Advertisement

Solar Physics

, Volume 2, Issue 4, pp 385–432 | Cite as

Generation of acoustic and gravity waves by turbulence in an isothermal stratified atmosphere

  • Robert F. Stein
Article

Abstract

Lighthill's method of calculating the aerodynamic emission of sound waves in a homogeneous atmosphere is extended to calculate the acoustic and gravity-wave emission by turbulent motions in a stratified atmosphere. The acoustic power output is Pac ≈ 103θou o 3 /loM5 ergs/cm3 sec, and the upward gravity wave flux is Fzgr ≈ 102θoU o 3 /lo (lo ergs/cm3 sec. Here u0 is the turbulence velocity scale, l0 is its length scale, and H the scale height at the atmosphere. M = u0/c0 is the Mach number of the turbulence. The acoustic power output is proportional to the maximum value of the turbulence spectrum, and inversely to its rate of falloff at high frequencies. The stratification cuts off the acoustic emission at low Mach numbers. The gravity emission occurs near the critical angle to the vertical θc = cos−1ω/ω2, where ω 2 2 = (γ - 1)/γ2 (c0/H), and at very short wavelengths. It is proportional to the large wave number tail of the turbulence spectrum. On the sun, gravity-wave emission is much more efficient than acoustic, but can occur only from turbulent motions in stable regions, whereas acoustic waves are produced by turbulence in the convection zone.

Keywords

Mach Number Acoustic Emission Gravity Wave Sound Wave Critical Angle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Batchelor, G. K.: 1953, Homogeneous Turbulence. Cambridge University Press, London.Google Scholar
  2. Brunt, D.: 1927, Quart. J. Roy. Meteorol. Soc. 53, 30.Google Scholar
  3. Curle, N.: 1955, Proc. Roy. Soc. A231, 505.Google Scholar
  4. Eckart, C.: 1960, Hydrodynamics of Oceans and Atmospheres. Pergamon Press, New York.Google Scholar
  5. Ffowcs Williams, J. E.: 1963, Phil. Trans. Roy. Soc. London A255, 469.Google Scholar
  6. Kato, S.: 1966, Astrophys. J. 143, 893.Google Scholar
  7. Kraichnan, R. H.: 1957, Phys. Rev. 107, 1485.Google Scholar
  8. Kraichnan, R. H.: 1965, private communication.Google Scholar
  9. Lamb, H.: 1945, Hydrodynamics. 6th ed., Dover, New York.Google Scholar
  10. Lighthill, M. J.: 1952, Proc. Roy. Soc. A211, 564.Google Scholar
  11. Lighthill, M. J.: 1954, Proc. Roy. Soc. A222, 1.Google Scholar
  12. Lighthill, M. J.: 1955, I.A.U. Symposium No. 2: Gas Dynamics of Cosmic Clouds. North-Holland Publ. Co., Amsterdam.Google Scholar
  13. Lighthill, M. J.: 1960, Phil. Trans. Roy. Soc. London A252, 397.Google Scholar
  14. Meecham, W. C. and Ford, G. W.: 1955, J. Acous. Soc. Amer. 30, 318.Google Scholar
  15. Moore, D. W. and Spiegel, E. A.: 1964, Astrophys. J. 139, 48.Google Scholar
  16. Muller, E. A. and Matschat, K. R.: 1958, Z. Flugwissenschaft 6, 161.Google Scholar
  17. Parker, E. N.: 1953, Phys. Rev. 90, 240.Google Scholar
  18. Proudman, I.: 1952, Proc. Roy. Soc. A214, 119.Google Scholar
  19. Unno, W.: 1964, Transactions I.A.U. XIIB, Academic Press, New York, p. 555.Google Scholar
  20. Unno, W. and Kato, S.: 1964, Publ. Astron. Soc. Japan 14, 417.Google Scholar
  21. Väisälä, V.: 1925, Soc. Sci. Fennica, Commentationes Phys.-Math. II 19, 37.Google Scholar

Copyright information

© D. Reidel Publishing Company 1967

Authors and Affiliations

  • Robert F. Stein
    • 1
  1. 1.Columbia University and Goddard Institute for Space Studies, NASANew York

Personalised recommendations