Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-21T17:57:29.969Z Has data issue: false hasContentIssue false

Valve effect of inhomogeneities on anisotropic wave propagation

Published online by Cambridge University Press:  29 March 2006

D. J. Acheson
Affiliation:
Geophysical Fluid Dynamics Laboratory, Meteorological Office, Bracknell, Berkshire

Abstract

A recent investigation of hydromagnetic waves in a rotating fluid has revealed certain ‘valve’-like critical levels associated with each wave which can be effectively penetrated from one side only. This effect is illustrated in the present paper by means of two further examples, namely (a) the propagation of hydromagnetio-gravity waves in a non-uniform magnetic field, and (b) the propagation of internal gravity waves in a wind which, though unidirectional, is both horizontally and vertically sheared.

Type
Research Article
Copyright
© 1973 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. 1971 The magnetohydrodynamics of rotating fluids. PhD. thesis, University of East Anglia.
Acheson, D. J. 1972a The critical level for hydromagnetic waves in a rotating fluid. J. Fluid Meoh. 53, 401415.Google Scholar
Acheson, D. J. 1972b Hydromagnetic waves and instabilities in rotating and stratified fluids. In preparation.
Acheson, D. J. 1972c On the hydromagnetic stability of a rotating fluid annulus. J. Fluid Mech. 52, 529541.Google Scholar
Acheson, D. J. & Hide, R. 1973 Hydromagnetics of rotating fluids. Rep. Prog. Phys. 36, 159221.Google Scholar
Alfvén, H. & Falthammar, C. O. 1963 Oosmical Electrodynamics. 2nd edn. Oxford University Press.
Baldwin, P. & Roberts, P. H. 1970 The critical layer in stratified shear flow. Mathematika, 17, 102119.Google Scholar
Baldwin, P. & Roberts, P. H. 1972 On resistive instabilities. Phil. Tram. Roy. SOC. A 272, 303330.Google Scholar
Booker, J. R. & Bretherton, F. P. 1967 The critical layer for internal gravity waves in a shear flow. J. Fluid Mech. 27, 513539.Google Scholar
Breeding, R. J. 1971 A non-linear investigation of critical levels for internal atmospheric gravity waves. J. Fluid Mech. 50, 545563.Google Scholar
Bretherton, F. P. 1966 The propagation of groups of internal gravity waves in a shear flow. Quart. J. Roy. Met. SOC. 92, 466480.Google Scholar
Bretherton, F. P. 1969 Momentum transport by gravity waves. Quart. J. Roy. Met. Soc. 95, 213243.Google Scholar
Chandraserhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Eliassen, A. & Palm, E. 1960 On the transfer of energy in stationary mountain waves. Geof. Publ. 22 (3), 1.Google Scholar
Furth, H. P., Killeen, J. & Rosenbluth, M. N. 1963 Finite-resistivity in stabilities of a sheet pinch. Phys. Fluids, 6, 459484.Google Scholar
Hazel, P. 1967 The effect of viscosity and heat conduction on internal gravity waves at a critical level. J. Fluid Mech. 30, 775783.Google Scholar
Hide, R. 1969 On hydromagnetic waves in a stratified rotating incompressible fluid. J. Fluid Mech. 39, 283288.Google Scholar
Hide, R. & Stewartson, K. 1972 Hydromagnetic oscillations of the Earth's core. Rev. Geophys. & Space Phys. 10, 579598.Google Scholar
Howard, L. N. 1961 Note on a paper of John W. Miles. J. Fluid Mech. 10, 509512.Google Scholar
Jones, W. L. 1967 Propagation of internal gravity waves in fluids with shear flow and rotation. J. fluid Mech. 30, 439448.Google Scholar
Jones, W. L. 1968 Reflexion and stability of waves in stably stratified fluids with shear flow: a numerical study. J. Fluid Mech. 34, 609624.Google Scholar
Lehnert, B. 1954 Magnetohydrodynamic waves under the action of the Coriolis force. Astrophys. J. 119, 647654.Google Scholar
Liuhthill, M. J. 1965 Group velocity. J. Inst. Math. Appl. 1, 128.Google Scholar
Lindzen, R. S. 1970 Internal equatorial planetary-scale waves in shear flow. J. Atmos. Sci. 27, 394407.Google Scholar
Lindzen, R. S. & Holton, J. R. 1968 A theory of the quasi-biennial oscillation. J. Atmos. Sci. 25, 10951107.Google Scholar
Mckenzie, J. F. 1972 Reflection and amplification of acousticgravity waves at a density and velocity discontinuity. J. Geophys. Res. 77, 29152926.Google Scholar
Mckenzie, J. F. 1973 On the existence of critical levels, with applications to hydro-magnetic waves. Submitted to J. Fluid Mech.Google Scholar
Miles, J. W. 1961 On the stability of heterogeneous shear flows. J. Fluid Mech. 10, 496808.Google Scholar
Mofbatt, H. K. 1972 An approach to a dynamic theory of dynamo action in a rotating conducting fluid. J. Fluid Mech. 53, 385399.Google Scholar
Roberts, P.H. & Soward, A.M. 1972 Magnetohydrodynamics of the Earth's core. Ann. Rev. Fluid Mech. 4, 117154.Google Scholar
Yih, C.-S. 1969 Stratified flows. Ann. Rev. Fluid Mech. 1, 73110.Google Scholar