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We derive the approximate pressure profiles, density profiles, andtemperature profiles of an atmosphere, also called barometric formulas. Ourvariant of a derivation goes beyond the common standard exercise of athermodynamics lecture, where commonly the discussion of the underlyingphysical assumptions is missed. We depart from the Navier-Stokes equation andexplicitly point our attention on the physical assumptions disregardedelsewhere. We show that the usual assumptions can be relaxed leading togeneralized formulas that hold even in the case of horizontal winds. Thisfundamental physics has some relevance to the current discussions on theclimate debate.

On The Barometric Formulas And Their Derivation From Hydrodynamics and Thermodynamics