Related Experiment Video
Updated: Jun 21, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Energy transfers in shell models for magnetohydrodynamics turbulence
Thomas Lessinnes1, Daniele Carati, Mahendra K Verma
1Physique Statistique et Plasmas, CP231, Université Libre de Bruxelles, B-1050 Bruxelles, Belgium.
Summary
This study introduces a systematic method for creating shell models of magnetohydrodynamic turbulence. It ensures conservation of key invariants and offers new insights into energy fluxes in these models.
Area of Science:
- Physics
- Fluid Dynamics
- Plasma Physics
Background:
- Magnetohydrodynamic (MHD) turbulence is crucial in astrophysical and laboratory plasmas.
- Existing shell models simplify MHD turbulence but have limitations in accurately representing conserved quantities.
- Understanding energy transfer mechanisms is key to modeling turbulent phenomena.
Purpose of the Study:
- To develop a systematic procedure for deriving shell models of MHD turbulence.
- To ensure the conservation of ideal quadratic invariants within these models.
- To provide clear definitions and simple expressions for energy exchanges and fluxes.
Main Methods:
- Proposed a systematic derivation procedure for shell models.
- Incorporated conservation laws for total energy, cross helicity, and magnetic helicity.
- Accounted for magnetic energy conservation via the advection term in the induction equation.
Main Results:
- Derived shell models that conserve ideal quadratic invariants.
- Obtained simplified expressions for energy exchanges between shells.
- Defined energy fluxes unambiguously.
- Reproduced known shell models and suggested reinterpretation of energy fluxes.
Conclusions:
- The proposed procedure offers a rigorous framework for constructing MHD shell models.
- The method ensures physical consistency by preserving fundamental invariants.
- The findings provide a refined understanding of energy cascade mechanisms in MHD turbulence.
Related Concept Videos
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...
01:29Maxwell's Equation Of Electromagnetism
James Clerk Maxwell (1831–1879) was one of the major contributors to physics in the nineteenth century. Although he died young, he made major contributions to the development of the kinetic theory of gases, to the understanding of color vision, and to understanding the nature of Saturn's rings. He is probably best known for having combined existing knowledge on the laws of electricity and magnetism with his insights into a complete overarching electromagnetic theory, which is represented by...
01:24Energy 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...
01:17Magnetic Damping
Eddy currents can produce significant drag on motion, called magnetic damping. For instance, when a metallic pendulum bob swings between the poles of a strong magnet, significant drag acts on the bob as it enters and leaves the field, quickly damping the motion.
If, however, the bob is a slotted metal plate, the magnet produces a much smaller effect. When a slotted metal plate enters the field, an emf is induced by the change in flux; however, it is less effective because the slots limit the...
If, however, the bob is a slotted metal plate, the magnet produces a much smaller effect. When a slotted metal plate enters the field, an emf is induced by the change in flux; however, it is less effective because the slots limit 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...
01:16Energy Conservation and Bernoulli's Equation
Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...