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

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

OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/bac62fa2-c0a1-46ce-a968-b29bff7b5b6d • DOI: https://doi.org/10.1093/imamat/hxt020

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.