= Plane-parallel stellar f-mode
{title2=$\omega^2=gk,\quad\xi\propto e^{-kz},\quad\Pi=0$}
The <plane-parallel Cowling displacement-pressure equations> admit this <stellar oscillation> for every compatible equilibrium density and <adiabatic sound speed> profile. In the upward-displacement convention its horizontal amplitude is $i\boldsymbol k\xi/k$, its Eulerian pressure amplitude is $\rho g\xi$, and its Lagrangian density and pressure perturbations vanish. Its displacement decays into the star but grows upward without bound, so a pure linear continuation to infinite height is not physical.
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