Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T14:18:41.907Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stability and over-reflexion of hydromagnetic–gravity waves

Published online by Cambridge University Press:  20 April 2006

I. A. Eltayeb
I. A. Eltayeb
Affiliation:
School of Mathematics, The University, Newcastle-upon-Tyne
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of a magnetic-velocity shear layer, of thickness L, to hydromagnetic-gravity waves of zonal wavenumber k is investigated analytically, within the Boussinesq approximation, in the situation where ε(= kL) is small. It is found that, in addition to the unstable modes of the corresponding sheet, new modes of instability of growth rate of order ε2 are also present provided one critical level exists within the layer. The existence of one critical level also effects over-reflexion of stable modes. Furthermore it is shown that a magnetic shear acting alone can lead to instability as well as effecting over-reflexion of stable modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 105 , April 1981 , pp. 1 - 18
Copyright
© 1981 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acheson, D. J. 1976 On over-reflexion. J. Fluid Mech. 77, 433.Google Scholar
Ahmed, B. A. & Eltayeb, I. A. 1980 On the propagation, reflexion, transmission and stability of atmospheric Rossby-gravity waves on a beta-plane in the presence of latitudinally sheared zonal flows. Phil. Trans. Roy. Soc. A 298, 45.Google Scholar
Baldwin, P. & Roberts, P. H. 1970 The critical layer in stratified shear flow. Mathematika 17, 102.Google Scholar
Baldwin, P. & Roberts, P. H. 1972 On resistive instabilities. Phil. Trans. Roy. Soc. A 272, 303.Google Scholar
Blumen, W., Drazin, P. G. & Billings, D. F. 1975 Shear layer instability of an inviscid compressible fluid. 2. J. Fluid Mech. 71, 305.Google Scholar
Booker, J. R. & Bretherton, F. P. 1967 The critical layer for internal gravity waves in a shear flow. J. Fluid Mech. 27, 513.Google Scholar
Dickinson, R. E. 1968 Planetary Rossby waves propagating vertically through westerly wind wave guides. J. Atmos. Sci. 25, 984.Google Scholar
Drazin, P. G. & Davey, A. 1977 Shear layer instability of an inviscid compressible fluid. Part 3. J. Fluid Mech. 82, 255.Google Scholar
Drazin, P. G. & Howard, L. N. 1966 Hydrodynamic stability of parallel flow of inviscid fluid. Adv. Appl. Mech. 9, 1.Google Scholar
El Mekki, O. M. H., Eltayeb, I. A & McKenzie, J. F. 1978 Hydromagnetic-gravity wave critical levels in the solar atmosphere. Solar Phys. 57, 261.Google Scholar
El Sawi, M. & Eltayeb, I. A. 1978 On the propagation of hydromagnetic-inertial-gravity waves in magnetic-velocity shear. Geophys. Astrophys. Fluid Dyn. 10, 289.Google Scholar
Eltayeb, I. A. 1977 On linear wave motions in magnetic-velocity shears. Phil. Trans. Roy. Soc. A 285, 607.Google Scholar
Eltayeb, I. A. & McKenzie, J. F. 1975 Critical level behaviour and wave amplification of a gravity wave incident upon a shear layer. J. Fluid Mech. 72, 661.Google Scholar
Eltayeb, I. A. & McKenzie, J. F. 1977 Propagation of hydromagnetic planetary waves on a beta-plane through magnetic and velocity shear. J. Fluid Mech. 81, 1.Google Scholar
Fejer, J. A. 1964 Hydromagnetic stability at a fluid velocity discontinuity between compressible fluids. Phys. Fluids 7, 499.Google Scholar
Grimshaw, R. H. J. 1976 Nonlinear aspects of an internal gravity wave coexisting with an unstable mode associated with a Helmholtz velocity profile. J. Fluid Mech. 76, 65.Google Scholar
Lighthill, M. J. 1965 Group velocity. J. Inst. Maths. Appl. 1, 1.Google Scholar
McKenzie, J. F. 1970 Hydromagnetic wave interaction with the magneto-pause and the bow shock. Planet. Space Sci. 18, 1.Google Scholar
Miles, J. W. 1957 On the reflexion of sound at an interface of relative motion. J. Acoust. Soc. Am. 29, 226.Google Scholar
Miles, J. W. 1961 On the stability of heterogeneous shear flows. J. Fluid Mech. 10, 496.Google Scholar
Moffatt, H. K. 1976 Generation of magnetic fields by fluid motions. Adv. Appl. Mech. 16, 119.Google Scholar