Unstable Motion of Free Spar Buoys in Waves 



due to the vertical motion of the buoy. Furthermore the large ampli- 

 tude of the vertical motion explains why the wave height chosen in our 

 experiments is small ( f ^0. 50 m. in real scale). For larger wave 

 height, the waves would sometimes overrun the buoy models, the mo- 

 tions would then become quite irregular and would not be amenable by 

 a simple theoretical approach. 



The present study was divided as follows : 



In Section I, we present results of experiments on regular 

 waves of various models. These experiments show the presence of 

 these phenomena of non linear origin : a double regime for the ver- 

 tical motions, a rolling motion and an unstable pitching motion. 



In section II we propose a theory to explain these pheno- 

 mena. This theory consists essentially in introducing non linear rest- 

 oring terms in the equations of motion. 



Section III deals with the behaviour of the buoy in irregular 

 waves. The unstable rolling motion is studied experimentally and 

 theoretically by using a stability criteria similar to that of J. B. Keller 

 and G. F. Carrier. 



TYPE OF BUOYS STUDIED 



The buoys studied here are made of a circular cylindrical 

 central part, while the upper and lower parts, though always axisym- 

 metric, may have, in some cases, rather complicated shapes which 

 can sensibly differ from a circular cylinder. The upper part which is 

 out of water is usually of small height. Sketches of the various types 

 of the buoys studied in this paper are given in Figure 1. Their charac- 

 teristics are given in Table 1 . 



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