= Internal-wave response of a sharp buoyancy interface
{title2=$T/W_i=2im/[k(1-S)+im]$}
For a lower uniformly stratified half-space and an upper well-mixed half-space, the <vertical velocity> amplitude is continuous and its derivative jumps by $[W']=-k^2\Delta b\,W/\omega^2$. A wave incident upwards with vertical phase factor $e^{-imz}$ therefore has upper evanescent amplitude $T/W_i=2im/[k(1-S)+im]$, where $m=k\sqrt{N^2/\omega^2-1}$ and $S=\Delta b k/\omega^2$. Its magnitude peaks at $S=1$, with amplitude twice the incident amplitude. Lossless reflection carries all incident <energy> back down; the evanescent upper field carries no mean outgoing vertical energy flux.
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