Taylor–Goldstein equation

The Taylor–Goldstein equation governs linear two-dimensional disturbances of an inviscid, vertically sheared, stably stratified parallel flow. For horizontal phase velocity $c$, base velocity $U(z)$, buoyancy frequency $N(z)$, and horizontal wavenumber $k$,

The Scorer parameter is the height-dependent coefficient $l^2$ in the stationary atmospheric-wave equation ${\hat{w}}^{\prime \prime }+(l^2-k^2)\hat{w}=0$. Regions with $l^2>k^2$ support vertically oscillatory disturbances, whereas $l^2<k^2$ makes them vertically evanescent.

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.