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For the normal modethe linear material derivative becomesSubstitution into the equation from part b and division by $-k^2(\overline{u}-c{)}^2$ gives the Taylor–Goldstein equationwhereand the Scorer parameter is

For a ridge-fixed disturbance, $c=0$. If the Scorer parameter varies on a height scale much longer than the vertical wavelength, the local WKB approximation giveswhere $m^2=l^2-k^2>0$. The disturbance is vertically oscillatory there and can carry wave activity upward. Where $l^2<k^2$, $m$ is imaginary and the solution is vertically evanescent.

A rigid ridge supplies the lower boundary condition and an upper radiation or decay condition selects the physical solution. If $l^2$ decreases through $k^2$, the crossing is a turning level: the wave is reflected or decays above it and is trapped beneath it. Increasing $\overline{u}$ normally reduces $N^2/{\overline{u}}^2$, while decreasing $N^2$ reduces it directly; subject to the curvature term $-{\overline{u}}_{zz}/\overline{u}$, either change therefore promotes 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.