Related Experiment Video
Updated: Aug 14, 2026
11:47
A 100 KW Class Applied-field Magnetoplasmadynamic Thruster
Published on: December 22, 2018
Shell-to-shell energy transfer in magnetohydrodynamics. II. Kinematic dynamo
Pablo Mininni1, Alexandros Alexakis, Annick Pouquet
1National Center for Atmospheric Research, P.O. Box 3000, Boulder, Colorado 80307, USA. mininni@ucar.edu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
Summary
Turbulent velocity fluctuations amplify magnetic fields at small scales, while large-scale flows amplify the large-scale magnetic field. Energy transfer in magnetohydrodynamics involves both direct velocity-to-magnetic field coupling and magnetic energy cascades.
Area of Science:
- Fluid dynamics
- Plasma physics
- Astrophysics
Background:
- Magnetohydrodynamics (MHD) describes electrically conducting fluids.
- Turbulence is a complex flow regime with chaotic dynamics.
- Kinematic dynamo theory explains magnetic field generation in conductive flows.
Purpose of the Study:
- Investigate energy transfer across scales in forced 3D MHD turbulence.
- Identify velocity scales responsible for dynamo action.
- Determine how magnetic energy is distributed across different scales.
Main Methods:
- Simulations of forced 3D MHD turbulence.
- Analysis of energy transfer in kinematic dynamo regime.
- Examination of nonhelical Taylor-Green and helical ABC flows.
- Varying magnetic Prandtl number (P(M)).
Main Results:
- Turbulent velocity fluctuations in the inertial range drive small-scale dynamo action.
- Large-scale flows amplify the large-scale magnetic field.
- A direct cascade of magnetic energy from large to small scales complements dynamo action.
- Velocity field energy input to small magnetic scales dominates up to the spectral peak.
Conclusions:
- Small-scale magnetic field amplification is primarily driven by turbulent velocity fluctuations.
- Large-scale magnetic field growth is linked to the large-scale flow.
- Both direct energy transfer and magnetic cascades contribute to magnetic field generation across scales.
Related Concept Videos
01:23Faraday Disk Dynamo
A Faraday disk dynamo is a DC generator, producing an emf that is constant in time. It consists of a conducting disk that rotates with a constant angular velocity in the magnetic field, perpendicular to the disk's plane. The rotation of the disk causes a change in magnetic flux, which induces an emf, causing opposite charges to develop on the rim and in the center of the disk. The polarity of the induced emf can be determined by the direction of the magnetic field and the direction of the...
01:13Torque On A Current Loop In A Magnetic Field
The most common application of magnetic force on current-carrying wires is in electric motors. These consist of loops of wire, which are placed between the magnets with a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate, thus converting electrical energy to mechanical energy.
Consider a rectangular current-carrying loop containing N turns of wire, placed in a uniform magnetic field. The net force on a current-carrying loop...
Consider a rectangular current-carrying loop containing N turns of wire, placed in a uniform magnetic field. The net force on a current-carrying loop...
01:28Magnetostatic Boundary Conditions
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
01:23Energy In A Magnetic Field
If a magnetic field is sustained, there must be a current in a closed circuit or loop, implying some energy has been spent in creating the field. If this energy is not dissipated via the circuit's resistance, it is stored in the field.
Take an ideal inductor with zero resistance. Although it's practically impossible, assume that the coil's resistance is so small that it is practically negligible. The loss of the field's energy to dissipate thermal energy (or heat) is thus negligible.
The energy...
Take an ideal inductor with zero resistance. Although it's practically impossible, assume that the coil's resistance is so small that it is practically negligible. The loss of the field's energy to dissipate thermal energy (or heat) is thus negligible.
The energy...
01:13Magnetic Force Between Two Parallel Currents
Two long, straight, and parallel current-carrying conductors exert a force of equal magnitude on one another. The direction of the force depends on the current direction in the conductors.
The force exerted by the magnetic field due to the first conductor over a finite length of the second conductor is given as the product of the current in the second conductor and the vector product of the length vector along the current element and the field due to the first conductor. According to the...
The force exerted by the magnetic field due to the first conductor over a finite length of the second conductor is given as the product of the current in the second conductor and the vector product of the length vector along the current element and the field due to the first conductor. According to the...
01:24Potential Due to a Magnetized Object
Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
The vector...
The vector...