Viscous effects on Bragg scattering of water waves by an array of piles
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Tabaei-2009-Viscous effects on B.pdf
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Author(s)
Tabaei, Ali
Mei, Chiang
Date Issued
February 2009
Journal
Physical Review E
Publisher
American Physical Society
Citation
Tabaei, Ali , and Chiang C. Mei. “Viscous effects on Bragg scattering of water waves by an array of piles.” Physical Review E 79.2 (2009): 026314. (C) 2010 The American Physical Society.
Version
Final published version
Abstract
We examine the effects of viscous damping in the boundary layers on the Bragg resonance of surface water waves by a two-dimensional array of vertical cylinders. For cylinders of small radius relative to the wavelength, we first derive an effective boundary condition for the radial derivative of the velocity potential to account for the viscous forces. Coupled-mode equations are then rederived by an asymptotic method for the envelopes of multiply resonated waves inside the array. Effects of viscosity on band gaps and scattering coefficients due to a plane incident wave are examined analytically for an infinitely long array of finite width surrounded by open water. For normal incidence the envelope physics is one dimensional. The transmission and reflection properties are studied first. Oblique incidence can in principle excite several wave trains in different directions. Explicit solutions are given and discussed when there are only two wave trains inside the array. Results are compared with recent theories where viscosity is not taken into account. The asymptotic theory can be modified for two-dimensional sound scattering by a cylinder array.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://dx.doi.org/10.1103/PhysRevE.79.026314
