Wiegel and Delmonte 



forces is given in Figure 17 (Bidde 1970). It is suggested that as an 

 approximation the case for regular waves can be extended to the case 

 of two dimensional random waves. For example, the highest wave in 

 Figure 17b has a height of 0. 3 ft. Using linear theory, N K q for this 

 wave (the wave "period" is about 1. 1 second) can be calculated, and 

 is approximately 7.0. One would then estimate the ratio of "lift" to 

 longitudinal force to be about 15 to 20%. 



Waves in the ocean are three dimensional, having a direction- 

 al wave spectrum. This presents a much more difficult problem than 

 the case of an irregular system of two dimensional waves. Some work 

 has been done in trying to analyse field studies made in the Gulf of 

 Mexico by consortium of oil companies (Schoettle, 1962 ; Blank, 1969). 

 The results of this attempt to analyze the field data to obtain informa- 

 tion on "lift" forces was unsuccessful (Abdel-Aal and Wiegel, 1971). 



CONCLUSIONS 



The Keulegan-Carpenter Number appears to te a useful para- 

 meter to predict the ratio of "lift" to longitudinal wave induced forces 

 in a regular system of two dimensional waves. For the case of a ver- 

 tical pile piercing the water surface, "lift" forces start to occur for 

 values .of Nj^c between 3 and 5, with the ratio of "lift" to longitu- 

 dinal force increasing rapidly with increasing Nj^c to a value of 

 NKC °^ a ^ >out 15 to 20. The ratio then remains about constant, or 

 perhaps decreases to some extent with increasing Nj^q. 



The value of the ratio of "lift" to longitudinal force, for N K q 

 greater than about 20 appears to be similar to the ratio of Cl/Cq 

 for one directional steady flow. 



For the higher values of N K q the "lift" force becomes irre- 

 gular and should be described by a distribution function. 



ACKNOWLEDGEMENTS 



The work presented herein was performed under Contract 

 DACW-72-69-C-0001 between the Coastal Engineering Research 

 Center, Corps of Engineers, U.S. Army, and the University of Cali- 

 fornia. 



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