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Linear instability of magnetic Taylor-Couette flow with Hall effect
Günther Rüdiger1, Dima Shalybkov
1Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany. gruediger@aip.de
Summary
The Hall effect can destabilize molecular hydrodynamic Taylor-Couette flow, but this instability depends on the magnetic field
Area of Science:
- Fluid dynamics
- Magnetohydrodynamics
- Plasma physics
Background:
- Taylor-Couette flow is a fundamental system in fluid dynamics.
- The Hall effect is a phenomenon observed in conductive fluids subjected to magnetic fields.
- Understanding flow stability is crucial for astrophysical and industrial applications.
Purpose of the Study:
- To investigate the impact of the Hall effect on the linear stability of Taylor-Couette flow.
- To analyze the influence of an axial magnetic field on this system.
- To determine conditions under which Hall-driven instabilities arise.
Main Methods:
- Linear stability analysis of a molecular hydrodynamic model.
- Consideration of an axial uniform magnetic field and the Hall effect.
- Examination of flow behavior for varying angular velocity ratios and magnetic field strengths.
Main Results:
- The Hall effect induces instability in Taylor-Couette flow regardless of angular velocity ratios.
- Instability is contingent on the sign of the axial magnetic field and Hartmann number.
- For negative shear, Hall instability merges with magnetorotational instability, lowering critical magnetic Reynolds numbers.
Conclusions:
- The Hall effect significantly alters the stability of Taylor-Couette flow.
- Specific magnetic field configurations are required to observe Hall-driven instabilities.
- Experimental verification in liquid metals necessitates extremely strong magnetic fields (approx. 10^7 G).