Two-dimensional flexural-gravity waves of finite amplitude in deep water

Z. Wang, J.-M. Vanden-Broeck, P. A. Milewski

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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 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.
Original languageEnglish
Pages (from-to)750-761
Number of pages12
JournalIMA Journal of Applied Mathematics
Volume78
Issue number4
Early online date1 May 2013
DOIs
Publication statusPublished - Aug 2013

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Periodic Wave
Gravity Waves
Gravity waves
Elastic waves
Solitary Waves
Solitons
Water
Branch
Fluid
Conformal mapping
Pseudospectral Method
Continuation Method
Fluids
Conformal Mapping
Fully Nonlinear
Arch
Nonlinear Waves
Arches
Bubble
Ice

Cite this

Two-dimensional flexural-gravity waves of finite amplitude in deep water. / Wang, Z.; Vanden-Broeck, J.-M.; Milewski, P. A.

In: IMA Journal of Applied Mathematics, Vol. 78, No. 4, 08.2013, p. 750-761.

Research output: Contribution to journalArticle

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