The Second-Order Diffraction Loads and Associated Motions of a Freely Floating Cylindrical Body in Regular Waves: An Eigenfunction Expansion Approach

Abstract

A solution, exact to the second-order in wave steepness, is presented for the hydrodynamic loads and associated wave-induced motions of a freely floating circular cylindrical body in regular waves. Due to the circular cylindrical 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 methods 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 first- and second-order hydrodynamic loads on and associated wave-induced motions an several example cylindrical structures.As well as providing information on the second-order hydrodynamics of a freely floating cylindrical body, the present solution serves as an important, independent benchmark for the numerical solution for the second-order hydrodynamic loads and associated motions of arbitrary floating structures in waves currently under development at the University of Houston and elsewhere.