Taylor–Goldstein equation
= Taylor–Goldstein equation
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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> $k$,
$$
\widehat w''+\left[
\frac{N^2}{(U-c)^2}
-\frac{U''}{U-c}-k^2
\right]\widehat w=0.
$$