Vortices of large scale appearing in the 2D stationary Navier-Stokes equations at large Reynolds numbers

被引:18
作者
Kim, Sun-Chul [2 ]
Okamoto, Hisashi [1 ]
机构
[1] Kyoto Univ, Math Sci Res Inst, Kyoto 6068502, Japan
[2] Chung Ang Univ, Dept Math, Seoul 156756, South Korea
关键词
Navier-Stokes equations; Subharmonic bifurcation; Proudman-Johnson equation; Vortex of large scale; SIMILARITY SOLUTIONS; FLOW;
D O I
10.1007/s13160-010-0010-0
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider Kolmogorov's problem for the two-dimensional (2D) Navier-Stokes equations. Stability of and bifurcation from the trivial solution are studied numerically. More specifically, we compute solutions with large Reynolds numbers with a family of prescribed external forces of increasing degree of oscillation. We find that, whatever the external force may be, a stable steady-state of simple geometric character exits for sufficiently large Reynolds numbers. We thus observe a kind of universal outlook of the solutions, which is independent of the external force. This observation is reinforced further by an asymptotic analysis of a simple equation called the Proudman-Johnson equation.
引用
收藏
页码:47 / 71
页数:25
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