Does anybody know who first derived this equation?

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The discussion revolves around the search for the original derivation of a differential equation related to oscillations of velocity in a vertically stratified atmosphere with a random temperature profile, excluding Coriolis force. The poster has derived the equation but cannot find any existing literature referencing it. A suggestion is made to explore plasma literature for potential sources. The community is encouraged to provide any relevant references or insights. The inquiry highlights the challenges of finding specific academic sources in niche areas of study.
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Does anybody know who first derived this equation?
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It is differential equation for oscillations of velocity U(z,t) of a vertically stratified atmosphere with random temperature profile without Coriolis force . I derived it in my work but could not find it anywhere in literature. I hope that someone might know some source (book or article) as a reference.
Please help me.


Daniel
 

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I guess you may find something like this in plasma literature.

Good luck :)
 

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