On the Solution of the Quasi-Third-Order Problem of Two-Dimensional Cylinders in Forced Motion

Abstract

A quasi third-order potential theory for two-dimensional arbitrarily shaped cylinders in forced oscillation on the free-surface of a fluid is presented. The imposed forced motion is assumed simple harmonic in frequency and the amplitude of oscillation is small but finite compared with a characteristic geometric dimension of the cylinder. A regular perturbation expansion in terms of small parameters to the third-order and Green's Function Integral-Equation Method has been employed to solve the resulting set of BVP's in the course to the third-order. Special attention has been paid to the evaluation of the quasi-third-order velocity potential, oscillating with simple frequency, but being of third-order with respect to the perturbation parameter. The corresponding BVP requires a split of the free-surface inhomogeneity into a slowly decaying and an oscillatory part, ensuring so well-posed BVP's for the contributing velocity potentials to the quasi third order.