Computations of fully nonlinear hydroelastic solitary waves on deep water

Guyenne, Philippe and Parau, Emilian I. ORCID: (2012) Computations of fully nonlinear hydroelastic solitary waves on deep water. Journal of Fluid Mechanics, 713. pp. 307-329. ISSN 0022-1120

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This paper is concerned with the two-dimensional problem of nonlinear gravity waves travelling at the interface between a thin ice sheet and an ideal fluid of infinite depth. 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. A Hamiltonian formulation for this hydroelastic problem is proposed in terms of quantities evaluated at the fluid–ice interface. For small-amplitude waves, a nonlinear Schrödinger equation is derived and its analysis shows that no solitary wavepackets exist in this case. For larger amplitudes, both forced and free steady waves are computed by direct numerical simulations using a boundary-integral method. In the unforced case, solitary waves of depression as well as of elevation are found, including overhanging waves with a bubble-shaped profile for wave speeds c much lower than the minimum phase speed cmin. It is also shown that the energy of depression solitary waves has a minimum at a wave speed cm slightly less than cmin, which suggests that such waves are stable for c < cm. This observation is verified by time-dependent computations using a high-order spectral method. These computations also indicate that solitary waves of elevation are likely to be unstable.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Fluid and Solid Mechanics
Depositing User: Users 2731 not found.
Date Deposited: 29 Jan 2013 14:39
Last Modified: 08 Nov 2022 12:30
DOI: 10.1017/jfm.2012.458

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