Nonlinear states of the screw dynamo

Area of Science:

• Magnetohydrodynamics (MHD)
• Fluid Dynamics
• Plasma Physics

Background:

• Investigating self-excitation of magnetic fields is crucial for understanding astrophysical phenomena and fusion energy.
• Spiral Couette flow provides a unique geometry for studying dynamo mechanisms.
• Previous studies often focused on linear regimes or specific parameter ranges.

Purpose of the Study:

• To numerically investigate the fully nonlinear, three-dimensional magnetohydrodynamic (MHD) equations for self-excitation of magnetic fields in a spiral Couette flow.
• To analyze the dynamo regimes and saturation mechanisms across a range of magnetic Prandtl numbers (Pm) and kinematic Reynolds numbers (Re).
• To examine the dependence of magnetic energy on the kinematic Reynolds number.

Main Methods:

• Numerical solution of fully nonlinear, three-dimensional MHD equations.
• Simulation of spiral Couette flow between two coaxial cylinders.
• Parameter variation including magnetic Prandtl numbers (0.14 to 10) and kinematic/magnetic Reynolds numbers (up to ~2000).

Main Results:

• The dynamo switches between distinct regimes as the magnetic field's radial width becomes smaller than the field maximum's distance from the boundary.
• Magnetic field growth saturates due to reduced velocity shear, primarily from the Lorentz force, consistent with asymptotic theory for Pm << 1.
• Magnetic energy decreases with Re^(-0.84), aligning with nonlinear asymptotic theory predictions (Re^-1).

Conclusions:

• The study elucidates the complex dynamics of magnetic field self-excitation in spiral Couette flow.
• Saturation mechanisms and regime transitions are identified, providing insights into kinematic dynamo processes.
• The dependence of magnetic energy on Re differs when the velocity field is maintained by a volume force versus viscous stress.