= Buoyancy frequency of an ideal-gas stratification
{title2=$N^2=g\left(\frac1\gamma\frac{d\ln p}{dz}-\frac{d\ln\rho}{dz}\right)$}
For uniform composition, upward coordinate $z$ and downward acceleration $g>0$, a pressure-equilibrated adiabatic parcel in a hydrostatic <ideal gas> has $\ddot\zeta=-N^2\zeta$ with $N^2=g[(d\ln p/dz)/\gamma-d\ln\rho/dz]$. A positive value gives restoring <buoyancy>; for a calorically <perfect gas> it is also $(g/c_p)ds/dz$. Heat or composition exchange requires a modified stability test.
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