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


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.


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.


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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

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