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Cloaking of a vertical cylinder in waves using variable bathymetry

Published online by Cambridge University Press:  30 May 2014

R. Porter  and
J. N. Newman
R. Porter*
Affiliation:
School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK
J. N. Newman
Affiliation:
Department of Mechanical Engineering, MIT, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

The paper describes a process which allows a vertical circular cylinder subject to plane monochromatic surface gravity waves to appear invisible to the far-field observer. This is achieved by surrounding the cylinder with an annular region of variable bathymetry. Two approaches are taken to investigate this effect. First a mild-slope approximation is applied to the governing linearised three-dimensional water wave equations to formulate a depth-averaged two-dimensional wave equation with varying wavenumber over the variable bathmetry. This is then solved by formulating a domain integral equation, solved numerically by discretisation. For a given set of geometrical and wave parameters, the bathymetry is selected by a numerical optimisation process and it is shown that the scattering cross-section is reduced towards zero with increasing refinement of the bathymetry. A fully three-dimensional boundary-element method, based on the WAMIT solver (see www.wamit.com) but adapted here to allow for depressions in the bed, is used to assess the accuracy of the mild-slope results and then further numerically optimise the bathymetry towards a cloaking structure. Numerical results provide strong evidence that perfect cloaking is possible for the fully three-dimensional problem. One practical application of the results is that cloaking implies a reduced mean drift force on the cylinder.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering Waves/Free-surface Flows: Wave-structure interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 750 , 10 July 2014 , pp. 124 - 143
Copyright
© 2014 Cambridge University Press 

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