= High-wavenumber instability of a non-monotone Prandtl layer
{title2=$\gamma=\alpha\operatorname{Im}c=O(\sqrt\alpha)$}
A <stationary point> in a non-monotone <velocity profile> can support a <quarter-power critical layer> whose phase-speed correction has positive imaginary part. The resulting <normal mode> grows at a rate proportional to the square root of the <wavenumber>. Such unbounded high-frequency amplification demonstrates <linear instability> of the frozen layer; nonlinear evolution and precise well-posedness consequences require separate analysis.
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