Nonlinear Diffraction by Eigenfunction Expansions

by Min-Chu Chen, Sr. Engr.; SONAT Offshore Drilling, Inc., Houston, Tex.,
Robert T. Hudspeth, (M.ASCE), Assoc. Prof.; Dept. of Civ. Engrg. and Ocean Engrg. Programs, Oregon State Univ., Corvallis, Oreg.,

Serial Information: Journal of the Waterway, Port, Coastal and Ocean Division, 1982, Vol. 108, Issue 3, Pg. 306-325

Document Type: Journal Paper


A nonlinear diffraction theory correct to second-order is presented which is based on an eigenfunction expansion of the Green's function for fixed axisymmetric bodies subjected to two-dimensional sinusoidal waves. The boundary value problem for the second-order scattered velocity potential is linearly decomposed into two separate boundary value problems, each having only one inhomogeneous boundary condition. Numerical results indicate that the second-order contributions to the total hydrodynamic pressure force from the inhomogeneous free surface boundary condition are much less than the second-order contributions from the inhomogeneous boundary condition on the axisymmetric body. Second-order contributions are also found to be greater in intermediate water depth conditions than for deep water wave conditions. Theoretical numerical results are also compared with experimental values measured on a fixed vertical circular cylinder.

Subject Headings: Boundary conditions | Axisymmetry | Numerical methods | Water waves | Nonlinear analysis | Nonlinear waves | Linear functions | Hydrodynamics

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