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On solitary wave diffraction by multiple, in-line vertical cylinders

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Abstract

The interaction of solitary waves with multiple, in-line vertical cylinders is investigated. The fixed cylinders are of constant circular cross section and extend from the seafloor to the free surface. In general, there are N of them lined in a row parallel to the incoming wave direction. Both the nonlinear, generalized Boussinesq and the Green–Naghdi shallow-water wave equations are used. A boundary-fitted curvilinear coordinate system is employed to facilitate the use of the finite-difference method on curved boundaries. The governing equations and boundary conditions are transformed from the physical plane onto the computational plane. These equations are then solved in time on the computational plane that contains a uniform grid and by use of the successive over-relaxation method and a second-order finite-difference method to determine the horizontal force and overturning moment on the cylinders. Resulting solitary wave forces from the nonlinear Green–Naghdi and the Boussinesq equations are presented, and the forces are compared with the experimental data when available.

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Notes

  1. This solution is the same as given by [37].

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Authors and Affiliations

  1. National Optical Astronomy Observatory, 950 N Cherry Ave., Tucson, AZ, 85719, USA

    Douglas R. Neill

  2. Civil Engineering Department, School of Science and Engineering, University of Dundee, Dundee, DD1 4HN, UK

    Masoud Hayatdavoodi

  3. College of Shipbuilding Engineering, Harbin Engineering University, Harbin, China

    R. Cengiz Ertekin

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  1. Douglas R. Neill
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  2. Masoud Hayatdavoodi
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  3. R. Cengiz Ertekin
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Correspondence to Masoud Hayatdavoodi.

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Neill, D.R., Hayatdavoodi, M. & Ertekin, R.C. On solitary wave diffraction by multiple, in-line vertical cylinders. Nonlinear Dyn 91, 975–994 (2018). https://doi.org/10.1007/s11071-017-3923-1

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