A multi-mode approximation to wave scattering by ice sheets of varying thickness

The problem of linear wave scattering by an ice sheet of variable thickness floating on water of variable quiescent depth is considered by applying the Rayleigh-Ritz method in conjunction with a variational principle. By using a multi-mode expansion to approximate the velocity potential that represents the fluid motion, Porter & Porter (J. Fluid Mech. vol. 509, 2004, p. 145) is extended and the solution of the problem may be obtained to any desired accuracy. Explicit solution methods are formulated for waves that are obliquely incident on two-dimensional geometry, comparisons are made with existing work and a range of new examples that includes both total and partial ice-cover is considered.