The Propagation and Stability of Hydromagnetic Waves in a Rotating Cylindrical Annulus with Distorted End-Surfaces

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Abstract

The linear stability of a differentially heated cylindrical annulus, of finite length, containing a dissipationless fluid and rotating uniformly in a nonuniform toroidal magnetic field is studied. The analysis is restricted to the situation where the instabilities are driven by buoyancy. If the end-surfaces are flat, the unstable waves propagate against the basic flow, i.e. westward. When the effect of slight distortions in the end-surfaces on the propagation speeds of these waves are investigated, it is found that these distortions can decrease or increase the propagation speeds depending on a variety of conditions. The application of these results to Hide's (1969) theory on the effects of bumps on the core-mantle interface of the Earth indicates that these topographical features may lead to irregular fluctuations in the westward drift.

Original languageEnglish
Pages (from-to)75-88
Number of pages14
JournalGeophysical and Astrophysical Fluid Dynamics
Volume9
Issue number1
DOIs
Publication statusPublished - 1977

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annuli
magnetohydrodynamic waves
propagation
Buoyancy
buoyancy
Wave propagation
flat surfaces
Earth mantle
Earth (planet)
Magnetic fields
magnetic field
mantle
Fluids
fluid
fluids
magnetic fields
effect
speed
analysis

ASJC Scopus subject areas

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

Cite this

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title = "The Propagation and Stability of Hydromagnetic Waves in a Rotating Cylindrical Annulus with Distorted End-Surfaces",
abstract = "The linear stability of a differentially heated cylindrical annulus, of finite length, containing a dissipationless fluid and rotating uniformly in a nonuniform toroidal magnetic field is studied. The analysis is restricted to the situation where the instabilities are driven by buoyancy. If the end-surfaces are flat, the unstable waves propagate against the basic flow, i.e. westward. When the effect of slight distortions in the end-surfaces on the propagation speeds of these waves are investigated, it is found that these distortions can decrease or increase the propagation speeds depending on a variety of conditions. The application of these results to Hide's (1969) theory on the effects of bumps on the core-mantle interface of the Earth indicates that these topographical features may lead to irregular fluctuations in the westward drift.",
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AB - The linear stability of a differentially heated cylindrical annulus, of finite length, containing a dissipationless fluid and rotating uniformly in a nonuniform toroidal magnetic field is studied. The analysis is restricted to the situation where the instabilities are driven by buoyancy. If the end-surfaces are flat, the unstable waves propagate against the basic flow, i.e. westward. When the effect of slight distortions in the end-surfaces on the propagation speeds of these waves are investigated, it is found that these distortions can decrease or increase the propagation speeds depending on a variety of conditions. The application of these results to Hide's (1969) theory on the effects of bumps on the core-mantle interface of the Earth indicates that these topographical features may lead to irregular fluctuations in the westward drift.

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