Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves
Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves
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DOI：
10.1017/jfm.2019.534
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发表时间：
2018-12
影响因子：
3.7
通讯作者：
T. Congy;G. El;M. Hoefer
中科院分区：
文献类型：
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作者：
T. Congy;G. El;M. Hoefer
一种新型的波平均流相互作用的识别和研究，其中一个小振幅，线性，色散调制波传播通过一个不断发展的，非线性的，大规模的流体状态，如膨胀（稀疏）波或色散冲击波（波状孔）。Korteweg-de弗里斯（KdV）方程被认为是一个典型的例子，动态波包平均流相互作用。推导了线性波调制与非线性平均流耦合的调制方程。这些方程承认一个特殊的解决方案，描述传输或捕获的线性波包的非定常流体动力学状态。确定了运动的两个绝热不变量，其确定了传输、捕获条件，并表明入射到平滑膨胀波或压缩、快速振荡的分散冲击波上的波包表现出最近在Maiden等人（Phys. Rev. Lett.，Vol.120，2018，144101）在流体动力学孤子隧穿的背景下。调制理论的结果是在良好的协议与直接数值模拟的完整KdV动力学。由于没有引入KdV方程的可积性，因此这些结果可以推广到其他非线性色散流体力学模型。
A new type of wave–mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a dispersive shock wave (undular bore). The Korteweg–de Vries (KdV) equation is considered as a prototypical example of dynamic wavepacket–mean flow interaction. Modulation equations are derived for the coupling between linear wave modulations and a nonlinear mean flow. These equations admit a particular class of solutions that describe the transmission or trapping of a linear wavepacket by an unsteady hydrodynamic state. Two adiabatic invariants of motion are identified that determine the transmission, trapping conditions and show that wavepackets incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves exhibit so-called hydrodynamic reciprocity recently described in Maiden et al. (Phys. Rev. Lett., vol. 120, 2018, 144101) in the context of hydrodynamic soliton tunnelling. The modulation theory results are in excellent agreement with direct numerical simulations of full KdV dynamics. The integrability of the KdV equation is not invoked so these results can be extended to other nonlinear dispersive fluid mechanic models.