Generation of three-dimensional patterns through wave interaction in a model of free surface swirling flow
Generation of three-dimensional patterns through wave interaction in a model of free surface swirling flow
复制标题
在自由表面旋流模型中通过波相互作用生成三维图案
DOI：
10.1088/0169-5983/46/6/061415
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发表时间：
2014
影响因子：
1.5
通讯作者：
Jérôme Mougel
中科院分区：
文献类型：
--
作者：
David Fabre;Jérôme Mougel
众所周知，在旋转底部上方的圆柱形储罐内的自由表面流动支持壮观的三维模式，包括内部自由表面变形为旋转多边形形状和上部自由表面的晃动行为（例如Iga等人2014 Fluid Dyn. Res. 46 031409）。通过对这种流动的简化模型的稳定性分析，我们表明这种模式可以解释为涉及不同波族的共振机制。该方法扩展了之前的工作（Tophøj et al . 2013 Phys）。Rev. Lett. 110 194502)，在假定基流可以模拟为势涡的情况下，将旋转多边形解释为重力波和离心波之间的相互作用。我们表明，先前的模型适用于强旋转速率（干势情况），对于较弱的旋转，可以通过在固体旋转中引入一个内部涡核来改进，该涡核可以延伸到板块中心（湿情况）或围绕一个干燥的中心区域（干复合情况）。该改进模型的研究预测了两种新的不稳定性。第一种发生在低旋转（湿情况），由重力波和开尔文-基尔霍夫波（即涡旋核心边界的振荡）之间的相互作用造成。这种不稳定性被认为是晃动现象的根源。第二种新的不稳定性发生在中等旋转（干复合情况）中，作为重力波和“开尔文-离心”波之间的相互作用，其特征是内表面和涡旋核心边界在相反方向上的变形。这种不稳定性存在于从m = 1开始的所有方位波数中，这种情况对应于“单偶子”模式。
The free surface flow in a cylindrical tank over a rotating bottom is known to support spectacular three-dimensional patterns, including deformation of the inner free surface into the shape of rotating polygons and sloshing behavior of the upper free surface (e.g. Iga et al 2014 Fluid Dyn. Res. 46 031409). Through a stability analysis of a simplified model of this flow, we show that such patterns can be explained as a resonance mechanism involving different families of waves. The approach extends a previous work (Tophøj et al 2013 Phys. Rev. Lett. 110 194502) which explained the rotating polygons as an interaction between gravity waves and centrifugal waves, under the assumption that the base flow can be modeled as a potential vortex. We show that this previous model is justified for strong rotation rates (Dry-Potential case), and that for weaker rotations it can be improved by introducing an inner vortex core in solid-body rotation, which either extends to the center of the plate (Wet case) or surrounds a dry central region (Dry-Composite case). The study of this improved model predicts two new kinds of instabilities. The first occurs at low rotations (Wet case) and results from an interaction between gravity waves and the Kelvin–Kirchhoff wave (namely, oscillation of the boundary of the vortex core). This instability is proposed to be at the origin of the sloshing phenomenon. The second new instability occurs, for moderate rotations, (Dry-Composite case) as an interaction between gravity waves and a ‘Kelvin-Centrifugal’ wave characterized by deformation of the inner surface and the vortex core boundary in opposite directions. This instability exists for all azimuthal wave numbers starting from m = 1, this case corresponding to a ‘monogon’ pattern.
影响因子：
4.6
作者：
Toshiyuki Suzuki;M. Iima;Y. Hayase
通讯作者：
Toshiyuki Suzuki;M. Iima;Y. Hayase