Non uniform Rotating Vortices and Periodic Orbits for the Two-Dimensional Euler Equations

This paper concerns the study of some special ordered structures in turbulent flows. In particular, a systematic and relevant methodology is proposed to construct non trivial and non radial rotating vortices with non necessarily uniform densities and with different m -fold symmetries, m ≧ 1 . In par...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2020-11, Vol.238 (2), p.929-1085
Main Authors: García, Claudia, Hmidi, Taoufik, Soler, Juan
Format: Article
Language:English
Subjects:
Analysis of PDEs
Bifurcations
Classical Mechanics
Complex Systems
Euler-Lagrange equation
Eulers equations
Fluid dynamics
Fluid- and Aerodynamics
Mathematical and Computational Physics
Mathematics
Orbits
Physics
Physics and Astronomy
Rarefaction
Rotation
Theoretical
Vortices
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Summary:This paper concerns the study of some special ordered structures in turbulent flows. In particular, a systematic and relevant methodology is proposed to construct non trivial and non radial rotating vortices with non necessarily uniform densities and with different m -fold symmetries, m ≧ 1 . In particular, a complete study is provided for the truncated quadratic density ( A | x | 2 + B ) 1 D ( x ) , with D the unit disc. We exhibit different behaviors with respect to the coefficients A and B describing the rarefaction of bifurcating curves.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-020-01561-z