Irregular points in wavemaker boundary value problem Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/xd07gx06c

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  • A global solution is presented that accurately accounts for the singular behavior at all irregular points. The linearized boundary value problem in a semi-infinite strip in the physical plane is transformed into a smooth unit disk by two successive conformal mappings. The global solution results from a Fredholm integral equation that is obtained from Green's third identity applied to the circumference of the unit disk. The irregular points in the physical domain are transformed into both weak and strong singular kernels in the Fredholm integral equation. The two irregular points that are located at 1) the intersection between the free surface and the wavemaker boundaries and at 2) the intersection between the wavemaker and the bottom boundaries exhibit integrable weakly singular kernels. The far-field radiation boundary becomes a strongly singular kernel. The strength of the singular behavior of these kernels significantly affects the solution near these irregular points. The irregular frequencies are readily included in the global solution from the Fredholm alternative.
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