Magnetohydrodynamic instabilities in rotating and precessing sheared flows: an asymptotic analysis

Area of Science:

• Fluid Dynamics
• Plasma Physics
• Astrophysics

Background:

• Magnetohydrodynamic (MHD) instabilities are crucial in astrophysical and geophysical phenomena.
• Understanding instabilities in rotating and precessing flows with magnetic fields is complex.
• Previous studies explored magnetoelliptical instabilities, providing a foundation for current research.

Purpose of the Study:

• To analytically investigate linear MHD instabilities in unbounded, inviscid, electrically conducting flows.
• To examine flows subjected to rotation, precession, shear, and an external magnetic field.
• To determine the conditions under which instabilities arise and their growth rates.

Main Methods:

• Analytical study of linear MHD instabilities.
• Application of the admissibility condition to determine base flow configurations.
• Floquet system analysis using asymptotic expansion in the small parameter ε (precession to rotation frequency ratio).
• Stability analysis performed in a transformed coordinate system accounting for symmetry and invariants.

Main Results:

• An admissible magnetic field must align with the absolute vorticity.
• The stability analysis depends on parameters ε, η (cyclotron to rotation frequency ratio), and χ (cos α).
• The subharmonic magnetic mode appears only when η > sqrt(5/2).
• At large η (>>1), hydrodynamic and magnetic modes approach a maximal growth rate of ε/2, while the mixed mode approaches zero.

Conclusions:

• The study provides a comprehensive analytical framework for understanding MHD instabilities in complex flows.
• Key parameters influencing instability thresholds and growth rates have been identified.
• The findings contribute to the understanding of magnetic field dynamics in rotating and precessing astrophysical systems.