= Internal-wave envelope radiation condition
{title2=$a_T+c_{gz}a_Z=0$}
For a slowly switched-on <plane internal gravity wave> in the half-space $z>0$, the <method of multiple scales> gives transport of its amplitude at the vertical <group velocity>. For $\omega^2=N^2k^2/(k^2+m^2)$, $c_{gz}=-\omega m/(k^2+m^2)$. Initially undisturbed fluid and forcing at the bottom require $c_{gz}>0$. The outgoing <radiation condition> therefore selects $m<0$ when $\omega>0$, although the vertical <phase velocity> is downward.
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