On the shallow-water limit for modelling ocean-wave induced ice-shelf vibrations

The solution to the problem of the vibration of an ice shelf of constant thickness is calculated using the eigenfunction matching method in water of finite depth, and accounting for the draught of the shelf.The eigenfunction matching solution is validated against a solution found using the finite element method. The finite-depth solution is carefully compared with the shallow-water solution, which is the standard model for ice-shelf vibrations. It is shown that the finite-depth and shallow-water solutions differ for periods below 50-100s and significantly differ for periods below 20s. •We present a highly efficient semi-analytic method to solve for the vibration of an ice shelf of constant thickness using the eigenfunction matching method.•We compare the solution against the much simpler case based on the assumption of shallow water and show that the two solutions for finite length ice shelves show significant differences for periods above 50 s.•We compare the finite and shallow solutions for the semi-finite ice shelf and show that here the differences between the models are only significant above 20 s.