Wave scattering by an ice sheet of variable thickness

This paper describes an investigation into the effect on wave propagation of an ice sheet of varying thickness floating on water of varying depth. A variational principle equivalent to the governing equations of linear theory in three dimensions is given, forming the basis of a Rayleigh-Ritz approximation. Here we invoke the mild-slope approximation in respect of the ice thickness and water depth variations to derive a relatively simple model for slowly modulating waves from which the vertical coordinate is absent. We consider both the scattering of flexural-gravity waves by variations in the thickness of an infinite ice sheet and the depth variations, and the scattering of free surface gravity waves by an ice sheet of finite extent and varying thickness, with arbitrary topography again incorporated. Existing work related to the present contribution includes that of Meylan (2001) who also used a variational principle for the full linearised equations to investigate wave interaction with rectangular plates of constant thickness in three dimensions. Andrianov & Hermans (2003) recently derived an integro-differential equation for the problem of an sheet of finite extent floating in a free surface.