Wang, Z;
Vanden-Broeck, J-M;
Milewski, PA;
(2013)
Two-dimensional flexural-gravity waves of finite amplitude in deep water.
IMA Journal of Applied Mathematics
, 78
(4)
pp. 750-761.
10.1093/imamat/hxt020.
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | Two-dimensional flexural-gravity waves of finite amplitude in deep water |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imamat/hxt020 |
| Publisher version: | http://dx.doi.org/10.1093/imamat/hxt020 |
| Language: | English |
| Additional information: | This is a pre-copyedited, author-produced PDF of an article accepted for publication in the IMA Journal of Applied Mathematics following peer review. The version of record, Wang, Z; Vanden-Broeck, J-M; Milewski, PA; (2013) Two-dimensional flexural-gravity waves of finite amplitude in deep water. IMA Journal of Applied Mathematics, 78 (4) pp. 750-761, is available online at: http://dx.doi.org/10.1093/imamat/htx020. |
| Keywords: | flexural–gravity, elevation branch, overhanging waves |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1396965 |
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