Analysis of water waves passing over a submerged permeable obstacle
Resource
Journal of the Chinese Institute of Engineers, 33(6), 845-861
Journal
Journal of the Chinese Institute of Engineers
Pages
845-861
Date Issued
2010
Date
2010
Author(s)
Abstract
Abstract A rare analytical solution is given for small‐amplitude waves passing over a rectangular, rigid, permeable, submerged obstacle in a viscous fluid. The Helmholtz decomposition theorem is applied to decompose the flow field into its irrotational and rotational parts. The rotational, viscous flow component is then simplified as boundary layer flow. Considering that the eigenvalues inside the permeable obstacle are complex and the eigenfunctions are not orthogonal in an inner product space, we introduce a small porous Reynolds number to perform the regular perturbation expansion. Important conclusions are: (1) nearly complete reflection may occur for a wide permeable submerged obstacle; (2) Stokes boundary layers appear inside and outside the permeable obstacle, with thickness 4.5√k/n0 inside the obstacle and 5.5√ν/ω outside the obstacle; (3) the horizontal velocity component inside the permeable obstacle acts as Darcy's flow; (4) the permeability of a submerged obstacle reduces its resulting drag force. Key words: permeable submerged obstacleviscous water wavesporous Reynolds numberregular perturbation expansion Notes Corresponding author. (Tel: 886–33662626; Fax: 886–2–33665866; Email: mylin@mac.com)
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Type
journal article
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