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Vortex dynamics on a Möbius strip
Journal of Fluid Mechanics ( IF 3.7 ) Pub Date : 2021-07-22 , DOI: 10.1017/jfm.2021.581
Jacques Vanneste 1
Affiliation  

We consider the dynamics of a two-dimensional incompressible perfect fluid on a Möbius strip embedded in $\mathbb {R}^{3}$ . The vorticity–stream function formulation of the Euler equations is derived from an exterior-calculus form of the momentum equation. The non-orientability of the Möbius strip and the distinction between forms and pseudo-forms this introduces lead to unusual properties: a boundary condition is provided by the conservation of circulation along the single boundary of the strip, and there is no integral conservation for the vorticity density or for any odd function thereof. A finite-difference numerical implementation is used to illustrate the Möbius-strip realisation of familiar phenomena: translation of vortices along boundaries, shear instability and decaying turbulence.

中文翻译:

莫比乌斯带上的涡流动力学

我们考虑嵌入在莫比乌斯带上的二维不可压缩完美流体的动力学 $\mathbb {R}^{3}$ . 欧拉方程的涡流函数公式是从动量方程的外微积分形式推导出来的。莫比乌斯带的不可定向性以及由此引入的形式和伪形式之间的区别导致了不寻常的性质:边界条件由沿带的单一边界的流通守恒提供,并且没有积分守恒涡量密度或其任何奇函数。使用有限差分数值实现来说明熟悉现象的莫比乌斯带实现:沿边界的涡流平移、剪切不稳定性和衰减湍流。
更新日期:2021-07-22
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