Hydrodynamic Forces on a Vertical Cylinder in Current and Waves

Abstract

A vertical cylinder in uniform current and regular waves is analysed based on potential flow theory and low current speed approximation. The perturbation theory is formulated by expanding the velocity potential in a power series of current speed U and by neglecting the terms of order O (U2). This reduces the boundary-value problem to the integral equation, whose kernel functions involve only the Green's function with zero current speed. The solutions are derived in explicit form for the first-order wave exciting force, mean wave drift force and wave drift damping force on the cylinder, where the nonlinear coupling between the steady and unsteady potentials at the free surface is taken into account. Numerical results are also presented, which lead to the following conclusions : i) The hydrodynamic forces on the vertical cylinder in current and waves are significantly influenced by the presence of current.ii) The wave drift force is more sensitive to current than the first-order wave exciting force. With the increase of current speed in the wave propagation direction, the mean drift force tends to increase compared with the force without current.iii) The nonlinear coupling between the steady and unsteady potentials at the free surface has a significant effect on the hydrodynamic forces, in particular on the wave drift force and wave drift damping. The inclusion of these effects results in an increase of the wave drift damping coefficient by one or two times the value predicted with the classical free surface condition.