Linear wave forcing of an array of axisymmetric ice floes
Under linear and time-harmonic conditions, a set of periodic Green's functions is derived to combine the interactions of an infinite number of identical equispaced floating bodies. The bodies themselves are compliant thin elastic plates that can represent ice floes, and unlike previous studies,...
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Online Access: | http://hdl.handle.net/2440/75458 https://doi.org/10.1093/imamat/hxp038 |
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ftunivadelaidedl:oai:digital.library.adelaide.edu.au:2440/75458 2023-12-24T10:24:46+01:00 Linear wave forcing of an array of axisymmetric ice floes Bennetts, L. Squire, V. 2010 http://hdl.handle.net/2440/75458 https://doi.org/10.1093/imamat/hxp038 en eng Oxford Univ Press IMA Journal of Applied Mathematics, 2010; 75(1):108-138 0272-4960 1464-3634 http://hdl.handle.net/2440/75458 doi:10.1093/imamat/hxp038 Bennetts, L. [0000-0001-9386-7882] © The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. http://dx.doi.org/10.1093/imamat/hxp038 Green's function periodic array sea ice flexural-gravity waves scattering Journal article 2010 ftunivadelaidedl https://doi.org/10.1093/imamat/hxp038 2023-11-27T23:19:13Z Under linear and time-harmonic conditions, a set of periodic Green's functions is derived to combine the interactions of an infinite number of identical equispaced floating bodies. The bodies themselves are compliant thin elastic plates that can represent ice floes, and unlike previous studies, they are permitted to vary axisymmetrically in thickness through both their upper and their lower surfaces, with a realistic draught also admitted. Initially, the governing equations are simplified by means of an expansion of the vertical dependence of the unknown velocity potential combined with a variational principle, which reduces calculations to the horizontal plane alone. The unknowns of the resulting equations are written as an integral representation in the free-surface domain and as a Fourier expansion in the domain of the ice-covered fluid, and these are matched at their common boundary to complete the solution process. Our method is validated using numerical results for example problems. The effects of varying the distance between the floes, as well as the introduction of thickness variations and submergence, are also demonstrated. Luke G. Bennetts and Vernon A. Squire Article in Journal/Newspaper Sea ice The University of Adelaide: Digital Library Luke ENVELOPE(-94.855,-94.855,56.296,56.296) IMA Journal of Applied Mathematics 75 1 108 138 |
institution |
Open Polar |
collection |
The University of Adelaide: Digital Library |
op_collection_id |
ftunivadelaidedl |
language |
English |
topic |
Green's function periodic array sea ice flexural-gravity waves scattering |
spellingShingle |
Green's function periodic array sea ice flexural-gravity waves scattering Bennetts, L. Squire, V. Linear wave forcing of an array of axisymmetric ice floes |
topic_facet |
Green's function periodic array sea ice flexural-gravity waves scattering |
description |
Under linear and time-harmonic conditions, a set of periodic Green's functions is derived to combine the interactions of an infinite number of identical equispaced floating bodies. The bodies themselves are compliant thin elastic plates that can represent ice floes, and unlike previous studies, they are permitted to vary axisymmetrically in thickness through both their upper and their lower surfaces, with a realistic draught also admitted. Initially, the governing equations are simplified by means of an expansion of the vertical dependence of the unknown velocity potential combined with a variational principle, which reduces calculations to the horizontal plane alone. The unknowns of the resulting equations are written as an integral representation in the free-surface domain and as a Fourier expansion in the domain of the ice-covered fluid, and these are matched at their common boundary to complete the solution process. Our method is validated using numerical results for example problems. The effects of varying the distance between the floes, as well as the introduction of thickness variations and submergence, are also demonstrated. Luke G. Bennetts and Vernon A. Squire |
format |
Article in Journal/Newspaper |
author |
Bennetts, L. Squire, V. |
author_facet |
Bennetts, L. Squire, V. |
author_sort |
Bennetts, L. |
title |
Linear wave forcing of an array of axisymmetric ice floes |
title_short |
Linear wave forcing of an array of axisymmetric ice floes |
title_full |
Linear wave forcing of an array of axisymmetric ice floes |
title_fullStr |
Linear wave forcing of an array of axisymmetric ice floes |
title_full_unstemmed |
Linear wave forcing of an array of axisymmetric ice floes |
title_sort |
linear wave forcing of an array of axisymmetric ice floes |
publisher |
Oxford Univ Press |
publishDate |
2010 |
url |
http://hdl.handle.net/2440/75458 https://doi.org/10.1093/imamat/hxp038 |
long_lat |
ENVELOPE(-94.855,-94.855,56.296,56.296) |
geographic |
Luke |
geographic_facet |
Luke |
genre |
Sea ice |
genre_facet |
Sea ice |
op_source |
http://dx.doi.org/10.1093/imamat/hxp038 |
op_relation |
IMA Journal of Applied Mathematics, 2010; 75(1):108-138 0272-4960 1464-3634 http://hdl.handle.net/2440/75458 doi:10.1093/imamat/hxp038 Bennetts, L. [0000-0001-9386-7882] |
op_rights |
© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. |
op_doi |
https://doi.org/10.1093/imamat/hxp038 |
container_title |
IMA Journal of Applied Mathematics |
container_volume |
75 |
container_issue |
1 |
container_start_page |
108 |
op_container_end_page |
138 |
_version_ |
1786199888171630592 |