Scattering of flexural-gravity waves by a crack in a floating ice sheet due to mode conversion during blocking
The scattering of flexural-gravity waves in a thin floating plate is investigated in the presence of compression. In this case, wave blocking occurs, which is associated with both a zero in the group velocity and coalition of two or more roots of the related dispersion relation. There exists a regio...
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ftunivnewcastnsw:uon:41905 2023-05-15T16:41:12+02:00 Scattering of flexural-gravity waves by a crack in a floating ice sheet due to mode conversion during blocking Barman, S. C. Das, S. Sahoo, T. Meylan, M. H. 2021 http://hdl.handle.net/1959.13/1443163 eng eng Cambridge University Press Journal of Fluid Mechanics Vol. 916, Issue 10 June 2021 , no. A11 10.1017/jfm.2021.200 http://hdl.handle.net/1959.13/1443163 uon:41905 ISSN:0022-1120 wave-structure interactions wave scattering ice sheets flexural-gravity waves journal article 2021 ftunivnewcastnsw 2022-08-15T22:24:59Z The scattering of flexural-gravity waves in a thin floating plate is investigated in the presence of compression. In this case, wave blocking occurs, which is associated with both a zero in the group velocity and coalition of two or more roots of the related dispersion relation. There exists a region in the frequency space in which there are three real roots of the dispersion equation and hence three propagating modes. This multiplicity leads to mode conversion when scattering occurs. In one of these modes, the energy propagation direction is opposite to the wavenumber, making enforcement of the Sommerfeld radiation condition challenging. The focus here is on a canonical problem in flexural-gravity wave scattering, the scattering of waves by a crack. Formulae are developed that apply uniformly at all frequencies, including through the blocking frequencies. This solution is developed by tracking the movement of the dispersion relation roots carefully in the complex plane. The mode conversion is verified by the scattering matrix of the process and through an energy identity. This energy identity for the case of more than one progressive modes is established using Green's theorem and later applied in the scattering matrix to identify the incident and transmitted waves in the scattering process and derive the radiation condition. Appropriate scaling of the reflection and transmission coefficients are provided with the energy identity. The solution method is illustrated with numerical examples. Article in Journal/Newspaper Ice Sheet NOVA: The University of Newcastle Research Online (Australia) |
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Open Polar |
collection |
NOVA: The University of Newcastle Research Online (Australia) |
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ftunivnewcastnsw |
language |
English |
topic |
wave-structure interactions wave scattering ice sheets flexural-gravity waves |
spellingShingle |
wave-structure interactions wave scattering ice sheets flexural-gravity waves Barman, S. C. Das, S. Sahoo, T. Meylan, M. H. Scattering of flexural-gravity waves by a crack in a floating ice sheet due to mode conversion during blocking |
topic_facet |
wave-structure interactions wave scattering ice sheets flexural-gravity waves |
description |
The scattering of flexural-gravity waves in a thin floating plate is investigated in the presence of compression. In this case, wave blocking occurs, which is associated with both a zero in the group velocity and coalition of two or more roots of the related dispersion relation. There exists a region in the frequency space in which there are three real roots of the dispersion equation and hence three propagating modes. This multiplicity leads to mode conversion when scattering occurs. In one of these modes, the energy propagation direction is opposite to the wavenumber, making enforcement of the Sommerfeld radiation condition challenging. The focus here is on a canonical problem in flexural-gravity wave scattering, the scattering of waves by a crack. Formulae are developed that apply uniformly at all frequencies, including through the blocking frequencies. This solution is developed by tracking the movement of the dispersion relation roots carefully in the complex plane. The mode conversion is verified by the scattering matrix of the process and through an energy identity. This energy identity for the case of more than one progressive modes is established using Green's theorem and later applied in the scattering matrix to identify the incident and transmitted waves in the scattering process and derive the radiation condition. Appropriate scaling of the reflection and transmission coefficients are provided with the energy identity. The solution method is illustrated with numerical examples. |
format |
Article in Journal/Newspaper |
author |
Barman, S. C. Das, S. Sahoo, T. Meylan, M. H. |
author_facet |
Barman, S. C. Das, S. Sahoo, T. Meylan, M. H. |
author_sort |
Barman, S. C. |
title |
Scattering of flexural-gravity waves by a crack in a floating ice sheet due to mode conversion during blocking |
title_short |
Scattering of flexural-gravity waves by a crack in a floating ice sheet due to mode conversion during blocking |
title_full |
Scattering of flexural-gravity waves by a crack in a floating ice sheet due to mode conversion during blocking |
title_fullStr |
Scattering of flexural-gravity waves by a crack in a floating ice sheet due to mode conversion during blocking |
title_full_unstemmed |
Scattering of flexural-gravity waves by a crack in a floating ice sheet due to mode conversion during blocking |
title_sort |
scattering of flexural-gravity waves by a crack in a floating ice sheet due to mode conversion during blocking |
publisher |
Cambridge University Press |
publishDate |
2021 |
url |
http://hdl.handle.net/1959.13/1443163 |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_relation |
Journal of Fluid Mechanics Vol. 916, Issue 10 June 2021 , no. A11 10.1017/jfm.2021.200 http://hdl.handle.net/1959.13/1443163 uon:41905 ISSN:0022-1120 |
_version_ |
1766031632629760000 |