Nonlinear Diffraction of Random Waves by a Vertical Cylinder

by Ahsan Kareem, Univ of Notre Dame, Notre Dame, United States,
C. C. Hsieh, Univ of Notre Dame, Notre Dame, United States,
A. N. Williams, Univ of Notre Dame, Notre Dame, United States,

Abstract: In this study, nonlinear diffraction of random waves by a vertical uniform circular cylinder in deep water is analyzed. The incident wave field is represented by a stationary random process, the nonlinear diffraction problem is analyzed utilizing the Stokes perturbation expansion procedure combined with a Fourier-Stieltjes spectral representation of the random wave kinematics. The second-order velocity potential is explicitly obtained by applying a modified form of Weber's Integral Theorem to invert the inhomogeneous second-order free-surface condition. Subsequently, the second-order diffraction forces on the cylinder are evaluated and a complete spectral description of the second-order diffraction forces is obtained. It is noted from the numerical results that the spectral density of the second-order diffraction forces in a random incident wave field is not only influenced by the self-interactions of the individual wave components but also by the interactions between different wave components.

Subject Headings: Random waves | Wave diffraction | Water waves | Wave spectrum | Nonlinear waves | Cylinders | Kinematic waves | Probability

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