Water wave scattering by a floating elastic plate over a plane incline

• Published in: The Quarterly Journal of Mechanics and Applied Mathematics
• Main Authors: Ehrenmark, Ulf T., Porter, David
• Format: Text
• Language: English
• Published: Oxford University Press 2012
• Subjects: Articles; Sea ice
• Online Access: http://qjmam.oxfordjournals.org/cgi/content/short/65/3/409; https://doi.org/10.1093/qjmam/hbs010

The effect of a shoreline on the interaction between surface water waves and a floating elastic plate is investigated on the basis of linear theory by considering the fluid motion over a plane inclined bed. The use of a radiation condition at the shoreline that removes reflected waves there both simulates energy dissipation in the shoaling region and allows comparisons to be made with the case of constant water depth. The model applies equally to floating sea ice and ‘very large floating structures’. A Green's function approach reduces the underlying boundary value problem to a pair of coupled integral equations to which Galerkin's method is applied. A sample of numerical results is given from which inferences may be drawn about the influence of the sloping bed. Discrete eigenvalues in sheet length are observed at which the formal scattering problem has no solution.