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Updated: Nov 5, 2025
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
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Linear and nonlinear hydromagnetic stability in laminar and turbulent flows
Itzhak Fouxon1,2, Joshua Feinberg1, Michael Mond2
1Department of Mathematics and Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Haifa 31905, Israel.
Physical Review. E
|May 19, 2021
Summary
This study investigates the stability of electrically conducting fluid flows, determining conditions under which hydrodynamic and magnetic field perturbations decay or grow. It establishes critical thresholds for hydrodynamic and magnetic Reynolds numbers to predict flow stability and dynamo processes.
Area of Science:
- Fluid Dynamics
- Magnetohydrodynamics (MHD)
- Plasma Physics
Background:
- Understanding the stability of fluid flows with embedded magnetic fields is crucial in astrophysics and geophysics.
- Previous studies often imposed restrictive boundary conditions on flow perturbations.
- The dynamo process, generating magnetic fields from fluid motion, requires detailed stability analysis.
Purpose of the Study:
- To analyze the evolution of large perturbations in hydrodynamically driven, electrically conducting fluid flows.
- To determine the conditions under which hydrodynamic and magnetic field perturbations decay or grow, indicating stability or dynamo action.
- To establish critical values for hydrodynamic and magnetic Reynolds numbers governing flow stability.
Main Methods:
- Derivation of a generalized Reynolds-Orr equation for the combined kinetic and magnetic energy of perturbations.
- Analysis of fluid flow within a finite volume with zero normal velocity boundary conditions and arbitrary tangential components.
- Application of classical boundary conditions for magnetic fields extending throughout space.
- Generalization of the Rayleigh-Faber-Krahn inequality for eigenvalue problems.
Main Results:
- Established critical values for hydrodynamic and magnetic Reynolds numbers below which arbitrarily large hydrodynamic perturbations decay.
- Demonstrated a generalization of the Rayleigh-Faber-Krahn inequality for stability analysis.
- Provided an estimate for the critical magnetic Reynolds number in high Reynolds number turbulence, below which magnetic field fluctuations decay.
Conclusions:
- Arbitrarily large perturbations in electrically conducting fluid flows decay under specific conditions related to hydrodynamic and magnetic Reynolds numbers.
- The study provides a theoretical framework for predicting the stability of MHD flows and the absence of dynamo action.
- The findings are relevant for understanding magnetic field generation and decay in various astrophysical and geophysical contexts.
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