Vertically integrated wave-drag acceleration (${\int }_{-\infty }^{\infty }{\overline{u}}_{t}dz=-G_0\sin (\pi y/L)$)

In the localized wave-drag response in a stratified channel, the full vertical integral of zonal acceleration equals the deposited wave momentum, $-G_0\sin (\pi y/L)$. The fraction inside the directly forced layer is $1-(1-e^{-2s})/(2s)$, where $s=\pi ND/(|f_0|L)$. A small $s$ spreads most acceleration outside the dissipation layer; a large $s$ confines most of it inside.