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Scattering of gravity waves by a periodically structured ridge of finite extent

Published online by Cambridge University Press:  21 May 2019

Agnès Maurel Open the ORCID record for Agnès Maurel [Opens in a new window] ,
Kim Pham  and
Jean-Jacques Marigo
Agnès Maurel*
Affiliation:
Institut Langevin, ESPCI ParisTech, CNRS UMR 7587, 1 rue Jussieu, 75005 Paris, France
Kim Pham
Affiliation:
IMSIA, ENSTA ParisTech – CNRS – EDF – CEA, Université Paris-Saclay, 828 Bd des Maréchaux, 91732 Palaiseau, France
Jean-Jacques Marigo
Affiliation:
Lab. de Mécanique des Solides, Ecole Polytechnique, Route de Saclay, 91120 Palaiseau, France
*
†Email address for correspondence: [email protected]
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Abstract

We study the propagation of water waves over a ridge structured at the subwavelength scale using homogenization techniques able to account for its finite extent. The calculations are conducted in the time domain considering the full three-dimensional problem to capture the effects of the evanescent field in the water channel over the structured ridge and at its boundaries. This provides an effective two-dimensional wave equation which is a classical result but also non-intuitive transmission conditions between the region of the ridge and the surrounding regions of constant immersion depth. Numerical results provide evidence that the scattering properties of a structured ridge can be strongly influenced by the evanescent fields, a fact which is accurately captured by the homogenized model.

JFM classification

Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 871 , 25 July 2019 , pp. 350 - 376
Copyright
© 2019 Cambridge University Press 

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