Strongly nonlinear effects on internal solitary waves in three-layer flows
Strongly nonlinear effects on internal solitary waves in three-layer flows
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DOI：
10.1017/jfm.2019.795
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发表时间：
2020-01-25
影响因子：
3.7
通讯作者：
Milewski, Paul A.
中科院分区：
文献类型：
--
作者：
Barros, Ricardo;Choi, Wooyoung;Milewski, Paul A.
本文考虑了两刚性边界间三层流中大振幅内波的强非线性长波模型。该模型扩展了两层Miyata- choi - camassa （MCC）模型（Miyata， IUTAM非线性水波研讨会论文集，编辑）。Horikawa & H. Maruo, 1988, pp. 399-406；流体力学。， vol. 396, 1999, pp. 1-36)，并且能够描述第一和第二斜压模态的长内波的传播。该模型的孤立波解被一个具有两个自由度的哈密顿系统所控制。重点讨论了第二斜压模态（模态2）的孤立波及其弱非线性模式不能捕捉到的强非线性特征。在与海洋应用和以前的实验室实验有关的某些渐近限制下，表明具有单驼峰剖面的大振幅模态2波可以用MCC模型的孤立波解来描述，MCC模型最初是为两层系统中的模态1波开发的。但在密度分层较弱、密度过渡层较薄的情况下，两自由度动力系统的丰富性就会显现出来，并可发现以多峰波剖面为特征的大振幅新类型的2型孤立波解。与MCC方程描述的经典孤立波解相反，对于给定层构型的连续波速集，这种多峰解不可能存在。我们基于渐近理论的分析预测随后被原始哈密顿系统的数值研究所证实。
We consider a strongly nonlinear long wave model for large amplitude internal waves in a three-layer flow between two rigid boundaries. The model extends the two-layer Miyata-Choi-Camassa (MCC) model (Miyata, Proceedings of the IUTAM Symposium on Nonlinear Water Waves, eds. H. Horikawa & H. Maruo, 1988, pp. 399-406; Choi & Camassa, J. Fluid Mech., vol. 396, 1999, pp. 1-36) and is able to describe the propagation of long internal waves of both the first and second baroclinic modes. Solitary-wave solutions of the model are shown to be governed by a Hamiltonian system with two degrees of freedom. Emphasis is given to the solitary waves of the second baroclinic mode (mode 2) and their strongly nonlinear characteristics that fail to be captured by weakly nonlinear models. In certain asymptotic limits relevant to oceanic applications and previous laboratory experiments, it is shown that large amplitude mode-2 waves with single-hump profiles can be described by the solitary-wave solutions of the MCC model, originally developed for mode-1 waves in a two-layer system. In other cases, however, e.g. when the density stratification is weak and the density transition layer is thin, the richness of the dynamical system with two degrees of freedom becomes apparent and new classes of mode-2 solitary-wave solutions of large amplitudes, characterized by multi-humped wave profiles, can be found. In contrast with the classical solitary-wave solutions described by the MCC equation, such multi-humped solutions cannot exist for a continuum set of wave speeds for a given layer configuration. Our analytical predictions based on asymptotic theory are then corroborated by a numerical study of the original Hamiltonian system.