Evolution of truncated and bent gravity wave solitons: the Mach expansion problem
Evolution of truncated and bent gravity wave solitons: the Mach expansion problem
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DOI：
10.1017/jfm.2020.952
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发表时间：
2020-07
影响因子：
3.7
通讯作者：
Samuel J. Ryskamp;M. Maiden;G. Biondini;M. Hoefer
中科院分区：
文献类型：
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作者：
Samuel J. Ryskamp;M. Maiden;G. Biondini;M. Hoefer
利用调制理论分析了Kadomtsev-Petviashvili （KPII）方程中初始截断线孤子和弯曲线孤子的动力学特性。与以往关于从锐角发展的斜相互作用孤子的研究不同，本工作侧重于两个或三个相互远离传播的部分线孤子的钝角的初值问题。尽管反向传播，显著的残余孤子相互作用被观察到新的物理后果。截断线孤子的初值问题-描述从宽通道出现的准一维孤子-被证明与斜孤子的相互作用有关。用局部孤子振幅和斜率调制方程的相互作用简单波解，得到了弱相互作用和强相互作用发展的解析描述。在弱相互作用情况下，截断和大钝角孤子的长时间演化表现为衰减的抛物波剖面，随着焦距的暂时增加，渐近于圆柱形Korteweg-de Vries孤子。相反，弱钝角相互作用孤子的强相互作用情况演变为稳定的一维线孤子，其振幅与入射斜率成比例地减小。这种强相互作用被认为是具有膨胀角的孤子的“马赫膨胀”，与众所周知的具有压缩角的孤子的马赫反射形成对比。有趣的是，马赫膨胀和反射的临界角是相同的。KPII方程的数值模拟定量地支持了分析结果。
Abstract The dynamics of initially truncated and bent line solitons for the Kadomtsev–Petviashvili (KPII) equation modelling internal and surface gravity waves is analysed using modulation theory. In contrast to previous studies on obliquely interacting solitons that develop from acute incidence angles, this work focuses on initial value problems for the obtuse incidence of two or three partial line solitons, which propagate away from one another. Despite counterpropagation, significant residual soliton interactions are observed with novel physical consequences. The initial value problem for a truncated line soliton – describing the emergence of a quasi-one-dimensional soliton from a wide channel – is shown to be related to the interaction of oblique solitons. Analytical descriptions for the development of weak and strong interactions are obtained in terms of interacting simple wave solutions of modulation equations for the local soliton amplitude and slope. In the weak interaction case, the long-time evolution of truncated and large obtuse angle solitons exhibits a decaying, parabolic wave profile with temporally increasing focal length that asymptotes to a cylindrical Korteweg–de Vries soliton. In contrast, the strong interaction case of slightly obtuse interacting solitons evolves into a steady, one-dimensional line soliton with amplitude reduced by an amount proportional to the incidence slope. This strong interaction is identified with the ‘Mach expansion’ of a soliton with an expansive corner, contrasting with the well-known Mach reflection of a soliton with a compressive corner. Interestingly, the critical angles for Mach expansion and reflection are the same. Numerical simulations of the KPII equation quantitatively support the analytical findings.