The sum- and difference-frequency wave loads and motions of a freely floating circular cylinder

Abstract

An exact, second-order solution is presented for the hydrodynamic loads and associated wave-induced motions of a freely floating circular cylinder in bichromatic waves. Due to the body geometry considered, a computationally efficient eigenfunction expansion technique may be utilized to obtain the linearized solution. Furthermore, the present geometry allows the complex free-surface integral which appears in the second-order loading formulation to be integrated analytically in the angular coordinate. An accurate and efficient method is developed to evaluate the remaining integral in the radial direction. In the near field this integral is evaluated numerically, while in the far-field an analytical solution based upon the asymptotic forms of the linearized potential components is utilized. Numerical results are presented which illustrate the second-order hydrodynamic loads on, and wave-induced motions of, several example cylindrical structures at both the sum- and difference-frequencies of the constituent linear waves.