On the symmetry breaking instability leading to vortex shedding
On the symmetry breaking instability leading to vortex shedding
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DOI：
10.1063/1.869372
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发表时间：
1997-09
影响因子：
4.6
通讯作者：
Shao-jie Tang;N. Aubry
中科院分区：
文献类型：
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作者：
Shao-jie Tang;N. Aubry
众所周知，在早期阶段，通过圆柱体的脉冲启动流动由双涡组成，它们是通过中间平面的反射而相互映象的。当雷诺数低于临界雷诺数(Rec≃48)时，孪生涡是稳定的，但超过临界雷诺数时，孪生涡变得不稳定。在Re>；Rec，流动在短时间内保持其对称的循环气泡结构，经历对称破缺不稳定性，并发展为卡门涡街。本文将Foppl的旋涡模型作为对称气泡的低维模型进行研究。对模型中固定气泡的稳定性分析表明，存在两种非对称本征模，一种是稳定的，另一种是不稳定的。本文用二维直接数值模拟方法，对脉冲启动的圆柱绕流流动进行了数值模拟，证明了模型的不稳定性与真实流动的不稳定性是如何定性地吻合的。
It is well known that at early stages an impulsively started flow past a circular cylinder consists of twin vortices which are images of one another by reflection through the mid-plane. While the twin vortices are stable for Reynolds numbers below the critical Reynolds number value (Rec≃48), they become unstable above the critical Reynolds number. At Re>Rec, the flow keeps its symmetric recirculating bubble structure for a short time, undergoes a symmetry-breaking instability, and develops into a Karman vortex street. Foppl’s vortex model is studied here as a low-dimensional model for the symmetric bubble. The stability analysis of a fixed bubble in the model shows that there are two asymmetric eigenmodes, a stable mode and an unstable one. In this paper, we show by two-dimensional direct numerical simulations (DNS) of the impulsively started flow past a circular cylinder how the instability properties of the model qualitatively mimic those of the real flow.