Approximations to wave scattering by an ice sheet of variable
thickness over undulating bed topography.
D. Porter & R. Porter 2005, J. Fluid Mech. 509, 145--179.
An investigation is carried out into the effect on wave propagation of
an ice sheet of varying thickness floating on water of varying depth,
in three dimensions. By deriving a variational principle equivalent to
the governing equations of linear theory and invoking the mild-slope
approximation in respect of the ice thickness and water depth variations,
a simplified form of the problem is obtained from which the vertical
coordinate is absent. Two situations are considered: the scattering of
flexural-gravity waves by variations in the thickness of an infinite
ice sheet and by depth variations; and the scattering of free surface
gravity waves by an ice sheet of finite extent and varying thickness,
again incorporating arbitrary topography. Numerical methods are devised
for the two-dimensional versions of these problems and a selection of
results is presented. The variational approach that is developed can
be used to implement more sophisticated approximations and is capable
of producing the solution of full linear problems by taking a large
enough basis in the Rayleigh-Ritz method. It is also applicable to other
situations that involve wave scattering by a floating elastic sheet.
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