Three-dimensional transition in the wake of a transversely oscillating cylinder
Three-dimensional transition in the wake of a transversely oscillating cylinder
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DOI：
10.1017/s0022112006004320
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发表时间：
2007-04
影响因子：
3.7
通讯作者：
J. Leontini;M. Thompson;K. Hourigan
中科院分区：
文献类型：
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作者：
J. Leontini;M. Thompson;K. Hourigan
对一个在垂直于自由流方向受迫振荡的圆柱尾流中向三维过渡进行了弗洛凯稳定性分析。针对接近自然脱落频率的振荡频率，确定了改变振荡振幅的影响。识别了出现的三维模式，并量化了振荡振幅对其结构和增长率的影响。研究表明，当二维尾流处于2S构型（类似于卡门涡街）时，出现的三维模式在性质和对称结构上与固定圆柱尾流中的模式相似。这些模式被称为A模式、B模式和QP模式，并且随着雷诺数（Re）的增加按此顺序出现。然而，增加振荡振幅会使A模式的临界雷诺数显著增加，以至于B模式在A模式之前达到临界。A模式的临界波长也受到振荡的影响，随着振幅增加而变小。椭圆不稳定性理论也被证明可以预测这一趋势，进一步支持了A模式主要是由椭圆不稳定性产生的这一观点。在更高的振荡振幅下，二维尾流的时空对称性发生变化，呈现出P + S构型，在每个振荡周期中，尾流的一侧有一对涡旋，另一侧有一个涡旋。随着这种构型的出现，A模式、B模式和QP模式不复存在。研究表明，从这种基流中出现了两种新的三维模式，我们称之为SL模式和SS模式。这两种模式都是次谐波的，在两个基流周期内重复。而且，根据圆柱的振荡振幅，这两种模式中的任何一种都可能首先达到临界。这两种新模式的出现，以及三维模式A和B起始顺序的反转，导致了这样一个观察结果：对于振荡圆柱尾流，根据振荡振幅的不同，有四种不同的模式可以导致向三维的过渡。因此，这种类型的流动为研究模式起始顺序对钝体尾流中通向湍流的路径的影响提供了一个很好的例子。在所研究的振幅范围内，流动保持二维的最大雷诺数（Re）值为280。
A Floquet stability analysis of the transition to three-dimensionality in the wake of a cylinder forced to oscillate transversely to the free stream has been undertaken. The effect of varying the oscillation amplitude is determined for a frequency of oscillation close to the natural shedding frequency. The three-dimensional modes that arise are identified, and the effect of the oscillation amplitude on their structure and growth rate quantified. It is shown that when the two-dimensional wake is in the 2S configuration (which is similar to the Kármán vortex street), the three-dimensional modes that arise are similar in nature and symmetry structure to the modes in the wake of a fixed cylinder. These modes are known as modes A, B and QP and occur in this order with increasing Re. However, increasing the amplitude of oscillation causes the critical Reynolds number for mode A to increase significantly, to the point where mode B becomes critical before mode A. The critical wavelength for mode A is also affected by the oscillation, becoming smaller with increasing amplitude. Elliptic instability theory is shown also to predict this trend, providing further support that mode A primarily arises as a result of an elliptic instability. At higher oscillation amplitudes, the spatio-temporal symmetry of the two-dimensional wake changes and it takes on the P + S configuration, with a pair of vortices on one side of the wake and a single vortex on the other side, for each oscillation cycle. With the onset of this configuration, modes A, B and QP cease to exist. It is shown that two new three-dimensional modes arise from this base flow, which we call modes SL and SS. Both of these modes are subharmonic, repeating over two base-flow periods. Also, either mode can be the first to become critical, depending on the amplitude of oscillation of the cylinder. The emergence of these two new modes, as well as the reversal of the order of inception of the three-dimensional modes A and B, leads to the observation that for an oscillating cylinder wake there are four different modes that can lead the transition to three-dimensionality, depending on the amplitude of oscillation. Therefore this type of flow provides a good example for studying the effect of mode-order inception on the path taken to turbulence in bluff-body wakes. For the range of amplitudes studied, the maximum Re value for which the flow remains two-dimensional is 280.