纵向受迫圆柱中的超谐波共振旋流波
Super-harmonically resonant swirling waves in longitudinally forced circular cylinders
AI总结：
本研究针对纵向受迫圆柱内的晃荡现象，通过弱非线性分析预测超谐波激励下可发生平面波对称性破缺产生稳定旋流，并经实验验证了三种超谐波状态及其稳定性边界与理论的定量匹配。
摘要：
Faltinsen等人（2016年）研究了圆柱体内的共振晃荡现象，他们的理论被用于描述容器做时间谐波椭圆轨道运动时产生的稳态共振波。在容器纵向运动的极限情形下，平面波解会发生对称性破缺，顺时针和逆时针旋流的出现概率均等。除了这种基波谐波动力学特性外，以往的实验还揭示，在远离基波共振的区域可观测到多种超谐波动力学行为。其中，所谓的双波峰（DC，double-crest）动力学尤其值得关注——它最早由Reclari等人（2014年）在旋转晃荡实验中观测到，其出现最易受外部驱动的空间结构促进。本文沿用Bongarzone等人（2022a）的方法，开展了弱非线性（WNL，weakly nonlinear）分析，以描述系统对超谐波纵向激励的响应。推导得到的幅值方程组预测，平面波的对称性破缺（通过稳定旋流实现）同样可在超谐波激励下发生。这一结论得到了我们实验观测的验证：实验识别出三种可能的超谐波状态，即（i）稳定平面DC波、（ii）不规则运动以及（iii）稳定旋流DC波，它们在激励频率-幅值平面内的对应稳定性边界，与本文的理论估计值在定量上相吻合。
英文摘要：
Resonant sloshing in circular cylinders was studied by Faltinsen et al. (2016), whose theory was used to describe steady-state resonant waves due to time-harmonic container's elliptic orbits. In the limit of longitudinal container motions, a symmetry-breaking of the planar wave solution occurs, with clockwise and anti-clockwise swirling equally likely. In addition to this primary harmonic dynamics, previous experiments have unveiled that diverse super-harmonic dynamics are observable far from primary resonances. Among these, the so-called double-crest (DC) dynamics, first observed by Reclari et al. (2014) for rotary sloshing, is particularly relevant, as its manifestation is the most favored by the spatial structure of the external driving. Following Bongarzone et al. (2022a), in this work we develop a weakly nonlinear (WNL) analysis to describe the system response to super-harmonic longitudinal forcing. The resulting system of amplitude equations predicts that a planar wave symmetry-breaking via stable swirling may also occur under super-harmonic excitation. This finding is confirmed by our experimental observations, which identify three possible super-harmonic regimes, i.e. (i) stable planar DC waves, (ii) irregular motion and (iii) stable swirling DC waves, whose corresponding stability boundaries in the forcing frequency-amplitude plane quantitatively match the present theoretical estimates.
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