iceFEM: A FreeFem package for wave induced ice-shelf vibrations

Abstract

Vibrations of ice-shelves in response to ocean waves were first investigated by Holdsworth & Glynn (1978) who proposed that resonant vibrations lead to icebergs calving from the shelf front. Since then seismometric measurements on the Ross ice-shelf, the largest Antarctic ice-shelf, confirmed the presence of this ocean wave-induced ice-shelf vibration (Bromirski et al., 2015;Massom et al., 2018). The period of vibration ranged from the long infragravity/tsunami waves to shorter, swell waves. More recently, Brunt et al. (2011) presented the first observational evidence that a Northern Hemisphere tsunami triggered calving on the Sulzberger ice-shelf. Mathematical models based on linear wave theory have been proposed to study these ocean-wave induced ice-shelf vibrations.

Modeling Ocean Wave Transfer to Ross Ice Shelf Flexure

“…Sergienko (2017) and Kalyanaraman et al. (2021) incorporated measured ice shelf and seabed geometries from Bedmap2 (Fretwell et al., 2013). Kalyanaraman et al.…”

“…Models have reached the sophistication of incorporating idealized geometrical variations, such as seabed undulations and shoaling (Ilyas et al, 2018;Meylan et al, 2021;Papathanasiou et al, 2019), and ice thickening away from the shelf front (Kalyanaraman et al, 2020;Meylan et al, 2021;Papathanasiou et al, 2015). Sergienko (2017) and Kalyanaraman et al (2021) incorporated measured ice shelf and seabed geometries from Bedmap2 (Fretwell et al, 2013). Kalyanaraman et al (2021)'s model is two-dimensional and the solution method is restricted to shelves up to tens of kilometers long.…”

“…Sergienko (2017) and Kalyanaraman et al (2021) incorporated measured ice shelf and seabed geometries from Bedmap2 (Fretwell et al, 2013). Kalyanaraman et al (2021)'s model is two-dimensional and the solution method is restricted to shelves up to tens of kilometers long. Sergienko (2017)'s model is three-dimensional, solved numerically using a commercial software that limited her study to only two frequencies, and applies wave forcing via a simplified boundary condition at the interface between the open ocean and sub-shelf water cavity, so that ocean wave to shelf transfer is not modeled.…”

A thin-plate approximation for ocean wave interactions with an ice shelf

“…The studies could be based on numerical solutions, for which the software presented by Kalyanaraman et al. (2021) is available if the present model is modified to a finite length shelf and the gravitational acceleration in the shelf is removed. Alternatively, similarly to the approach proposed above to extend the single-mode approximation in water, the thin-plate ansatzes (4.1) could be extended with additional terms to improve accuracy.…”