= Pressure matching at a piecewise-linear shear interface
{title2=$[(U-c)\phi'-U'\phi]=0$}
For a <normal mode> of an inviscid parallel flow, the perturbation <pressure> is $p=-(U-c)\phi'+U'\phi$. At an interface where $U$ is continuous but $U'$ jumps, continuity of normal velocity and <pressure> gives continuity of $\phi$ and the displayed flux. Consequently $(U-c)[\phi']=[U']\phi$. A <sinuous mode of a planar jet> may therefore have a cusp at a symmetric velocity-profile corner: even parity alone does not force its one-sided derivative to vanish.
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