Finite depth effects on solitary waves in a floating ice sheet

Guyenne, P and Parau, Emilian ORCID: https://orcid.org/0000-0001-5134-2068 (2014) Finite depth effects on solitary waves in a floating ice sheet. Journal of Fluids and Structures, 49. 242–262. ISSN 0889-9746

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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.

Item Type:	Article
Additional Information:	© 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/).
Uncontrolled Keywords:	finite depth,flexural-gravity waves,hamiltonian theory,solitary waves,water waves
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Fluid and Solid Mechanics (former - to 2024) Faculty of Science > Research Groups > Fluids & Structures
Depositing User:	Pure Connector
Date Deposited:	09 Jun 2014 13:34
Last Modified:	07 Nov 2024 12:37
URI:	https://ueaeprints.uea.ac.uk/id/eprint/48544
DOI:	10.1016/j.jfluidstructs.2014.04.015

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