Cloaking of a vertical cylinder in waves using variable bathymetry

R. Porter, J. N. Newman

Research output: Contribution to journalArticle (Academic Journal)peer-review

26 Citations (Scopus)
361 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)124- 143
Number of pages20
JournalJournal of Fluid Mechanics
Volume750
Early online date30 May 2014
DOIs
Publication statusPublished - 10 Jul 2014

Keywords

  • surface gravity waves
  • wave scattering
  • wave-structure interactions

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