Vortices of large scale appearing in the 2D stationary Navier-Stokes equations at large Reynolds numbers
- Authors
- Kim, Sun-Chul; Okamoto, Hisashi
- Issue Date
- Jun-2010
- Publisher
- SPRINGER JAPAN KK
- Keywords
- Navier-Stokes equations; Subharmonic bifurcation; Proudman-Johnson equation; Vortex of large scale
- Citation
- JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, v.27, no.1, pp 47 - 71
- Pages
- 25
- Journal Title
- JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
- Volume
- 27
- Number
- 1
- Start Page
- 47
- End Page
- 71
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/22423
- DOI
- 10.1007/s13160-010-0010-0
- ISSN
- 0916-7005
1868-937X
- Abstract
- 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.
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