Variational Necessary and Sufficient Stability Conditions for Inviscid Shear Flow
Variational Necessary and Sufficient Stability Conditions for Inviscid Shear Flow
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无粘剪切流变分必要和充分稳定性条件
DOI：
10.1098/rspa.2014.0322
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
P. J. Morrison and Y. Hattori
中科院分区：
文献类型：
--
作者：
M. Hirota;P. J. Morrison and Y. Hattori
通过发展一种新的变分原理，给出了无粘平行剪切流线性稳定的充分必要条件，其中速度剖面假定为单调的解析型。证明了Rayleigh方程（非自伴随特征值问题）的不稳定特征值可以与某自伴随算子的正特征值相关联。因此，稳定性是通过最大化二次型来确定的，这在理论上和数值上比直接求解瑞利方程更容易处理。该变分稳定性判据基于对连续谱Kreĭn特征的理解，适用于其他无限维哈密顿系统的稳定性问题。
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that unstable eigenvalues of Rayleigh's equation (which is a non-self-adjoint eigenvalue problem) can be associated with positive eigenvalues of a certain self-adjoint operator. The stability is therefore determined by maximizing a quadratic form, which is theoretically and numerically more tractable than directly solving Rayleigh's equation. This variational stability criterion is based on the understanding of Kreĭn signature for continuous spectra and is applicable to other stability problems of infinite-dimensional Hamiltonian systems.