Abstract
The paper describes a process which allows a vertical circular cylinder subject to plane monochromatic surface gravity waves to appear invisible to the farfield 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 mildslope approximation is applied to the governing linearised threedimensional water wave equations to formulate a depthaveraged twodimensional 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 crosssection is reduced towards zero with increasing refinement of the bathymetry. A fully threedimensional boundaryelement 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 mildslope 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 threedimensional problem. One practical application of the results is that cloaking implies a reduced mean drift force on the cylinder.
Original language  English 

Pages (fromto)  124 143 
Number of pages  20 
Journal  Journal of Fluid Mechanics 
Volume  750 
Early online date  30 May 2014 
DOIs  
Publication status  Published  10 Jul 2014 
Keywords
 surface gravity waves
 wave scattering
 wavestructure interactions
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Profiles

Dr Richard Porter
 Cabot Institute for the Environment
 School of Mathematics  Senior Lecturer in Applied Mathematics
 Fluids and materials
 Applied Mathematics
Person: Academic , Member