A circular cylinder in water waves |
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| Authors: | Even Mehlum |
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| Institution: | Sentralinstitutt For Industriell Forskning, Forskningsv. 1, P.B. 350 Blindern, Oslo 3, Norway |
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| Abstract: | This paper treats the problem in linearized water wave theory that arises when a wave travels across a submerged cylinder. This problem is classical and was first treated by Dean. The solution presented is novel and explicit. This is achieved through the use of certain recursive relations. The basic results are of course the same as in the older literature: (1) the coefficient of reflection is zero; (2) the only effect of the cylinder, is a phase shift relative to the undisturbed wave. However, the practical computation of the velocity potential and the phase shift is reduced almost to hand calculations. This is in contrast to the older literature which requires, in principle, the inversion of an infinite matrix. The work is motivated by the Institue's efforts to focus water waves. Cylinders are possible bodies to create the necessary phase shifts to achieve such focusing. |
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