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

  • Sun-Chul Kim
  • Hisashi OkamotoEmail author
Original Paper Area 1


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.


Navier–Stokes equations Subharmonic bifurcation Proudman–Johnson equation Vortex of large scale 


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© The JJIAM Publishing Committee and Springer 2010

Authors and Affiliations

  1. 1.Department of MathematicsChung-Ang UniversitySeoulKorea
  2. 2.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

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