Hydrodynamic inertial forces on a single-point moored vessel due to time-varying current

Abstract

Whilst the concept of the current drag and lift forces on ship-like vessels is widely used, the hydrodynamic inertial forces due to time-varying current are usually not considered and not captured in the calculation methods. The objective of this article is to examine such forces on a weathervaning vessel by applying classical formulations of fluid mechanics. Based on the general expressions for the inertial forces on a body moving in an accelerating flow of an ideal fluid, the formulation applicable for a single-point moored vessel is presented and illustrated by examples. The effect of an oscillatory current is considered further and two limiting scenarios are examined: a periodically oscillating current acting on a vessel with a fixed mooring point (turret) and oscillatory motion of the vessel in a stationary fluid; the two scenarios corresponding to a relatively stiff and soft mooring system, respectively. Both problems are solved by the direct separation of motions, a perturbation method known in vibrational mechanics, and expressions for the mean drift forces are obtained. In both cases, the mean surge force is found to be positive, acting towards the mooring point, and the mean sway force produces a restoring moment which tends to stabilize the vessel in the direction of the current flow. A calculation example is presented and results are discussed. This study concludes that, depending on the current regime, the inertial forces due to time-varying current may be of the same order of magnitude as the quasi-steady forces, their importance increasing for lower mean current speeds.