= Inviscid Couette continuous spectrum
{title2=$\omega_\xi=\alpha\xi,\ -1<\xi<1$}
For inviscid plane <Couette flow> $U=z$ between impermeable walls at $z=\pm1$, the nonzero real streamwise <wavenumber> $\alpha$ gives no nontrivial smooth discrete vertical-velocity modes. Instead, the vorticity variable $q=(D^2-\alpha^2)w$ obeys $(\partial_t+i\alpha z)q=0$. Localized <vorticity sheets> give <generalized eigenfunctions> with real frequencies $\omega_\xi=\alpha\xi$. Their closure forms a neutral <continuous spectrum>.
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