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Updated: May 25, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Paradoxical transitions to instabilities in hydromagnetic Couette-Taylor flows
Oleg N Kirillov1, Dmitry E Pelinovsky, Guido Schneider
1Helmholtz-Zentrum Dresden-Rossendorf, PO Box 510119, D-01314 Dresden, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2012
Summary
We analyzed hydromagnetic Couette-Taylor flow stability using spectral analysis. The vanishing magnetic field limit reveals a discontinuous transition to instability, known as the Velikhov-Chandrasekhar paradox.
Area of Science:
- Fluid dynamics
- Plasma physics
- Magnetohydrodynamics
Background:
- The Couette-Taylor flow is a fundamental system in fluid dynamics.
- Understanding flow stability is crucial for predicting fluid behavior.
- The Velikhov-Chandrasekhar paradox highlights discrepancies in stability criteria.
Purpose of the Study:
- To rigorously determine eigenvalue distributions for linearized operators in ideal hydromagnetic Couette-Taylor flow.
- To investigate the transition to instability in the limit of a vanishing magnetic field.
Main Methods:
- Modern spectral analysis techniques were employed.
- Linearized operators associated with the flow were analyzed.
- Eigenvalue distributions were rigorously calculated.
Main Results:
- The study successfully found the distributions of eigenvalues for the relevant operators.
- A discontinuous change in the transition to instability was observed as the magnetic field vanished.
- This finding contrasts with the Rayleigh stability criterion for purely hydrodynamical flows.
Conclusions:
- The Velikhov-Chandrasekhar paradox is confirmed and elucidated through spectral analysis.
- The behavior of hydromagnetic flows differs significantly from purely hydrodynamical flows under certain conditions.
- This research provides a rigorous mathematical basis for understanding magnetohydrodynamic instabilities.
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