A ship, towing a heavier-than-water cable with a neutrally buoyant slender cylinder attached to the downstream end of the cable, is considered. The neutrally buoyant element contains a sonar array. Linear changes in the ship's velocity cause perturbations of both the cable and cylinder. The form of transverse vibrations of the neutrally buoyant cylinder was determined in Part 1. The propagation of disturbances along the cable is investigated in this paper. In particular, the effectiveness of the cable at isolating the sonar array from forcing due to unsteady ship motion is examined.The cable and cylinder are found to be stable under constant towing conditions. It is therefore appropriate to investigate their response to forcing. Meanderings in the ship's track produce transverse displacements of both the cable and the cylinder. These transverse oscillations entirely decouple from any in-plane motion. The propagation of disturbances of frequency ω along the cable depends strongly on the value of the non-dimensional frequency ωlC/U, where lC is the cable length and U is the towing speed, and only weakly on the other cable parameters. The cable acts as an effective low-pass filter to transverse oscillations, the amplitude of disturbances with non-dimensional frequency greater than 10 being reduced by at least 90% as they propagate along the cable.Unsteadiness in the ship's speed can result in in-plane deflections of the cable, and vertical oscillations of the cylinder containing the sonar array. In contrast to the transverse oscillations a significant proportion of the in-plane disturbances at the ship travels to the sonar array at all values of the frequency. Low- and high-frequency analytical forms are derived to explain why this occurs. Perturbations in the ship's position are most effectively transformed into vertical oscillations of the array at a frequency of 2.8U/lC. The effect of cable properties on transmission along the cable is investigated. The transmission again depends on the value of the non-dimensional frequency ωlC/U. Parameter changes, which increase the cable critical angle, increase the proportion of the disturbance at the towing point that is transformed into vertical array motion, for a fixed value of ωlC/U. This is explained by reference to the low- and high-frequency analytical solutions.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112088000540

The dynamics of towed flexible cylinders Part 2. Negatively buoyant elements

A three-dimensional dynamic analysis of a towed system

Nonlinear vibrations of suspended cables—Part III: Random excitation and interaction with fluid flow

A numerical and experimental study on dynamics of a towed low tension cable

Abstract This paper presents a numerical and experimental investigation into the dynamic behaviour of a towed low tension cable applicable to a towed array sonar system for detecting submarines. In the numerical study, an implicit finite difference algorithm is employed for solving the three-dimensional cable equations. Bending stiffness is considered in order to cope with the low tension problem. Fluid and geometric non-linearities are solved by Newton-Raphson iteration. Block tri-diagonal matrix method is applied for the fast calculation of very large matrices. In order to verify the numerical results and to observe real physical phenomena, an experiment was carried out for a 6 m cable in a deep towing tank. In the experiment, the cable was towed in two different ways; one was towed at a constant speed and the other was towed at a constant speed with top end horizontal oscillations. Cable tension and shear forces were measured at the top end. Numerical results are compared with experimental data. Good agreements are only achieved by employing enhanced drag coefficients due to vortex induced vibrations. It is also found that in the numerical modelling, non-uniform element lengths are necessary to cope with the sharp variation of tension and shear forces near the top fixed end.

A Numerical And Experimental Study On Dynamics of A Towed Low-Tension Cable

This paper is an attempt to formulate a comprehensive theory with which the forces and motions of a submarine cable can be determined in typical laying and recovery situations. In addition to the fundamental case of a cable being laid or recovered with a ship sailing on a perfectly calm sea over a horizontal bottom, the effects of ship motion, varying bottom depth, ocean cross currents, and the problem of cable laying control are considered. Most of the results reduce to simple formulas and graphs. Their application is illustrated by examples.

E. E. Zajac

Papers

Dynamics and kinematics of the laying and recovery of submarine cable