On the stability of periodic 2D Euler-alpha flows

Details On the stability of periodic 2D Euler-alpha flows On the stability of periodic 2D Euler-alpha flows

2000-07-09

arxiv.org/abs/math/0007050v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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