Abstract

This talk is very loosely motivated by the topic of calving of ice shelves, discussed at the 2023 INI Programme on the “Mathematical theory and applications of multiple wave scattering”, and at KOZ Waves 2024. Here we tentatively propose a possible new mechanism for this breakup, related to the existence of unattenuated edge waves on ice shelves. We shall commence the talk with an elementary discussion of waves on thin elastic plates, including fluid loaded plate waves and Konenkov edge waves1, and review an earlier work by the author on the existence of edge waves on thin elastic plates submerged in compressible fluids2. We shall then employ a highly simplified model of an ice shelf to reduce the problem to the finding of eigensolutions of a simple Wiener-Hopf boundary value problem, which we can solve explicitly. Some simple conclusions will be drawn at the end of the talk. 1. Konenkov, Yu. K. 1960 A Rayleigh-type flexural wave. Soviet Physics Acoustics 6, 122-123. 2. Abrahams, I. D. & Norris, A. N. 2000 On the existence of flexural edge waves on submerged elastic plates. Proceedings of the Royal Society of London A 456 (1999), 1559-1582.