Normal modes of a coupled ice-shelf/sub-ice-shelf cavity system

Ice shelves and ice tongues are dynamically coupled to their cavities. Here we compute normal modes (eigenfrequencies and eigenfunctions) of this coupled system using a thin-plate approximation for the ice shelf and potential water flow in the ice-shelf cavity. Our results show that normal modes depend not only on the ice-shelf parameters (length, thickness, Young's modulus, etc.) but also on the cavity depth. The dominant eigenmodes are higher for ice shelves floating over deeper cavities; they are also higher for shorter ice shelves and ice tongues (<50 km long). The high-eigenfrequency eigenmodes are primarily controlled by the ice flexure and have similar periods to sea swell. These results suggest that both long ocean waves with periods of 100-400 s and shorter sea swell with periods of 10-20s can have strong impacts on relatively short ice shelves and ice tongues by exciting oscillations with their eigenfrequencies, which can lead to iceberg calving and, in some circumstances, ice-shelf disintegration.