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.