L. G. Bennetts | Searcharxiv

arXiv2026

Modelling hydroelastic flexure of arbitrarily shaped ice shelves forced by long ocean waves

Flexure of Antarctic ice shelves under excitation from long ocean waves induces mechanical ice shelf stresses that amplify fractures and, hence, contribute to calving events. Here, a solution method is developed for a hydroelastic mathematical model of wave-induced ice shelf flexure, based on the conventional theory of a Kirchoff-Love plate floating on shallow water under linearised conditions, but allowing wave forcing of ice shelves with variations in both horizontal dimensions, and where the ice shelves are of arbitrary shape, including non-uniform thickness. The method uses finite elements specifically designed for the high-order hydroelastic system, and a Dirichlet-to-Neumann map to bound the computational domain in the open ocean. Following verification, the method is used to conduct novel studies on how the ice-shelf deflection is affected by the ice shelf shape, the incident wave direction and the proportion of the shelf that is grounded. The efficiency of the method allows the studies to be conducted over a broad frequency range, such that resonant responses are identified.

physics.flu-dyn↗

arXiv2024

Acoustic Lattice Resonances and Generalised Rayleigh--Bloch Waves

The intrigue of waves on periodic lattices and gratings has resonated with physicists and mathematicians alike for decades. In-depth analysis has been devoted to the seemingly simplest array system: a one-dimensionally periodic lattice of two-dimensional scatterers embedded in a dispersionless medium governed by the Helmholtz equation. We investigate such a system and experimentally confirm the existence of a new class of generalised Rayleigh--Bloch waves that have been recently theorised to exist in classical wave regimes, without the need for resonant scatterers. Airborne acoustics serves as such a regime and here we experimentally observe the first generalised Rayleigh--Bloch waves above the first cut-off, i.e., in the radiative regime. We consider radiative acoustic lattice resonances along a diffraction grating and connect them to generalised Rayleigh--Bloch waves by considering both short and long arrays of non-resonant 2D cylindrical Neumann scatterers embedded in air. On short arrays, we observe finite lattice resonances under continuous wave excitation, and on long arrays, we observe propagating Rayleigh--Bloch waves under pulsed excitation. We interpret their existence by considering multiple wave scattering theory and, in doing so, unify differing nomenclatures used to describe waves on infinite periodic and finite arrays and the interpretation of their dispersive properties.

physics.class-ph↗