A variational approach for the dynamics of unsteady point vortices
A variational approach for the dynamics of unsteady point vortices
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DOI：
10.1016/j.ast.2018.05.010
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发表时间：
2018-07
影响因子：
5.6
通讯作者：
A. A. Hussein-A.;Haithem E. Taha;S. Ragab;M. Hajj
中科院分区：
文献类型：
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作者：
A. A. Hussein-A.;Haithem E. Taha;S. Ragab;M. Hajj
引入并实现了非定常点涡动力学的拉格朗日公式。本文提出的拉格朗日量与先前构造的点涡拉格朗日量通过定强涡旋的规范对称联系起来；也就是说，它们产生完全相同的动力。然而，在非定常点涡的情况下，得到了不同的动力学。由最小作用量原理导出的欧拉-拉格朗日方程与从完全不同的角度导出的非定常点涡的布朗-迈克尔演化方程完全匹配；基于线性动量守恒。所提出的拉格朗日量允许将伽辽金技术应用于涡旋动力学的弱公式。将建立的时变涡动力学模型应用于脉冲起动平板以及加速和俯仰平板问题。在每种情况下，使用所提出的拉格朗日动力学得到的升力系数与使用先前构建的拉格朗日、文献中的其他模型和实验数据得到的升力系数进行比较。
A Lagrangian formulation for the dynamics of unsteady point vortices is introduced and implemented. The proposed Lagrangian is related to previously constructed Lagrangian of point vortices via a gauge-symmetry in the case of vortices of constant strengths; i.e., they yield the exact same dynamics. However, a different dynamics is obtained in the case of unsteady point vortices. The resulting Euler–Lagrange equation derived from the principle of least action exactly matches the Brown–Michael evolution equation for unsteady point vortices, which was derived from a completely different point of view; based on conservation of linear momentum. The proposed Lagrangian allows for applying Galerkin techniques to the weak formulation of the vortex dynamics. The resulting dynamic model of time-varying vortices is applied to the problem of an impulsively started flat plate as well as an accelerating and pitching flat plate. In each case, the resulting lift coefficient using the dynamics of the proposed Lagrangian is compared to that using previously constructed Lagrangian, other models in literature, and experimental data.