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Magnetically Induced Rotating Rayleigh-Taylor Instability

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Transitions in overstable rotating magnetoconvection.

Ankan Banerjee¹, Manojit Ghosh¹, Pinaki Pal¹

¹Department of Mathematics, National Institute of Technology, Durgapur 713209, India.

Physical Review. E

|August 16, 2020

Summary

This study reveals simultaneous subcritical and supercritical convection branches in Rayleigh-Bénard convection (RBC) for electrically conducting fluids. This novel phenomenon, observed under magnetic fields and rotation, depends on initial conditions.

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Area of Science:

Fluid Dynamics
Magnetohydrodynamics
Nonlinear Dynamics

Background:

Rayleigh-Bénard convection (RBC) typically shows either subcritical or supercritical transitions.
Simultaneous subcritical and supercritical branches in plane layer RBC have not been previously reported.
External factors like rotation and magnetic fields influence RBC transitions.

Purpose of the Study:

To report the simultaneous occurrence of subcritical and supercritical convection branches in RBC.
To investigate this phenomenon in overstable, electrically conducting, low Prandtl number fluids.
To explore the influence of magnetic fields, rotation, and initial conditions on these transitions.

Main Methods:

Extensive three-dimensional (3D) direct numerical simulations (DNS).
Low-dimensional modeling based on DNS data.
Bifurcation analysis of a derived 3D model.
Exploration of the effect of the Prandtl number.

Main Results:

Demonstrated the simultaneous occurrence of subcritical and supercritical branches of convection.
Identified the phenomenon in liquid metals under horizontal magnetic fields and vertical rotation.
Established the ranges for Taylor number (Ta) and Chandrasekhar number (Q) where this occurs.
Revealed that a supercritical Hopf bifurcation and a subcritical pitchfork bifurcation drive these transitions.

Conclusions:

The study convincingly establishes the simultaneous exhibition of subcritical and supercritical convection branches in plane layer RBC.
This phenomenon is driven by distinct supercritical Hopf and subcritical pitchfork bifurcations of the conduction state.
The findings offer new insights into the complex dynamics of convective systems under external forcing.