Generation of acoustic and gravity waves by turbulence in an isothermal stratified atmosphere |
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| Authors: | Robert F Stein |
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| Institution: | (1) Columbia University and Goddard Institute for Space Studies, NASA, New York, N. Y.;(2) Present address: California Institute of Technology, Pasadena, Calif., USA |
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| 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 P
ac  103
o
u
o
3
/l
o
M
5 ergs/cm3 sec, and the upward gravity wave flux is F
zgr 102
o
U
o
3
/l
o (l
o ergs/cm3 sec. Here u
0 is the turbulence velocity scale, l
0 is its length scale, and H the scale height at the atmosphere. M = u
0/c
0 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
c = cos–1
 /
2, where
2
2
= ( - 1)/
2 (c
0/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. |
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| Keywords: | |
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