Pinch instabilities in Taylor-Couette flow.

Area of Science:

• Fluid Dynamics
• Magnetohydrodynamics
• Plasma Physics

Background:

• Taylor-Couette flow is a fundamental fluid dynamics problem.
• The influence of azimuthal magnetic fields on flow stability is crucial for various applications.
• Previous studies often focused on ideal flows, neglecting dissipative effects.

Purpose of the Study:

• To investigate the linear stability of dissipative Taylor-Couette flow with an azimuthal magnetic field.
• To characterize the stabilizing and destabilizing effects of magnetic fields based on their radial distribution.
• To identify the critical parameters and modes of instability.

Main Methods:

• Linear stability analysis of the dissipative Taylor-Couette flow.
• Introduction of an azimuthal magnetic field with two parameters: eta (radius ratio) and muB (magnetic field ratio).
• Analysis of different instability modes (m=0 sausage and m=1 kink) and their dependence on parameters like Hartmann number and Prandtl number.

Main Results:

• A stable magnetic field (0
• An unstable magnetic field can destabilize the flow, even without rotation, leading to instabilities within specific axial wave number intervals.
• Critical Hartmann numbers for kink modes are smaller than for sausage modes.
• The transition between sausage and kink instabilities depends on the Prandtl number.

Conclusions:

• Azimuthal magnetic fields significantly alter the stability of Taylor-Couette flow.
• The nature of the magnetic field's radial profile is critical in determining flow stability.
• The findings provide insights into controlling fluid behavior in magnetized systems.