Critical-height approach of a stationary wave in linear shear
= Critical-height approach of a stationary wave in linear shear
{title2=$z_c=U_0/|S|$}
For $S<0$ and constant positive <buoyancy frequency>, the critical height is $U_0/|S|$. A stationary upward ray approaches it with vertical <group velocity> proportional to $U^2$, requiring infinite ideal ray travel time. Large <gradient Richardson number> can preserve the short-wavelength <WKB approximation>, but parcel-displacement amplitude grows and eventually invalidates linearity.