= Airy reduction of the Orr-Sommerfeld equation in constant shear
{c}
{title2=$Z=e^{i\pi/6}(y-c-i\delta^3)/\delta,\quad\delta=Re^{-1/3}$}
For nondimensional constant shear $U=y$ and streamwise wavenumber one, put $W=(D^2-1)\widehat v$. The <Orr-Sommerfeld equation> gives $W''=[1+iRe(y-c)]W$. The displayed substitution transforms it into the <Airy ordinary differential equation>, because $(e^{i\pi/6})^3=i$. The scale $Re^{-1/3}$ balances shear advection against viscous diffusion.
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