Quasigeostrophic equations

From Glossary of Meteorology

quasigeostrophic equations

The system of momentum and thermodynamic equations, derived through the quasigeostrophic approximation, that fulfill the requirements of quasigeostrophic theory.

At the momentum level and using the pseudoheight coordinate z = [1 - (p/p0)κ]cpθ0/g the equations are
in which x, y, and z form a Cartesian coordinate system with ug and vg the eastward and northward geostrophic wind components, uag and vag the eastward and northward ageostrophic wind components, w the vertical velocity in the pseudoheight coordinate, φ the geopotential, θ the potential temperature, g the acceleration of gravity, f the Coriolis parameter, ρ the density in z space, θ0 the reference potential temperature, and N the Brunt–Väisälä frequency.