Three-dimensional dynamics of long pipes towed underwater. Part 1: The equations of motion

This paper is the first in a two-part study of the dynamics of long pipes towed underwater. In this part, Part 1, the three-dimensional equations of motion are derived for the dynamics of the system. Inviscid forces are modelled by adapting Lighthill's slender-body work to the problem at hand, while the viscous forces are modelled by elaboration of Taylor's expressions. The effect of cross-currents is also considered in the equations of motion. The pipeline is flexibly connected to the towing and trailing vessels via cables at its upstream and downstream ends. The cables are modelled as linear springs and the body is assumed to be of null buoyancy. The linearized equations of motion and boundary conditions are solved in Part 2 by using a finite difference technique, and the results are discussed therein.

► In the equations of motion Taylor's expressions are extended for 3-D motions.
► The effect of cross-currents has been considered in the equations of motion.
► The linearized form of generally nonlinear boundary conditions is used.
► The linear steady and linearized unsteady equations for a towed pipe are obtained.