Vertical trapping of an atmospheric gravity wave

An atmospheric internal gravity wave is vertically trapped when its squared vertical wavenumber changes from positive to negative with altitude. A decrease of the Scorer parameter, caused for example by increasing wind speed or decreasing buoyancy frequency, creates a turning level and an evanescent upper region.

A vertically propagating stationary topographic internal gravity wave meets a turning level when its squared vertical wavenumber changes from positive to negative. The stationary internal-wave WKB solution then fails locally. A simple zero is resolved by an Airy function transition connecting incident and reflected waves below to a decaying evanescent wave above. For negligible wind curvature the condition is $|kU(z_t)|=N(z_t)$, distinct from the zero-intrinsic-frequency critical layer in a shear flow.

For constant buoyancy frequency $N$ and $U=U_0+Sz$ with $S>0$, a stationary component of horizontal wavenumber $k$ turns at $z_t=(N/k-U_0)/S$ if it propagates at the source. Its vertical wavenumber vanishes there; WKB approximation fails and an Airy function transition connects reflection to an upper evanescent wave.