellipse is distorted slightly, due to the small drag 

 forces acting in the horizontal direction, 90° out of phase with the 

 larger horizontal inertial forces. 



The horizontal components of the resultant wave force are also 

 affected by the proximity of the bottom boundary. Although the horizon- 

 tal water particle velocities and accelerations increase with distance 

 above the bottom, the corresponding horizontal drag and inertial forces 

 are larger when the pipe is close to the bottom than when it is located 

 above at larger clearances. 



Figures 35, 36, and 37 show the resultant force plots at both large 

 and small bottom clearances, for a wave with a period of 0.95 to 0.96 

 second and a height of 0.24 to 0.25 foot. Because the wave period is 

 small, the horizontal excursions of the water particles at the bottom 

 and the duration of the horizontal flow are too small for the lift 

 effect to develop. So the forces acting in both the horizontal and ver- 

 tical directions are mostly inertial, with a small drag component in the 

 horizontal direction. The resultant force plots therefore take the form 

 of an ellipse. 



70 



