= Localized wave-drag response in a stratified channel
{title2=$m=\pi N/(|f_0|L)$}
For a sinusoidal <Eliassen–Palm flux> whose vertical divergence is constant in $-D<z<D$ and zero elsewhere, the <residual mean circulation> is determined by a forced one-dimensional modified Helmholtz equation. With $v^*=C'(z)\sin(\pi y/L)$ and $w^*=-(\pi/L)C(z)\cos(\pi y/L)$, a forcing proportional to $-G_0\sin(\pi y/L)/(2D)$ gives
$$
C(z)=\frac{G_0}{4f_0Dm}\left[e^{-m|z-D|}-e^{-m|z+D|}\right].
$$
The response is uniquely selected by decay of the residual circulation at both vertical infinities. An <Eulerian mean> vertical flow can persist in the undamped wave region even where this residual response vanishes.
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