Solitary wave fission of a large disturbance in a viscous fluid conduit
Solitary wave fission of a large disturbance in a viscous fluid conduit
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DOI：
10.1017/jfm.2019.830
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发表时间：
2019-04
影响因子：
3.7
通讯作者：
M. Maiden;N. Franco;E. Webb;G. El;M. Hoefer
中科院分区：
文献类型：
--
作者：
M. Maiden;N. Franco;E. Webb;G. El;M. Hoefer
本文提出了一个长期存在的流体力学问题的理论和实验研究，涉及到一个大的局部初始扰动的时间分辨率到一个序列的孤立波。这个问题在一系列应用中具有根本的重要性，包括海啸和内部海浪建模。这项研究是在粘性流体管道系统的背景下进行的-驱动，圆柱形，两个可混溶的Stokes流体之间的自由界面，具有高粘度对比度。由于浮力引起的非线性自陡与应力引起的界面色散相平衡，扰动演化为缓慢调制的波列，并进一步演化为孤立波序列。本文将Whitham调制理论推广到孤立波分解，将初始扰动分解为孤立波。所开发的理论预测的初始扰动的配置文件，涌现孤立波的数量和它们的振幅分布之间的关系，量化的扩展著名的孤子分辨率猜想从可积系统到非可积系统，往往提供一个更准确的物理系统建模。流体管道系统的理论预测证实了数值和实验。观测到的孤立波的数量始终在预测的一到两个波之内，振幅分布显示出显着的一致性。孤立波裂变在其他流体动力学问题的普遍性质。
This paper presents a theoretical and experimental study of the long-standing fluid mechanics problem involving the temporal resolution of a large localised initial disturbance into a sequence of solitary waves. This problem is of fundamental importance in a range of applications, including tsunami and internal ocean wave modelling. This study is performed in the context of the viscous fluid conduit system – the driven, cylindrical, free interface between two miscible Stokes fluids with high viscosity contrast. Owing to buoyancy-induced nonlinear self-steepening balanced by stress-induced interfacial dispersion, the disturbance evolves into a slowly modulated wavetrain and further into a sequence of solitary waves. An extension of Whitham modulation theory, termed the solitary wave resolution method, is used to resolve the fission of an initial disturbance into solitary waves. The developed theory predicts the relationship between the initial disturbance’s profile, the number of emergent solitary waves and their amplitude distribution, quantifying an extension of the well-known soliton resolution conjecture from integrable systems to non-integrable systems that often provide a more accurate modelling of physical systems. The theoretical predictions for the fluid conduit system are confirmed both numerically and experimentally. The number of observed solitary waves is consistently within one to two waves of the prediction, and the amplitude distribution shows remarkable agreement. Universal properties of solitary wave fission in other fluid dynamics problems are identified.