Finite depth effects on solitary waves in a floating ice sheet
A theoretical and numerical study of two-dimensional nonlinear flexural-gravity waves propagating at the surface of an ideal fluid of finite depth, covered by a thin ice sheet, is presented. The ice-sheet model is based on the special Cosserat theory of hyperelastic shells satisfying Kirchhoff׳s hyp...
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ftuniveastangl:oai:ueaeprints.uea.ac.uk:48544 2023-05-15T16:40:15+02:00 Finite depth effects on solitary waves in a floating ice sheet Guyenne, P Parau, Emilian 2014-08 application/pdf https://ueaeprints.uea.ac.uk/id/eprint/48544/ https://ueaeprints.uea.ac.uk/id/eprint/48544/1/Guyenne_Parau_2014.pdf https://doi.org/10.1016/j.jfluidstructs.2014.04.015 en eng https://ueaeprints.uea.ac.uk/id/eprint/48544/1/Guyenne_Parau_2014.pdf Guyenne, P and Parau, Emilian (2014) Finite depth effects on solitary waves in a floating ice sheet. Journal of Fluids and Structures, 49. 242–262. ISSN 0889-9746 doi:10.1016/j.jfluidstructs.2014.04.015 Article PeerReviewed 2014 ftuniveastangl https://doi.org/10.1016/j.jfluidstructs.2014.04.015 2023-01-30T21:38:27Z A theoretical and numerical study of two-dimensional nonlinear flexural-gravity waves propagating at the surface of an ideal fluid of finite depth, covered by a thin ice sheet, is presented. The ice-sheet model is based on the special Cosserat theory of hyperelastic shells satisfying Kirchhoff׳s hypothesis, which yields a conservative and nonlinear expression for the bending force. From a Hamiltonian reformulation of the governing equations, two weakly nonlinear wave models are derived: a 5th-order Korteweg–de Vries equation in the long-wave regime and a cubic nonlinear Schrödinger equation in the modulational regime. Solitary wave solutions of these models and their stability are analysed. In particular, there is a critical depth below which the nonlinear Schrödinger equation is of focusing type and thus admits stable soliton solutions. These weakly nonlinear results are validated by comparison with direct numerical simulations of the full governing equations. It is observed numerically that small- to large-amplitude solitary waves of depression are stable. Overturning waves of depression are also found for low wave speeds and sufficiently large depth. However, solitary waves of elevation seem to be unstable in all cases. Article in Journal/Newspaper Ice Sheet University of East Anglia: UEA Digital Repository Journal of Fluids and Structures 49 242 262 |
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Open Polar |
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University of East Anglia: UEA Digital Repository |
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ftuniveastangl |
language |
English |
description |
A theoretical and numerical study of two-dimensional nonlinear flexural-gravity waves propagating at the surface of an ideal fluid of finite depth, covered by a thin ice sheet, is presented. The ice-sheet model is based on the special Cosserat theory of hyperelastic shells satisfying Kirchhoff׳s hypothesis, which yields a conservative and nonlinear expression for the bending force. From a Hamiltonian reformulation of the governing equations, two weakly nonlinear wave models are derived: a 5th-order Korteweg–de Vries equation in the long-wave regime and a cubic nonlinear Schrödinger equation in the modulational regime. Solitary wave solutions of these models and their stability are analysed. In particular, there is a critical depth below which the nonlinear Schrödinger equation is of focusing type and thus admits stable soliton solutions. These weakly nonlinear results are validated by comparison with direct numerical simulations of the full governing equations. It is observed numerically that small- to large-amplitude solitary waves of depression are stable. Overturning waves of depression are also found for low wave speeds and sufficiently large depth. However, solitary waves of elevation seem to be unstable in all cases. |
format |
Article in Journal/Newspaper |
author |
Guyenne, P Parau, Emilian |
spellingShingle |
Guyenne, P Parau, Emilian Finite depth effects on solitary waves in a floating ice sheet |
author_facet |
Guyenne, P Parau, Emilian |
author_sort |
Guyenne, P |
title |
Finite depth effects on solitary waves in a floating ice sheet |
title_short |
Finite depth effects on solitary waves in a floating ice sheet |
title_full |
Finite depth effects on solitary waves in a floating ice sheet |
title_fullStr |
Finite depth effects on solitary waves in a floating ice sheet |
title_full_unstemmed |
Finite depth effects on solitary waves in a floating ice sheet |
title_sort |
finite depth effects on solitary waves in a floating ice sheet |
publishDate |
2014 |
url |
https://ueaeprints.uea.ac.uk/id/eprint/48544/ https://ueaeprints.uea.ac.uk/id/eprint/48544/1/Guyenne_Parau_2014.pdf https://doi.org/10.1016/j.jfluidstructs.2014.04.015 |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_relation |
https://ueaeprints.uea.ac.uk/id/eprint/48544/1/Guyenne_Parau_2014.pdf Guyenne, P and Parau, Emilian (2014) Finite depth effects on solitary waves in a floating ice sheet. Journal of Fluids and Structures, 49. 242–262. ISSN 0889-9746 doi:10.1016/j.jfluidstructs.2014.04.015 |
op_doi |
https://doi.org/10.1016/j.jfluidstructs.2014.04.015 |
container_title |
Journal of Fluids and Structures |
container_volume |
49 |
container_start_page |
242 |
op_container_end_page |
262 |
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1766030629415157760 |