# Wave scattering at the sea-ice/ice-shelf transition with other applications

TDC Williams, VA Squire

Research output: Contribution to journalArticle (Academic Journal)peer-review

18 Citations (Scopus)

## Abstract

We present a mathematical model that describes how ice-coupled (flexural-gravity) waves traveling beneath a uniform, floating sea-ice sheet, defined over $(-\infty,0)$, propagate into a second ice sheet $(l,\infty)$ of different thickness by way of an arbitrarily defined transition region of finite width $(0,l)$. Each ice sheet is represented as an Eulerâ€“Bernoulli thin plate with a prescribed thickness and material properties, either or both of which vary across the transition. The most familiar application of this geometry is to sea-ice abutting an ice-shelfâ€”a common occurrence found in the waters around Antarctica and parts of the Arctic or to sea-ice skirting sikussakâ€”the band of extremely thick coastal fast ice that can form when local ice is sheltered from destructive storms. Another application is to breakwaters, and this is also discussed. By using Green's theorem two coupled integral equations are derived: one defined over $(0,l)$ and the second of the Wienerâ€“Hopf type, defined over $(l,\infty)$. The latter is solved analytically, allowing the integral equations to be decoupled and the first equation to be solved numerically. Results are presented for the geophysical and engineering examples referred to above.
Translated title of the contribution Wave scattering at the sea-ice/ice-shelf transition with other applications English 938 - 959 22 SIAM Journal on Applied Mathematics 67 (4) https://doi.org/10.1137/060659351 Published - Jul 2007

### Bibliographical note

Publisher: SIAM Society for Industrial and Applied Mathematics

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