Does anybody know who first derived this equation?

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SUMMARY

The discussion centers on the derivation of a differential equation for oscillations of velocity U(z,t) in a vertically stratified atmosphere with a random temperature profile, excluding the Coriolis force. The original poster, seeking references for their work, has not found existing literature on this specific equation. Daniel suggests that similar equations may be found in plasma literature, indicating a potential avenue for further research.

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  • Understanding of differential equations, particularly in atmospheric science.
  • Familiarity with the concepts of stratified atmospheres and temperature profiles.
  • Knowledge of Coriolis force and its effects on atmospheric dynamics.
  • Basic principles of plasma physics and its literature.
NEXT STEPS
  • Research differential equations in atmospheric science literature.
  • Explore plasma physics texts for related equations and concepts.
  • Investigate the role of temperature profiles in stratified atmospheres.
  • Review academic articles on oscillatory motion in fluid dynamics.
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Researchers in atmospheric science, physicists studying fluid dynamics, and anyone interested in the mathematical modeling of oscillations in stratified environments.

9smartcats
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Does anybody know who first derived this equation?
(attached)
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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    Ðовый риÑунок (1).png
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I guess you may find something like this in plasma literature.

Good luck :)
 

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