On the realization of nonlinear wave profiles using the Banach fixed-point theorem: Stokes wave in a finite depth |
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| Authors: | Taek S Jang SH Kwon Takeshi Kinoshita |
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| Institution: | (1) Department of Naval Architecture and Ocean Engineering, Pusan National University, Busan, 609-735, Korea;(2) Civil Engineering Department, Texas A&M University, TX, USA;(3) Institute of Industrial Science, The University of Tokyo, Tokyo, Japan |
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| Abstract: | A new mathematical formulation for the realization of nonlinear wave profiles and its nonlinear solution procedure, based
on the Banach fixed-point theorem, is proposed. To apply the formulation, a nonlinear equation for the Stokes wave in a finite
depth was derived, and some numerical solutions are given. A numerical study showed that the proposed iteration method, based
on linear progressive wave potential only, enabled us to realize the Stokes nonlinear wave profiles in a finite depth. The
nonlinear strategy of iteration has a very fast convergence rate, i.e., only about 6–10 iterations are required to obtain
a numerically converged solution. |
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| Keywords: | Banach fixed-point theorem Stokes wave in a finite depth Fast convergence rate |
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