Dynamias of Submerged Towed Cylinders 



We observe in Fig, 3 that both the ^eroth and first modes 

 lead to instabilities for small, finite u. The instability associated 

 with the zeroth mode is a yawing one, while that associated with the 

 first mode is oscillatory. We see that for u > 3.05 the oscillatory 

 instability ceases in the first mode, re-appearing at u « 3,65. 

 However, at much lower towing speed (u « 2,3) the system loses 

 stability in its second (flexural) mode, as shown in Fig, 4, and at 

 u ~ 4 in its third mode. In short, this particular system is subject 

 to several types of instabilities; at low towing speeds it is subject to 

 quasi- rigid body instabilities, and at higher towing speeds to flexural 

 oscillatory instabilities as well. 



Figure 5 shows the zeroth and first mode of a system with a 

 well streamlined nose and a very blunt tail. We see that it is not 

 subject to yawing instability, and the first mode is only unstable in 

 the range 0<u<0.9. It is, however, subject to flexural oscillatory 

 instability (not shown) in its second mode for u> 5,29. Accordingly, 

 a blunt tail stabilises the system considerably. Also shown in Fig, 5 

 is the first mode of a system with a less than perfectly streamlined 

 nose; we see that the range of first-mode oscillatory instability in 

 •this case is larger , i. e. < u < 1. 75. 



J!B:1 



Re(u)-0 



Fig. 5 The dimenslonless complex frequencies of the zeroth and 

 first modes of a flexible cylinder with ec^= eq^ = 1 , 

 f|=i, C|=0, f2= 0, C2=l, A=l, X, =X2 = 0»01» Also 

 the first mode with f = 0,8. (Theory of [ 26]) . 



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