Two-dimensional flexural-gravity waves of finite amplitude in deep water
Steady periodic and solitary waves propagating in a 2D fluid bounded above by a flexible sheet—which may be viewed as modelling an ice sheet—are considered in deep water. The non-linear elastic model is based on the special Cosserat theory of hyperelastic shells proposed by Toland (2008, Steady peri...
Main Authors: | , , |
---|---|
Format: | Article in Journal/Newspaper |
Language: | English |
Published: |
2013
|
Subjects: | |
Online Access: | https://discovery.ucl.ac.uk/id/eprint/1396965/1/Vanden-Broeck_PerOverturnFGWangVdBM.pdf https://discovery.ucl.ac.uk/id/eprint/1396965/ |
id |
ftucl:oai:eprints.ucl.ac.uk.OAI2:1396965 |
---|---|
record_format |
openpolar |
spelling |
ftucl:oai:eprints.ucl.ac.uk.OAI2:1396965 2023-12-24T10:17:37+01:00 Two-dimensional flexural-gravity waves of finite amplitude in deep water Wang, Z Vanden-Broeck, J-M Milewski, PA 2013-08 text https://discovery.ucl.ac.uk/id/eprint/1396965/1/Vanden-Broeck_PerOverturnFGWangVdBM.pdf https://discovery.ucl.ac.uk/id/eprint/1396965/ eng eng https://discovery.ucl.ac.uk/id/eprint/1396965/1/Vanden-Broeck_PerOverturnFGWangVdBM.pdf https://discovery.ucl.ac.uk/id/eprint/1396965/ open IMA Journal of Applied Mathematics , 78 (4) pp. 750-761. (2013) flexural–gravity elevation branch overhanging waves Article 2013 ftucl 2023-11-27T13:07:32Z Steady periodic and solitary waves propagating in a 2D fluid bounded above by a flexible sheet—which may be viewed as modelling an ice sheet—are considered in deep water. The non-linear elastic model is based on the special Cosserat theory of hyperelastic shells proposed by Toland (2008, Steady periodic hydroelastic waves. Arch. Ration. Mech. Anal., 189, 325–362) for this problem. Numerical solutions are computed via conformal mapping and a pseudo-spectral method. New solitary waves are found by using a continuation method to follow the branch of elevation waves. The results extend Guyenne and Părău's findings (2012, Computations of fully non-linear hydroelastic solitary wave on deep water. J. Fluid Mech., 713, 307–329). It is shown that, for periodic waves, far along the branches the profiles become overhanging and ultimately approach configurations with a trapped bubble at their troughs. Article in Journal/Newspaper Ice Sheet University College London: UCL Discovery |
institution |
Open Polar |
collection |
University College London: UCL Discovery |
op_collection_id |
ftucl |
language |
English |
topic |
flexural–gravity elevation branch overhanging waves |
spellingShingle |
flexural–gravity elevation branch overhanging waves Wang, Z Vanden-Broeck, J-M Milewski, PA Two-dimensional flexural-gravity waves of finite amplitude in deep water |
topic_facet |
flexural–gravity elevation branch overhanging waves |
description |
Steady periodic and solitary waves propagating in a 2D fluid bounded above by a flexible sheet—which may be viewed as modelling an ice sheet—are considered in deep water. The non-linear elastic model is based on the special Cosserat theory of hyperelastic shells proposed by Toland (2008, Steady periodic hydroelastic waves. Arch. Ration. Mech. Anal., 189, 325–362) for this problem. Numerical solutions are computed via conformal mapping and a pseudo-spectral method. New solitary waves are found by using a continuation method to follow the branch of elevation waves. The results extend Guyenne and Părău's findings (2012, Computations of fully non-linear hydroelastic solitary wave on deep water. J. Fluid Mech., 713, 307–329). It is shown that, for periodic waves, far along the branches the profiles become overhanging and ultimately approach configurations with a trapped bubble at their troughs. |
format |
Article in Journal/Newspaper |
author |
Wang, Z Vanden-Broeck, J-M Milewski, PA |
author_facet |
Wang, Z Vanden-Broeck, J-M Milewski, PA |
author_sort |
Wang, Z |
title |
Two-dimensional flexural-gravity waves of finite amplitude in deep water |
title_short |
Two-dimensional flexural-gravity waves of finite amplitude in deep water |
title_full |
Two-dimensional flexural-gravity waves of finite amplitude in deep water |
title_fullStr |
Two-dimensional flexural-gravity waves of finite amplitude in deep water |
title_full_unstemmed |
Two-dimensional flexural-gravity waves of finite amplitude in deep water |
title_sort |
two-dimensional flexural-gravity waves of finite amplitude in deep water |
publishDate |
2013 |
url |
https://discovery.ucl.ac.uk/id/eprint/1396965/1/Vanden-Broeck_PerOverturnFGWangVdBM.pdf https://discovery.ucl.ac.uk/id/eprint/1396965/ |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_source |
IMA Journal of Applied Mathematics , 78 (4) pp. 750-761. (2013) |
op_relation |
https://discovery.ucl.ac.uk/id/eprint/1396965/1/Vanden-Broeck_PerOverturnFGWangVdBM.pdf https://discovery.ucl.ac.uk/id/eprint/1396965/ |
op_rights |
open |
_version_ |
1786205862092603392 |