### Abstract

When a horizontal magnetic field B(z) is sheared vertically on a lengthscale L in a diffusionless fluid, critical layers occur at z//c where the local Alfven speed V(z//c) matches the phase speed c of the wave. However, when a vertical field B//z is introduced, all the critical layers disappear. The present study investigates the solution in the neighborhood of z//c when B//z/B is very small, in order to clarify the manner in which the vertical field annihilates the critical layers. It is found that the solution across the critical layer is adjusted in a thin magnetic layer whose thickness is determined by the parameter epsilon **2( equals U/ alpha V, where U, V are measures of the vertical and horizontal components of the Alfven velocity and alpha /L is the horizontal wavenumber). The influence of the vertical field on the resistive instabilities present in its absence is also examined.

Original language | English |
---|---|

Pages (from-to) | 117-130 |

Number of pages | 14 |

Journal | Journal of Fluid Mechanics |

Volume | 167 |

Publication status | Published - Jun 1986 |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*167*, 117-130.

**ON HYDROMAGNETIC CRITICAL LAYERS.** / Eltayeb, I. A.; Hassan, M. H A.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 167, pp. 117-130.

}

TY - JOUR

T1 - ON HYDROMAGNETIC CRITICAL LAYERS.

AU - Eltayeb, I. A.

AU - Hassan, M. H A

PY - 1986/6

Y1 - 1986/6

N2 - When a horizontal magnetic field B(z) is sheared vertically on a lengthscale L in a diffusionless fluid, critical layers occur at z//c where the local Alfven speed V(z//c) matches the phase speed c of the wave. However, when a vertical field B//z is introduced, all the critical layers disappear. The present study investigates the solution in the neighborhood of z//c when B//z/B is very small, in order to clarify the manner in which the vertical field annihilates the critical layers. It is found that the solution across the critical layer is adjusted in a thin magnetic layer whose thickness is determined by the parameter epsilon **2( equals U/ alpha V, where U, V are measures of the vertical and horizontal components of the Alfven velocity and alpha /L is the horizontal wavenumber). The influence of the vertical field on the resistive instabilities present in its absence is also examined.

AB - When a horizontal magnetic field B(z) is sheared vertically on a lengthscale L in a diffusionless fluid, critical layers occur at z//c where the local Alfven speed V(z//c) matches the phase speed c of the wave. However, when a vertical field B//z is introduced, all the critical layers disappear. The present study investigates the solution in the neighborhood of z//c when B//z/B is very small, in order to clarify the manner in which the vertical field annihilates the critical layers. It is found that the solution across the critical layer is adjusted in a thin magnetic layer whose thickness is determined by the parameter epsilon **2( equals U/ alpha V, where U, V are measures of the vertical and horizontal components of the Alfven velocity and alpha /L is the horizontal wavenumber). The influence of the vertical field on the resistive instabilities present in its absence is also examined.

UR - http://www.scopus.com/inward/record.url?scp=0022489540&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022489540&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0022489540

VL - 167

SP - 117

EP - 130

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -