Growth rate degeneracies in kinematic dynamos.

Area of Science:

• Geophysics
• Astrophysics
• Fluid dynamics

Background:

• The kinematic dynamo problem investigates how fluid motion generates magnetic fields.
• Understanding magnetic field generation is crucial for astrophysical phenomena and geophysics.
• Previous studies often focused on specific boundary conditions, limiting generalizability.

Purpose of the Study:

• To investigate the impact of different magnetic boundary conditions on kinematic dynamo growth rates.
• To demonstrate a general property of dynamo growth rates related to flow reversibility.
• To provide insights applicable to both numerical simulations and laboratory experiments.

Main Methods:

• Analysis of the induction operator's adjointness in kinematic dynamo theory.
• Comparison of dynamo growth rates under normal (pseudovacuum) and tangent (perfect conductor) magnetic boundary conditions.
• Application of the theoretical findings to S2T2 type flows in spherical geometry.

Main Results:

• The growth rate of a kinematic dynamo is identical for both normal and tangent magnetic boundary conditions.
• This equality holds for any reversible velocity field (u transforms to -u).
• While growth rates are identical, the magnetic eigenmodes differ significantly between the two boundary conditions.

Conclusions:

• The adjointness of the induction operator leads to a universal dynamo growth rate regardless of specific magnetic boundary conditions for reversible flows.
• This finding simplifies the study of kinematic dynamos, unifying results from different physical limits.
• The results offer a valuable theoretical framework for interpreting laboratory dynamo experiments and numerical models.