On the stability of periodic 2D Euler-alpha flows

2000/07/09 by Sergey Pekarsky, Pekarsky, Sergey, Steve Shkoller +1
Mathematics · Physics and Astronomy · #35Q35 #53C99 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math.AP #math.DG #msc:35Q35 #msc:53C99

paper · pdf · doi:10.48550/arxiv.math/0007050

arxiv created 2000/07/09 · openalex publication_date 2000/07/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 > alpha₀, where 0 < alpha₀ < 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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