Cloaking of a vertical cylinder in waves using variable bathymetry. (30th May 2014)

• Record Type: Journal Article
• Authors: Porter, R.; Newman, J. N.
• Is Part Of: Journal of fluid mechanics. Volume 750(2014:Jul.)
• Page Start: 124
• Page End: 143
• Publication Date: 2014-05-30
• Subjects: surface gravity waves, -- wave scattering, -- wave-structure interactions; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2014.254
• Languages: English
• ISSNs: 0022-1120

Abstract

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 (seewww.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.