Controlling dispersive hydrodynamic wavebreaking in a viscous fluid conduit
Controlling dispersive hydrodynamic wavebreaking in a viscous fluid conduit
复制标题
DOI：
10.1103/physrevfluids.4.074804
复制
发表时间：
2018-12
影响因子：
2.7
通讯作者：
Dalton V. Anderson;M. Maiden;M. Hoefer
中科院分区：
文献类型：
--
作者：
Dalton V. Anderson;M. Maiden;M. Hoefer
驱动，圆柱形，自由界面之间的两个可混溶，斯托克斯流体具有高粘度对比度已被证明表现出色散流体动力学。色散流体动力介质的一个标志性特征是导致色散冲击波的波破碎的色散分辨率。在粘性流体管道系统的背景下，目前的工作介绍了一种简单，实用的方法来精确地控制的位置，时间和空间分布的波破碎的色散流体动力系统，只有边界控制。该方法是基于从所需的破波剖面到边界跟踪无色散特性。除了生成近似阶梯状的黎曼和盒问题，该方法被推广到其他，近似分段线性色散流体动力学剖面，包括三角波和N波。色散流体动力破波的定义是用来获得预测的位置和时间之间的定量协议的破波，粘性流体管道实验，并直接数值模拟的范围内的流动条件。观察到的时空特征也同意三角形和N波的预测。这里介绍的特征边界控制方法，使实验研究的各种破波剖面，并预计将在其他色散流体动力学介质中是有用的。作为这种方法的一个应用，从一个大的，盒状扰动的孤子裂变观察实验和数值，激励未来的分析处理。
The driven, cylindrical, free interface between two miscible, Stokes fluids with high viscosity contrast have been shown to exhibit dispersive hydrodynamics. A hallmark feature of dispersive hydrodynamic media is the dispersive resolution of wavebreaking that results in a dispersive shock wave. In the context of the viscous fluid conduit system, the present work introduces a simple, practical method to precisely control the location, time, and spatial profile of wavebreaking in dispersive hydrodynamic systems with only boundary control. The method is based on tracking the dispersionless characteristics backward from the desired wavebreaking profile to the boundary. In addition to the generation of approximately step-like Riemann and box problems, the method is generalized to other, approximately piecewise-linear dispersive hydrodynamic profiles including the triangle wave and N-wave. A definition of dispersive hydrodynamic wavebreaking is used to obtain quantitative agreement between the predicted location and time of wavebreaking, viscous fluid conduit experiment, and direct numerical simulations for a range of flow conditions. Observed space-time characteristics also agree with triangle and N-wave predictions. The characteristic boundary control method introduced here enables the experimental investigation of a variety of wavebreaking profiles and is expected to be useful in other dispersive hydrodynamic media. As an application of this approach, soliton fission from a large, box-like disturbance is observed both experimentally and numerically, motivating future analytical treatment.