Finite-depth effects on solitary waves in a floating ice sheet
Finite-depth effects on solitary waves in a floating ice sheet
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DOI：
10.1016/j.jfluidstructs.2014.04.015
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发表时间：
2014-08-01
影响因子：
3.6
通讯作者：
Parau, Emilian I.
中科院分区：
文献类型：
--
作者：
Guyenne, Philippe;Parau, Emilian I.
本文对二维非线性弯曲重力波在薄冰层覆盖下有限深理想流体表面传播的问题进行了理论和数值研究。冰盖模型是基于特殊的Cosserat理论的超弹性壳满足基尔霍夫的假设，它产生一个保守的和非线性的表达式的弯曲力。从控制方程的Hamilton变换出发，推导出两个弱非线性波动模型：长波区的五阶Korteweg-de弗里斯方程和调制区的三次非线性薛定谔方程。分析了这些模型的孤立波解及其稳定性。特别地，存在一个临界深度，低于该临界深度，非线性薛定谔方程是聚焦型的，从而允许稳定的孤子解。这些弱非线性的结果进行了验证与直接数值模拟的完整的控制方程。数值模拟结果表明，低压的小振幅到大振幅孤立波是稳定的。低波速和足够大的深度也发现了倾覆波的抑郁症。然而，孤立波的海拔似乎是不稳定的，在所有情况下。(C)2014作者由Elsevier Ltd.发布。这是CC BY许可下的开放获取文章（http：//creativecommons.org/licenses/by/3.0/）。
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 Schrodinger 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 Schrodinger 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. (C) 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/).