Linear magnetohydrodynamic Taylor-Couette instability for liquid sodium.

Area of Science:

• Fluid Dynamics
• Magnetohydrodynamics (MHD)
• Plasma Physics

Background:

• Taylor-Couette flow is a fundamental configuration in fluid dynamics.
• Magnetohydrodynamics describes the behavior of electrically conducting fluids in magnetic fields.
• Understanding stability is crucial for applications like fusion energy and geophysics.

Purpose of the Study:

• To investigate the linear stability of MHD Taylor-Couette flow for liquid sodium.
• To analyze the influence of a small magnetic Prandtl number (Pm) and boundary conditions on flow stability.
• To determine the scaling of critical parameters like Reynolds number (Re) and magnetic Reynolds number (Rm).

Main Methods:

• Linear stability analysis of the MHD Taylor-Couette flow equations.
• Numerical calculations for a specific geometry (R(out)=2R(in)) with an axial magnetic field.
• Consideration of both vacuum and perfect conducting boundary conditions.

Main Results:

• Subcritical excitation for a resting outer cylinder disappears at small Pm.
• For a rotating outer cylinder, instability scales with Pm(-1/2) at moderate Re, and 1/Pm at higher Re, where Rm dominates.
• Instability onset is easier for axisymmetric modes than non-axisymmetric modes with vacuum boundaries.
• Crossovers in marginal stability lines for conducting walls suggest potential for dynamo experiments.

Conclusions:

• The stability of MHD Taylor-Couette flow is highly sensitive to Pm, boundary conditions, and cylinder rotation.
• Magnetic Reynolds number (Rm) plays a critical role in directing instability at higher Reynolds numbers.
• Conducting walls can lead to instabilities like overstability and exhibit unique marginal stability crossovers, relevant for dynamo research.