### Abstract

The propagation properties of hydromagnetic-inertial-gravity waves in a Boussinesq fluid are studied for two representative models. One model is characterised by horizontal rotation, magnetic field and flow, the magnetic field and flow being perpendicular and vertically sheared. In the other model both magnetic field and rotation are vertical and uniform but the flow is horizontal and latitudinally sheared. In a slowly varying shear, when the WKBJ approximation is applicable, the wave normal surfaces for different values of magnetic field and flow are used to construct the various types of ray trajectories. In a full wave treatment, in which variations in the basic state are taken into account, it is found that the total wave energy flux (or the wave action flux), d, in the direction of the shear is constant except at critical layers (i.e. singularities predicted by the WKBJ treatment), where it jumps from one constant value to another. The invariance of d is used to show that MAC-waves can be over-reflected by a finite shear layer free of critical layers. By adopting the correct matching procedure across critical layers the influence of hydromagnetic critical layers on the reflexion of hydromagnetic-inertial-gravity waves by finite shear layers is investigated. It is found that such critical layers can facilitate over-reflexion by ‘emitting‘ energy flux.

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

Pages (from-to) | 289-309 |

Number of pages | 21 |

Journal | Geophysical and Astrophysical Fluid Dynamics |

Volume | 10 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 1978 |

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### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics
- Computational Mechanics
- Astronomy and Astrophysics
- Mechanics of Materials

### Cite this

**On the Propagation of Hydromagnetic-Inertial-Gravity Waves in Magnetic-Velocity Shear.** / Sawi, M. El; Eltayeb, I. A.

Research output: Contribution to journal › Article

*Geophysical and Astrophysical Fluid Dynamics*, vol. 10, no. 1, pp. 289-309. https://doi.org/10.1080/03091927808242642

}

TY - JOUR

T1 - On the Propagation of Hydromagnetic-Inertial-Gravity Waves in Magnetic-Velocity Shear

AU - Sawi, M. El

AU - Eltayeb, I. A.

PY - 1978/1/1

Y1 - 1978/1/1

N2 - The propagation properties of hydromagnetic-inertial-gravity waves in a Boussinesq fluid are studied for two representative models. One model is characterised by horizontal rotation, magnetic field and flow, the magnetic field and flow being perpendicular and vertically sheared. In the other model both magnetic field and rotation are vertical and uniform but the flow is horizontal and latitudinally sheared. In a slowly varying shear, when the WKBJ approximation is applicable, the wave normal surfaces for different values of magnetic field and flow are used to construct the various types of ray trajectories. In a full wave treatment, in which variations in the basic state are taken into account, it is found that the total wave energy flux (or the wave action flux), d, in the direction of the shear is constant except at critical layers (i.e. singularities predicted by the WKBJ treatment), where it jumps from one constant value to another. The invariance of d is used to show that MAC-waves can be over-reflected by a finite shear layer free of critical layers. By adopting the correct matching procedure across critical layers the influence of hydromagnetic critical layers on the reflexion of hydromagnetic-inertial-gravity waves by finite shear layers is investigated. It is found that such critical layers can facilitate over-reflexion by ‘emitting‘ energy flux.

AB - The propagation properties of hydromagnetic-inertial-gravity waves in a Boussinesq fluid are studied for two representative models. One model is characterised by horizontal rotation, magnetic field and flow, the magnetic field and flow being perpendicular and vertically sheared. In the other model both magnetic field and rotation are vertical and uniform but the flow is horizontal and latitudinally sheared. In a slowly varying shear, when the WKBJ approximation is applicable, the wave normal surfaces for different values of magnetic field and flow are used to construct the various types of ray trajectories. In a full wave treatment, in which variations in the basic state are taken into account, it is found that the total wave energy flux (or the wave action flux), d, in the direction of the shear is constant except at critical layers (i.e. singularities predicted by the WKBJ treatment), where it jumps from one constant value to another. The invariance of d is used to show that MAC-waves can be over-reflected by a finite shear layer free of critical layers. By adopting the correct matching procedure across critical layers the influence of hydromagnetic critical layers on the reflexion of hydromagnetic-inertial-gravity waves by finite shear layers is investigated. It is found that such critical layers can facilitate over-reflexion by ‘emitting‘ energy flux.

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U2 - 10.1080/03091927808242642

DO - 10.1080/03091927808242642

M3 - Article

AN - SCOPUS:84963458204

VL - 10

SP - 289

EP - 309

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

SN - 0309-1929

IS - 1

ER -