Kinematic dynamos in spheroidal geometries

Area of Science:

• Geophysics
• Plasma Physics
• Magnetohydrodynamics

Background:

• The kinematic dynamo problem describes the generation and maintenance of magnetic fields by fluid motion.
• Solving this problem for non-spherical geometries like spheroids is computationally challenging.
• Previous models often simplified the geometry or fluid properties.

Purpose of the Study:

• To numerically solve the kinematic dynamo problem for conducting spheroidal fluids.
• To investigate the influence of large aspect ratios on magnetic field generation.
• To develop a scalable computational method for spheroidal geometries.

Main Methods:

• Utilized solenoidal representations of magnetic and velocity fields using spheroidal toroidal and poloidal fields.
• Employed a non-orthogonal coordinate system and scaled the problem to spherical geometry.
• Applied spherical harmonic techniques for angular components and solved the exterior current-free condition explicitly.

Main Results:

• Developed a modified kinematic dynamo problem with anisotropic diffusion and exterior conditions.
• Found dynamo solutions for axisymmetric flows in oblate spheroids with aspect ratios up to 25.
• Observed that strong internal magnetic fields can arise, with external fields being weak and localized.

Conclusions:

• The numerical method is effective for spheroidal geometries, even with large aspect ratios.
• Fluid flow within the spheroid significantly influences the distribution of generated magnetic fields.
• The study provides insights into magnetic field generation in celestial bodies with non-spherical shapes.