Dynumios of Submerged Towed Cylinders 



1 — 'i — I \ — r — 1 — I — |— r 



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 / 



THIRD-MODE 



OSCILLATORY INSTABILITY 

 / 



/ 



/ 



/ 



"I I 1 — I — I — I — r 



THIRD MODE 



5- 



3- 



-T 



cv^\TT-TTr?PCT-"rTrTr^r^r^"\\r^r^vYs 



YAWING AND FIRST-MODE 

 OSCILLATORY INSTABILITY 



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/ 



J I I I I 1 L_L 



J L_l L_J- 



0.2 0.3 



Fig, 7 Stability map showing the effect of A for a flexible cylinder 

 with ecN=ecj=l, f,= l, c, = 0, f2=0.6, C2=0.4, 

 X, =X2=0«01' (Theory of [ 26]). 



Some experiments were performed designed to test the theory 

 [ 26] , Rubber cylinders of neutral buoyancy were held in vertical 

 water flow by a nylon 'tow-rope'. Provided the tall was streamlined 

 and the tow-rope not too short, 'criss-crossing', essentially non- 

 flexural oscillations developed at very low flow; these were inter- 

 preted as corresponding to first-mode oscillatory instability. At 

 higher flow velocities, flexural oscillations developed with a modal 

 shape corresponding to that of the second mode; sometimes, at yet 

 higher flow velocities, oscillations with a third-mode modal shape 

 developed. These flexural oscillations were interpreted to cor- 

 respond to second- and third-naode oscillatory instabilities. Se- 

 quences of cin^-film frannes depicting these oscillations are shown 

 in Figs, 8 and 9. Finally, it was observed that for sufficiently blunt 

 tail and short tow-rope, the system was conapletely stable. Thus 

 the experimental results were in generally good qualitative agree- 

 ment with theory. 



995 



