Transient Shallow Water Wave Interactions with a Partially Fragmented Ice Shelf

Abstract

This work investigates the interaction between water waves and multiple ice shelf fragments in front of a semi-infinite ice sheet. The hydrodynamics are modelled using shallow water wave theory and the ice shelf vibration is modelled using Euler–Bernoulli beam theory. The ensuing multiple scattering problem is solved in the frequency domain using the transfer matrix method. The appropriate conservation of energy identity is derived in order to validate our numerical calculations. The transient scattering problem for incident wave packets is constructed from the frequency domain solutions. By incorporating multiple scattering, this paper extends previous models that have only considered a continuous semi-infinite ice shelf. This paper serves as a fundamental step towards developing a comprehensive model to simulate the breakup of ice shelves.

Keywords

• ice shelf
• transfer matrix
• energy conservation
• shallow water
• time domain