= Stationary internal-wave WKB solution
{title2=$w\sim m^{-1/2}e^{i(kx+\int m\,dz)}$}
For a stationary <internal gravity wave>, the <Taylor–Goldstein equation> gives $m^2=N^2/U^2-U''/U-k^2$. In a propagating interval with slowly varying $m$, the <WKB approximation> has amplitude proportional to $m^{-1/2}$ and phase derivative $m$. The conditions $|m'|\ll m^2$ and $|m''|\ll |m|^3$ fail at a regular turning level. With $U>0$, the upward branch has $m>0$ and negative <intrinsic frequency>; laboratory <group velocity> is $U(k^2,km)/(k^2+m^2)$ when the curvature term is negligible.
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