Plesio-geostrophy for Earth's core: I. Basic equations, inertial modes and induction

Area of Science:

• Geophysics
• Fluid Dynamics
• Magnetohydrodynamics

Background:

• Planetary cores exhibit complex fluid motions and magnetic field generation.
• Accurate modeling of these phenomena requires approximations for computational efficiency.
• Rapid rotation is a key characteristic of planetary interiors.

Purpose of the Study:

• To develop a novel approximation for fluid dynamics and motional induction.
• To accurately model geophysical processes in planetary cores on decadal timescales.
• To simplify complex 3D equations into a more manageable form.

Main Methods:

• Developed the "plesio-geostrophy" approximation by integrating equations along the rotation axis.
• Represented fluid flow as columnar, invariant along the rotation axis.
• Neglected magnetic diffusion, reducing 3D quantities to 2D scalars.
• Derived fifteen partial differential equations for the isothermal magnetic case.
• Solved for normal modes (inertial modes) in the absence of forcing and viscous damping.

Main Results:

• The plesio-geostrophy approximation accurately describes fluid motions and motional induction.
• The method successfully collapses 3D quantities into 2D scalars.
• Eigenfunctions and eigenfrequencies of inertial modes were accurately captured by the approximation.
• The model is suitable for short timescales relevant to planetary cores.

Conclusions:

• Plesio-geostrophy offers a powerful tool for studying rapidly rotating planetary systems.
• The approximation provides a computationally efficient yet accurate method for geophysical modeling.
• This work advances our understanding of fluid dynamics and magnetic induction in planetary interiors.