On The Barometric Formulas And Their Derivation From Hydrodynamics and Thermodynamics

TL;DR

This paper derives generalized atmospheric pressure, density, and temperature profiles from hydrodynamics and thermodynamics, explicitly examining assumptions and extending formulas to include horizontal winds, with implications for climate discussions.

Contribution

It presents a derivation of barometric formulas that relax common assumptions, incorporating horizontal winds and clarifying physical assumptions often overlooked.

Findings

Derived generalized pressure and temperature profiles.

Relaxed assumptions allow for horizontal wind effects.

Relevance to climate debate discussions.

Abstract

We derive the approximate pressure profiles, density profiles, and temperature profiles of an atmosphere, also called barometric formulas. Our variant of a derivation goes beyond the common standard exercise of a thermodynamics lecture, where commonly the discussion of the underlying physical assumptions is missed. We depart from the Navier-Stokes equation and explicitly point our attention on the physical assumptions disregarded elsewhere. We show that the usual assumptions can be relaxed leading to generalized formulas that hold even in the case of horizontal winds. This fundamental physics has some relevance to the current discussions on the climate debate.