Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Stability criteria of 3D inviscid shears

Author: Y. Charles Li
Journal: Quart. Appl. Math. 69 (2011), 379-387
MSC (2010): Primary 76E05, 37K45; Secondary 35Q31
DOI: https://doi.org/10.1090/S0033-569X-2011-01213-7
Published electronically: March 10, 2011
MathSciNet review: 2729894
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Abstract: Recent numerical studies in the area of transition to turbulence discovered that the classical plane Couette flow, plane Poiseuille flow, and pipe Poiseuille flow share some universal 3D steady coherent structure in the form of a ``streak-roll-critical layer''. As the Reynolds number approaches infinity, the steady coherent structure approaches a 3D limiting shear of the form ( $ U(y,z), 0, 0$) in velocity variables. All such 3D shears are steady states of the 3D Euler equations. This raises the importance of investigating the stability of such inviscid 3D shears in contrast to the classical Rayleigh theory of inviscid 2D shears. Several general criteria of stability for such inviscid 3D shears are derived. In the Appendix, an argument is given to show that a 2D limiting shear can only be the classical laminar shear.

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Additional Information

Y. Charles Li
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: liyan@missouri.edu

DOI: https://doi.org/10.1090/S0033-569X-2011-01213-7
Received by editor(s): November 21, 2009
Published electronically: March 10, 2011
Article copyright: © Copyright 2011 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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