Stability of towed, totally submerged flexible cylinders

Abstract

A general theory is presented to account for the small, free, lateral motions of a flexible, slender, cylindrical body with tapered ends, totally submerged in liquid and towed at steady speed U. For particular shapes of the ends and length of tow-rope, it is shown that the body may be subject to oscillatory and non-oscillatory instabilities for U > 0; at small U, these instabilities correspond to those of a rigid body. At higher U, the system generally regains stability in the above modes, but may be subject to higher-mode, flexural oscillatory instabilities. The critical conditions of stability are calculated extensively and the effect on stability of a number of dimensionless parameters is discussed. It is shown that optimum stability is achieved with a streamlined nose, a blunt tail and a short tow-rope.Some experiments are described which were designed to test the theory. Rubber cylinders of neutral buoyancy were held in vertical water flow by a nylon ‘tow-rope’. Provided the tail was streamlined and the tow-rope not too short, ‘criss-crossing’, non-flexural oscillations developed at very low flow. Increasing the flow, these oscillations ceased and the cylinder buckled like a column; subsequently higher-mode flexural oscillations developed. However, for a sufficiently blunt tail and short tow-rope, the system was completely stable.The experimental observations are generally in qualitative agreement with theory. Quantitative comparison of the various instability thresholds and stable zones between experiment and theory, based on estimated values of some of the theoretical dimensionless parameters, is also fairly good.