Nonlinear travelling periodic waves for the Euler equations in three-layer flows
Nonlinear travelling periodic waves for the Euler equations in three-layer flows
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DOI：
10.1017/jfm.2024.73
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发表时间：
2024-02
影响因子：
3.7
通讯作者：
Xin Guan;A. Doak;P. Milewski;J. Vanden-Broeck
中科院分区：
文献类型：
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作者：
Xin Guan;A. Doak;P. Milewski;J. Vanden-Broeck
本文在刚性盖子假设下，研究了三层系统中的周期行波。用边界积分法对解进行数值恢复。我们考虑两层之间密度差很小的情况(即弱分层流体)。我们考虑了有和没有Boussinesq假设的系统，以探讨该假设对解空间的影响。求出了模式1和模式2的周期解，并详细描述了它们的分叉结构和极限构型。两层结构的情况也有相似之处，在这种情况下，大幅度的解被发现以120美元的内角突出。然而，第二个界面的加入导致了更丰富的分叉空间，部分原因是模2波的存在及其与模1波的共振。发现了新的极限剖面。
Abstract In this paper, we investigate periodic travelling waves in a three-layer system with the rigid-lid assumption. Solutions are recovered numerically using a boundary integral method. We consider the case where the density difference between the layers is small (i.e. a weakly stratified fluid). We consider the system both with and without the Boussinesq assumption to explore the effect the assumption has on the solution space. Periodic solutions of both mode-1 and mode-2 are found, and their bifurcation structure and limiting configurations are described in detail. Similarities are found with the two-layer case, where large-amplitude solutions are found to overhang with an internal angle of $120^{\circ }$. However, the addition of a second interface results in a richer bifurcation space, in part due to the existence of mode-2 waves and their resonance with mode-1 waves. New limiting profiles are found.