Linear dynamics of the Lamb-Chaplygin dipole in the two-dimensional limit
Linear dynamics of the Lamb-Chaplygin dipole in the two-dimensional limit
复制标题
二维极限下 Lamb-Chaplygin 偶极子的线性动力学
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
L. Jacquin
中科院分区：
文献类型：
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作者：
V. Brion;D. Sipp;L. Jacquin
本文用线性分析的方法研究了Lamb-Chaubergin偶极子在大波长极限下的动力学。以Billant [“Three-dimensional stability of a vortex pair，”Phys.Fluids11，2069（1999）]计算的Lamb-Chaobergin偶极子的三维谱作为参考，我们首先表明谱中存在额外的不稳定模式族。其中，一族对称模和一族反对称模，都存在于大波长极限，是本研究的主要内容。在这两个家庭中的最不稳定的模式是纯二维的，二维动力学更特别的调查。计算结果表明，反对称不稳定性的放大率明显大于对称不稳定性。此外，虽然二维对称模式是固定的，并引起相对于偶极子自传播速度矢量的偶极子朝向上游或下游方向的移位，反对称模式是不稳定的，并使偶极子围绕其初始直线轨迹移动成波浪振荡。这些二维不稳定性的主要物理机制是发生在偶极子下游的旋涡脱落。这种脱落是外部流动对偶极子运动的反应，基本上能够保持流动冲量。随着位移偶极子产生更多的脱落，尾流的不稳定作用被放大。偶极子运动和尾流因此相互加强，导致不稳定。应变相互施加的偶极子，被称为三维涡对不稳定性的一个重要机制的涡，也被证明参与这种不稳定。
The dynamics of the Lamb-Chaplygin dipole in the large-wavelength limit is investigated by means of linear analysis. Taking the three-dimensional spectrum of the Lamb-Chaplygin dipole calculated by Billant [“Three-dimensional stability of a vortex pair,” Phys. Fluids11, 2069 (1999)] as a reference, we first show that additional families of unstable modes are present in the spectrum. Among them, a family of symmetric modes and one of antisymmetric modes, both present in the large-wavelength limit, are the main topic of this investigation. The most unstable modes in these two families being purely two-dimensional, the two-dimensional dynamics is more particularly investigated. Our calculations show that the amplification rate of the antisymmetric instability is significantly larger than that of the symmetric instability. Also, while the two-dimensional symmetric mode is stationary and induces a shift of the dipole toward the upstream or downstream direction relatively to the dipole self-propagation velocity vector, the antisymmetric mode is unsteady and displaces the dipole into wavy oscillations about its initial straight trajectory. The leading physical mechanism of these two-dimensional instabilities is the vortex shedding that occurs downstream of the dipole. This shedding is the reaction of the external flow to the dipole motion and basically enables the conservation of the flow impulse. The destabilizing action of the wake is amplified as the displaced dipole generates more shedding. The dipole motion and the wake thus reinforce each other, leading to the instability. The strain mutually exerted by the vortices of the dipole, known as an essential mechanism of three-dimensional vortex pair instabilities, is also shown to participate to this destabilization.