Approximate Equations for Large Scale Atmospheric Motions

TL;DR

This paper systematically derives a set of simplified equations for large-scale atmospheric motions using a small parameter expansion, resulting in hydrostatic and geostrophic equations similar to Charney's model.

Contribution

It introduces a new derivation method for atmospheric equations based on variable scaling and power series expansion, providing a rigorous foundation for existing models.

Findings

Derivation of hydrostatic pressure equations

Derivation of geostrophic wind equations

Equations align with Charney's model

Abstract

A systematic derivation of a set of equations governing large scale atmospheric motions is presented. They are derived by introducing new variables scaled in terms of a small parameter.The solution is expanded in powers of this parameter.This leads to the hydrostatic pressure and geostrophic wind equations.The resulting set of equations is similar to that proposed by J. Charney.