Projects per year
Abstract
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.
Original language | English |
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Pages (from-to) | 242–262 |
Number of pages | 21 |
Journal | Journal of Fluids and Structures |
Volume | 49 |
DOIs | |
Publication status | Published - Aug 2014 |
Keywords
- Finite depth
- Flexural-gravity waves
- Hamiltonian theory
- Solitary waves
- Water waves
Profiles
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Emilian Parau
- School of Engineering, Mathematics and Physics - Professor of Applied Mathematics
- Fluids & Structures - Member
Person: Research Group Member, Academic, Teaching & Research
Projects
- 1 Finished
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Nonlinear Hydroelastic Waves with Applications to Ice Sheets (Joint Proposal, Lead - UCL)
Parau, E., Espin, L., Milewski, P., Vanden-Broeck, J. & Guyenne, P.
Engineering and Physical Sciences Research Council
12/11/12 → 11/05/16
Project: Research