Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-02-11T12:06:18.249Z Has data issue: false hasContentIssue false
  • English
  • Français

On the generation and radiation of magneto-acoustic waves

Published online by Cambridge University Press:  12 April 2006

L. M. B. C. Campos
L. M. B. C. Campos
Affiliation:
Engineering Department, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

The generation, and thence the dissipation, propagation and radiation, of waves in a compressible fluid subjected to a magnetic field is studied as an extension of the ‘acoustic analogy’ (Lighthill 1952) to magneto-acoustics. A formal theory of magneto-acoustic waves introduces (i) a single differential operator describing propagation, (ii) a dynamic and a magnetic tensor modelling generation and (iii) a dissipation tensor to complete the wave equation. The interpretation of these tensors indicates the magnitude of the physical processes of wave generation, by turbulence and inhomogeneities, and of wave dissipation, by viscous and electrical resistance and heat conduction. The total quadrupole components are classified according to the mode of emission. If the magnetic field or compressibility is neglected we obtain, respectively, ‘aerodynamic acoustics’ and a corresponding theory for Alfvén waves. These hydrodynamic and hydromagnetic results contrast with magnetodynamics, when the magnetic field is dominant. The magneto-acoustic far field implies a law of directivity and intensity of radiation. The main results have been collected in three summary tables (see appendix).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 81 , Issue 3 , 13 July 1977 , pp. 529 - 549
Copyright
© 1977 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

Alfvén, H. 1942 The existence of electromagnetic — hydrodynamic waves. Ark. Mat. Astr. Fys. B 29 (2), 1.
Alfvén, H. 1943 On sunspots and the solar cycle. Ark. Mat. Astr. Fys. A 29 (2), 1.
Alfvén, H. 1948 Cosmical Electrodynamics, Oxford University Press.
Alfvén, H. & Falthammar, C. G. 1962 Cosmical Electrodynamics. Oxford University Press.
Astrom, E. 1950 Magnetohydrodynamic waves in a plasma. Nature 165, 1019.Google Scholar
Batchelor, G. K. 1950 On the spontaneous magnetic field in a conducting fluid in turbulent motion. Proc. Roy. Soc. A 201, 406.Google Scholar
Candel, S. M. 1972 Analytical studies of some acoustic problems of jet engines. Ph.D. thesis, Caltech.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Chapman, S. & Cowling, T. G. 1952 The Mathematical Theory of Non-Uniform Gases. Cambridge University Press.
Cowling, T. G. 1957 Magnetohydrodynamics. Interscience.
Curle, N. 1955 On the influence of solid boundaries upon aerodynamic sound. Proc. Roy. Soc. A 231, 505.Google Scholar
D'Alembert, J. Le R. 1747 Recherches sur les vibrations des cordes. Mém. Acad. Sci. Paris. (See Opuscules Math., vol. 1, p. 1.)
Ffowcs Williams, J. E. 1963 The noise from turbulence convected at high speed. Phil. Trans. Roy. Soc. A 255, 469.Google Scholar
Ffowcs Williams, J. E. & Hawkins, D. L. 1968 Generation of sound by turbulence and surfaces in arbitrary motion. Phil. Trans. Roy. Soc. A 264, 321.Google Scholar
Herlofson, N. 1950 Waves in a compressible fluid conductor. Nature 165, 1020.Google Scholar
Howe, M. S. 1969 On gravity-coupled magnetohydrodynamic waves in the sun's atmosphere. Astrophys. J. 156, 27.Google Scholar
Howe, M. S. 1975a The generation of sound by aerodynamic sources in an inhomogeneous steady flow. J. Fluid Mech. 67, 597.Google Scholar
Howe, M. S. 1975b Contribution to the theory of aerodynamic sound with application to excess jet noise and the theory of the flute. J. Fluid Mech. 71, 625.Google Scholar
Jeans, J. 1968 Science and Music. Dover.
Landau, L. D. & Lifshitz, E. M. 1959 Course of Theoretical Physics, vols 2, 5, 6, 8. Pergamon.
Lehnert, B. 1952 On the behaviour of an electrically conductive liquid in a magnetic field. Ark. Fys. 5, 69.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically. Proc. Roy. Soc. A 211, 564.Google Scholar
Lighthill, M. J. 1960 Studies on magneto hydrodynamic waves and other anisotropic wave motions. Phil. Trans. Roy. Soc. A 252, 397.Google Scholar
Lighthill, M. J. 1967 Predictions on the velocity field coming from acoustic noise and generalized turbulence in a layer overlying a convectively unstable atmospheric region. I.A.U. Symp. no. 28, p. 429.Google Scholar
Lundquist, S. 1949 Experimental investigation of magnetohydrodynamic waves. Phys. Rev. 76, 1805.Google Scholar
Moffatt, H. K. 1976 Generation of magnetic fields by fluid motion. Adv. in Appl. Mech. 16, 119.Google Scholar
Moore, D. W. & Spiegel, E. A. 1964 The generation and propagation of waves in a compressible atmosphere, Astrophys. J. 139, 48.Google Scholar
Phillips, O. M. 1960 On the generation of sound by supersonic turbulent shear layers. J. Fluid Mech. 9, 1.Google Scholar
Powell, A. 1961 Vortex sound. Dept. Engng, U.C.L.A. Rep. no. 61–70.Google Scholar
Rayleigh, Lord 1877 The Theory of Sound. Reprinted by Dover, 1945.
Shermann, A. & Sutton, G. W. 1965 Engineering Magneto Hydro Dynamics. McGraw-Hill.