Cloaking of a vertical cylinder in waves using variable bathymetry

• Published in: Journal of fluid mechanics Vol. 750; pp. 124 - 143
• Main Authors: Porter, R., Newman, J. N.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.07.2014
• Subjects: Bathymetry; Cylinders; Drift; Exact sciences and technology; Fluid dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); Gravity; Gravity waves; Hydrodynamic waves; Mathematical analysis; Mathematical models; Physics; Solid mechanics; Structural and continuum mechanics; Surface chemistry; Three dimensional; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Water depth; Water waves; Wave equations; Wave power; Wavenumber; wave scattering; surface gravity waves; wave-structure interactions; Vertical cylinder; Wave diffraction; Digital simulation; Wave scattering; Fluid-structure interactions; Modelling; Surface gravity wave
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2014.254

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.