= Dry parcel buoyancy in a homogeneous atmosphere
{title2=$N^2=(g/T)(dT/dz+g/C_p)$}
For a dry, homogeneous <ideal gas> in <hydrostatic equilibrium>, a displaced parcel undergoing an <adiabatic process> follows $dT/dz=-g/C_p$, where $C_p$ is <specific heat capacity at constant pressure>. At a common pressure its buoyancy depends on its temperature difference from the environment, giving $N^2=(g/T)(dT/dz+g/C_p)$. Negative $N^2$ means growing displacements; zero $N^2$ means neutral stability. This is the homogeneous dry limit of the <Schwarzschild criterion>.
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