Underwater cable dynamics for beginners

Underwater cables are used for a variety of applications such as moorings, fisheries, petroleum exploration, defense and communication. Mathematical models of underwater cables can be used for computer simulations, predicting cable behavior during maneuvering. External forces such as sea current and buoyancy can be included in the models. In the present study, a popular three-dimensional mathematical model of the dynamics of a towed or other underwater cable under tension is outlined in detail. The equations include tension, cable stretch, inertial forces, buoyancy and gravity. Morison’s equation is employed for hydrodynamic loading. The equations are outlined in a step-by-step fashion, where sufficient sub steps are included so that non-mathematicians can follow the outline. There are three equations resulting from the cable kinematics, and three further equations from the cable dynamics or equilibrium of forces. The result is a set of six coupled nonlinear differential equations, which ultimately are presented in matrix form. Typical as well as alternative boundary conditions are mentioned. Further, notes about typical numerical techniques for solving the equations, such as finite difference and finite element methods, are included. It is the author’s hope that this study can be of help for students, researchers and anyone else seeking understanding of the mathematics governing the behavior of underwater cable dynamics.