 Critical level of a shear-flow wave

For a wave with zonal phase velocity $c$ in a basic shear $U(z)$, a critical level is a height $z_c$ at which $U(z_c)=c$. The Doppler-shifted material frequency then vanishes. This means equality of the laboratory velocities; the $U$ and $-c$ terms cancel in the wave frame. It does not mean $U=-c$. A semi-infinite Eady edge wave with zero interior potential vorticity anomaly can remain regular through its steering height.