= Vorticity-jump matching for an inviscid shear flow
{title2=$[\widehat w]=0,\quad[(U-c)\widehat w'-U'\widehat w]=0$}
Across a jump of $U'$ in a constant-density parallel flow with continuous $U$, the <normal mode> vertical velocity and pressure are continuous. The linearized momentum equation gives $\widehat p=\rho[(U-c)\widehat w'-U'\widehat w]/(ik)$, yielding the displayed conditions. Equivalently, away from $U=c$, $(U-c)[\widehat w']=[U']\widehat w$. Derivative continuity is generally incorrect when the background <vorticity> jumps. This is the constant-density, continuous-velocity specialization of <jump conditions for stratified inviscid shear flow>.
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