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arXiv physics/9901055physics.flu-dyncond-mat.stat-mech
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超流模型中的旋涡脱落

Vortex shedding in a model of superflow

C. Josserand, Y. Pomeau, S. Rica

摘要:

本文是博士论文的一部分。C的论文。约瑟兰本文讨论二维圆盘绕流非线性薛定谔方程中量子化涡旋的成核问题。当流动局部地(在盘的边缘)变成超音速时,涡似乎成核。详细研究了复场$ψ$的相位方程,给出了阈值以下定态解的Euler-Tricomi型方程。这个方程与气体冲击波动力学中已知的方程密切相关。然后使用可解性条件,我们提取一个依赖于时间的方案的振幅的演变,我们,最后,涉及到一个已知的家庭解决方案的NLS,从而产生一个漩涡成核。考虑到流动的几何形状,我们还给出了在朗道成核速度下的一阶修正。

英文摘要:

The present article represents part of the PhD. dissertation by C. Josserand. We discuss the nucleation of quantized vortices in the nonlinear Schrödinger equation (NLS) for a flow around a disk in two spatial dimensions. It appears that the vortices are nucleated when the flow becomes locally (at the edge of the disk) supersonic. A detailed study of the phase equation for the complex field $ψ$ gives an Euler-Tricomi type equation for the stationary solutions below threshold. This equation is closely related to the one known in shock wave dynamics for gas. Then using solvability condition, we extract a time-dependent scenario for the evolution of the amplitude of the solution, which we, finally, relate to a known family solution of NLS which gives rise to a vortex nucleation. We also give a first order correction at the Landau velocity of nucleation, taking into account the geometry of the flow.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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