On the stability of periodic 2D Euler-alpha flows
偏微分方程分析
2007-05-23 v1 微分几何
摘要
An explicit expression is obtained for the sectional curvature in the plane spanned by two stationary flows, cos(k, x) and cos(l, x). It is shown that for certain values of the wave vectors k and l the curvature becomes positive for alpha > alpha_0, where 0 < alpha_0 < 1 is of the order 1/k. This suggests that the flow corresponding to such geodesics becomes more stable as one goes from usual Eulerian description to the Euler-alpha model.
引用
@article{arxiv.math/0007050,
title = {On the stability of periodic 2D Euler-alpha flows},
author = {Sergey Pekarsky and Steve Shkoller},
journal= {arXiv preprint arXiv:math/0007050},
year = {2007}
}