= Dry atmospheric Ertel potential vorticity
{title2=$q_E=\rho^{-1}(\nabla\times\mathbf u+2\boldsymbol\Omega)\cdot\nabla\theta$}
For dry atmospheric thermodynamics, choose <potential temperature> as the materially conserved scalar in <Ertel's theorem>. The displayed density-normalized scalar has units $\mathrm{K\,m^2\,kg^{-1}\,s^{-1}}$. Its conservation in adiabatic inviscid motion depends on conservative body forces and a composition-fixed equation of state. It differs in normalization from the <Boussinesq approximation> convention using buoyancy without the variable density factor. Large-scale balanced weather can be organized by its distribution, with <potential-vorticity inversion> additionally requiring balance and boundary information.
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