The dynamics of towed flexible cylinders Part 1. Neutrally buoyant elements

Abstract

The transverse vibrations of a thin, flexible cylinder under nominally constant towing conditions are investigated. The cylinder is neutrally buoyant, of radius a A with a free end and very small bending stiffness. As the cylinder is towed with velocity U , the tangential drag causes the tension in the cylinder to increase from zero at its free end to a maximum at the towing point. Transverse vibrations of the cylinder are opposed by a normal viscous drag force. Both the normal and tangential viscous forces can be described conveniently in terms of drag coefficients C N and C T . The ratio C N / C T has a crucial effect on the motion of the cylinder. The form of the transverse displacement is found to be greatly influenced by the existence of a critical point at which the effect of tension in the cylinder is cancelled by a fluid loading term. Matched asymptotic expansions are used to extend the solution across this critical point to apply the downstream boundary condition. Displacements well upstream of the critical point have a simple form, while nearer to the critical point the solution depends on whether the normal drag coefficient C N is greater or less than one-half C T . The typical acoustic streamer geometry considered is found to be stable to transverse displacements at all towing speeds. Forced perturbations of frequency ω are investigated. At low frequencies they propagate effectively along the cylinder with speed U . At higher frequencies they are attenuated. The effect of a rope drogue of length l R , radius a R is investigated. Provided ω l R a R / Ua A is very small, the drogue has the same effect as a small increase in the length of the cylinder. However at higher frequencies and for small values of the ratio C N / C T attaching a drogue may be disadvantageous because it reduces the attenuation of high-frequency disturbances as they propagate down the cylinder.