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

Published online by Cambridge University Press:  21 April 2006

A. P. Dowling
A. P. Dowling
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
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Abstract

The transverse vibrations of a thin, flexible cylinder under nominally constant towing conditions are investigated. The cylinder is neutrally buoyant, of radius aA 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 CN and CT. The ratio CN/CT 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 CN is greater or less than one-half CT.

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 lR, radius aR is investigated. Provided ωlRaR/UaA 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 CN/CT attaching a drogue may be disadvantageous because it reduces the attenuation of high-frequency disturbances as they propagate down the cylinder.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 187 , February 1988 , pp. 507 - 532
Copyright
© 1988 Cambridge University Press

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