Non-linear wave loads on large circular cylinders: a perturbation technique

Abstract

The forces and overturning moments exerted by second order waves on large vertical circular cylinders are analysed. The mathematical equations governing the physical system are the three-dimensional Laplace's equation satisfied by the velocity potential ϕ( x, y, z, t) and the boundary conditions, namely the dynamic boundary condition which is obtained from the Bernoulli's equation, kinematic boundary condition, radiation condition, bottom boundary condition and the zero radial velocity condition on the surface of the cylinder. The non-linearity of the mathematical problem is evidenced in the free surface boundary conditions viz. dynamic and kinematic boundary conditions. Analytical solutions are obtained using the perturbation technique. These solutions are compared with various experimental data. The comparison shows favourable agreement between the theory and the experimental results.