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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.
|Number of pages||12|
|Journal||IMA Journal of Applied Mathematics|
|Early online date||1 May 2013|
|Publication status||Published - Aug 2013|
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- 1 Finished
Nonlinear Hydroelastic Waves with Applications to Ice Sheets
Engineering and Physical Sciences Research Council
12/11/12 → 11/11/15
Project: Research council