= Prandtl critical layer at a stationary shear profile
{c}
{title2=$y-y_c=O(\alpha^{-1/4}),\quad c-c_0=O(\alpha^{-1/2})$}
= Quarter-power critical layer
{synonym}
For the <Prandtl normal-mode equation> with viscosity scaled to one and a profile having a nondegenerate <stationary point>, $U-c_0\sim (y-y_c)^2/2$. A piecewise outer mode proportional to $U-c_0$ has a second-derivative jump. Balancing the advective and third-derivative terms smooths that jump over width $\alpha^{-1/4}$, with <velocity> amplitude $\alpha^{-1/2}$ and a phase-speed correction of the same order. Matching selects the <eigenvalue> through a third-order inner problem.
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