Spectral properties of the linearization at the Burgers vortex in the high rotation limit
Spectral properties of the linearization at the Burgers vortex in the high rotation limit
复制标题
高旋转极限下伯格斯涡旋线性化的光谱特性
DOI：
10.1007/s00021-010-0048-4
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发表时间：
2011
影响因子：
1.3
通讯作者：
Y. Maekawa
中科院分区：
文献类型：
--
作者：
Fujii;Jun Ichi; Fujii;Masatoshi.; Moslehian;M. S.; Seo;Y;Y. Maekawa
本文研究了轴对称Burgers涡方程的线性化算子，它给出了具有轴对称背景应变流的三维Navier-Stokes方程的定常解。数值计算表明，随着环量数（或涡雷诺数）的增加，Burgers涡的稳定性得到改善。虽然轴对称Burgers涡的全局稳定性已经得到严格的证明，但对这种数值观测缺乏数学理解。本文研究了一个以循环数为参数的线性化算子，证明了当该算子被限制在一个合适的不变子空间上时，当循环数趋于无穷大时，其谱向左移动.作为一个应用，我们表明，具有高旋转的轴对称Burgers涡具有更好的稳定性，在这个意义上，非径向对称部分的解决方案，相关的发展方程的时间衰减得更快，如果循环数是足够大的。
We study a linearized operator of the equation for the axisymmetric Burgers vortex which gives a stationary solution to the three dimensional Navier–Stokes equations with an axisymmetric background straining flow. It is numerically known that the Burgers vortex obtains better stabilities as the circulation number (or the vortex Reynolds number) is increasing. Although the global stability of the axisymmetric Burgers vortex is already proved rigorously, mathematical understanding of this numerical observation has been lacking. In this paper we study a linearized operator that includes the circulation number as a parameter, and prove that if the operator is restricted on a suitable invariant subspace, then its spectrum moves to the left as the circulation number goes to infinity. As an application, we show that the axisymmetric Burgers vortex with a high rotation has a better stability, in the sense that the non-radially symmetric part of solutions to the associated evolution equation decays faster in time if the circulation number is sufficiently large.