Computations of fully nonlinear hydroelastic solitary waves on deep water
Computations of fully nonlinear hydroelastic solitary waves on deep water
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DOI：
10.1017/jfm.2012.458
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发表时间：
2012-12-25
影响因子：
3.7
通讯作者：
Parau, Emilian I.
中科院分区：
文献类型：
--
作者：
Guyenne, Philippe;Parau, Emilian I.
本文研究了非线性重力波在薄冰与无限深度理想流体交界面上传播的二维问题。冰盖模型基于满足Kirchhoff假设的超弹性壳的特殊Cosserat理论，该理论给出了弯曲力的保守的非线性表达式。提出了该水弹性问题的哈密顿公式，以计算流体冰界面处的量。对于小振幅波，导出了一个非线性薛定谔方程，分析表明在这种情况下不存在孤立波包。对于较大的振幅，采用边界积分法直接数值模拟计算了受迫波和自由稳定波。在非强迫情况下，发现了低洼和高程的孤立波，包括波速c远低于最小相速c（min）的泡状剖面的悬垂波。低洼孤立波在波速c -m略小于c（min）时能量最小，说明低洼孤立波在c < c(m)时稳定，在c > c(m)时不稳定。用高阶谱法进行时变计算，验证了这一观测结果。这些计算还表明，孤立的高程波很可能是不稳定的。
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 Schrodinger 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 c(min). It is also shown that the energy of depression solitary waves has a minimum at a wave speed C-m slightly less than c(min), which suggests that such waves are stable for c < c(m) and unstable for C > c(m). 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.