Potentially singular solutions of the 3D axisymmetric Euler equations

Significance Whether infinitely fast spinning vortices can develop in initially smooth, incompressible inviscid flow fields in finite time is one of the most challenging problems in fluid dynamics. Besides being a difficult mathematical question that has remained open for more than 250 years, the pr...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2014-09, Vol.111 (36), p.12968-12973
Main Authors: Luo, Guo, Hou, Thomas Y.
Format: Article
Language:English
Subjects:
Axes of rotation
Boundary conditions
Coordinate systems
Cylinders
Estimating techniques
Euler equations
Eulers equations
Finite element analysis
Geometric planes
Mathematical problems
Physical Sciences
Rotation
Symmetry
Three dimensional imaging
Vorticity
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Summary:Significance Whether infinitely fast spinning vortices can develop in initially smooth, incompressible inviscid flow fields in finite time is one of the most challenging problems in fluid dynamics. Besides being a difficult mathematical question that has remained open for more than 250 years, the problem also attracts great attention in the physics and engineering communities due to its potential connection to the onset of turbulence in viscous flows. This paper attempts to provide an affirmative answer to this long-standing open question from a numerical point of view, by describing a class of rotationally symmetric flows from which infinitely fast spinning vortices can form in finite time. It suggests, after decades of controversies, a promising direction to the resolution of the problem.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.1405238111