# Resistive and viscous dynamics of finite-amplitude shear waves at a magnetic X-point

## Abstract

The dynamics and dissipation of axial shear waves, superposed on a planar magnetic X-point in a resistive viscous incompressible plasma, are analyzed numerically and analytically. The interplay of viscous and resistive effects is demonstrated by deriving solutions for various values of the scalar coefficients of viscosity and resistivity. These solutions show that viscous-resistive coupling can dramatically affect the global energy dissipation. When either viscosity or resistivity vanishes, the solutions are characterized by oscillatory decaying eigenmodes that maintain equipartition between the magnetic and kinetic energies. This behavior persists when resistivity is the dominant dissipation mechanism. When viscosity is the dominant dissipation mechanism, initial oscillations are followed by exponential decay at sufficiently long times. The applicability of the results to flares in solar active regions, where the viscous Reynolds number can be much smaller than the resistive one, is discussed.

- Authors:

- Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton (New Zealand)
- (United States)

- Publication Date:

- OSTI Identifier:
- 20782327

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 12; Journal Issue: 11; Other Information: DOI: 10.1063/1.2132249; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; CHARGED-PARTICLE TRANSPORT; COUPLING; ENERGY LOSSES; KINETIC ENERGY; MAGNETOHYDRODYNAMICS; MATHEMATICAL SOLUTIONS; NUMERICAL ANALYSIS; PLASMA; PLASMA INSTABILITY; PLASMA WAVES; REYNOLDS NUMBER; SCALARS; SHEAR; SOLAR FLARES; VISCOSITY

### Citation Formats

```
Craig, I.J.D., Litvinenko, Yuri E., and Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Durham, New Hampshire 03824-3525.
```*Resistive and viscous dynamics of finite-amplitude shear waves at a magnetic X-point*. United States: N. p., 2005.
Web. doi:10.1063/1.2132249.

```
Craig, I.J.D., Litvinenko, Yuri E., & Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Durham, New Hampshire 03824-3525.
```*Resistive and viscous dynamics of finite-amplitude shear waves at a magnetic X-point*. United States. doi:10.1063/1.2132249.

```
Craig, I.J.D., Litvinenko, Yuri E., and Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Durham, New Hampshire 03824-3525. Tue .
"Resistive and viscous dynamics of finite-amplitude shear waves at a magnetic X-point". United States.
doi:10.1063/1.2132249.
```

```
@article{osti_20782327,
```

title = {Resistive and viscous dynamics of finite-amplitude shear waves at a magnetic X-point},

author = {Craig, I.J.D. and Litvinenko, Yuri E. and Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Durham, New Hampshire 03824-3525},

abstractNote = {The dynamics and dissipation of axial shear waves, superposed on a planar magnetic X-point in a resistive viscous incompressible plasma, are analyzed numerically and analytically. The interplay of viscous and resistive effects is demonstrated by deriving solutions for various values of the scalar coefficients of viscosity and resistivity. These solutions show that viscous-resistive coupling can dramatically affect the global energy dissipation. When either viscosity or resistivity vanishes, the solutions are characterized by oscillatory decaying eigenmodes that maintain equipartition between the magnetic and kinetic energies. This behavior persists when resistivity is the dominant dissipation mechanism. When viscosity is the dominant dissipation mechanism, initial oscillations are followed by exponential decay at sufficiently long times. The applicability of the results to flares in solar active regions, where the viscous Reynolds number can be much smaller than the resistive one, is discussed.},

doi = {10.1063/1.2132249},

journal = {Physics of Plasmas},

number = 11,

volume = 12,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}