尹梦迪++林伟华

[摘 要]观察一在水中半浸没的竖直振动水平圆柱周围的水波，圆柱的振动频率对其周围水波流向有明显影响。在低频率时，平面波自振子向周围推进；增加频率，交叉波逐渐取代平面波，在振子周围形成不稳定流场；继续增加频率，振子周围形成拉格朗日相干结构，并满足Lighthill判据，继而发生水波逆向流动现象。实验通过改变振动频率、幅度及振子材质观察水波流动现象，来探究水波逆向流动的因素，并尝试用流形解释这一现象。通过振动驱动水波流向改变，这一非线性动力学现象，可在日后的水运中得到应用，达到节能、高效生产的目的。

[关键词]竖直振动，表面水波流向， 拉格朗日相干结构，Lighthill判据，流形

The study of the effect of oscillation frequency of vertical oscillator on the flow direction of surface water wave

YIN Mengdi， LIN Weihua

（School of Physics and Technology， National Demonstration Center for Experimental Physics Education（Wuhan University）， Wuhan University， Hubei， Wuhan 430072， China）

[Abstract]Observing the surface water wave generated by a half-submerged vertically oscillating cylinder， the frequency of oscillation would have great influence on the propagating direction of the flow. When the cylinder is vibrating with a low frequency， the waves are observed escaping from the cylinder as plane waves. As the frequency is increased， cross-waves appear and the field around the object becomes unstable. When the frequency is high enough， Lagrangian Coherent Structures is formed around the cylinder and Lighthill criterion is satisfied， as well as the propagating direction of waves reversed. The influence effectors of the reversed flow are experimentally studied by changing the oscillating frequency and amplitude of the oscillators， as well as the materials. Whats more， the effectors could be explained using manifold. The method of changing the propagating direction of water flow by oscillations， a nonlinear dynamic phenomenon， could be applied in water carriage in the future with more energy conservation and higher efficiency.

[Key words]vertical oscillation，flow direction of surface water wave， Lagrangian Coherent Structures， Lighthill criterion， manifold

中图分类号：TU763 文献标识码：A 文章编号：1009-914X（2017）42-0261-03

0 引言

在很长一段时间里，由于水波现象对水运水利工程生产中的方方面面有着显著影响，人们对水波现象进行了不断的研究，并取得了显著成果。而通过技术手段产生能将远处物体运输到近处的水波更拥有广泛的应用前景，例如帮助人们更好地理解海洋中船舶的运动，从而指导人们进行技术改革，发明出更加节能有效的水运工具。

一个半浸没在水中的圆柱竖直振动时，振子周围会产生水波。在之前的研究已经表明圆柱振幅[1]、容器壁对水流的反射作用以及振子形状对水波和流场具有显著影响[2]，同时发现有限振幅水波的调制不稳定性和交叉波的产生是导致水波流向转变为朝向振子流动的主要因素之一[2]。……