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...
| Published in: | IMA Journal of Applied Mathematics |
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| Main Authors: | , , |
| Format: | Article in Journal/Newspaper |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://researchportal.bath.ac.uk/en/publications/bac62fa2-c0a1-46ce-a968-b29bff7b5b6d https://doi.org/10.1093/imamat/hxt020 https://purehost.bath.ac.uk/ws/files/17659850/PerOverturnFGWangVdBM.pdf http://www.scopus.com/inward/record.url?scp=84880519771&partnerID=8YFLogxK |
| Summary: | 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 Pǎrǎu'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. |
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