= Squire mode
{c}
A Squire mode has zero wall-normal velocity and nonzero wall-normal <vorticity>, satisfying the homogeneous <Squire equation>. For real base velocity, positive finite <Reynolds number>, and zero boundary terms,
$$
\operatorname{Im}\omega=-\frac{\int(|\widehat\eta'|^2+\kappa^2|\widehat\eta|^2)\,dy}{Re\int|\widehat\eta|^2\,dy}<0
$$
for a nontrivial mode in a finite channel with no-slip walls. This follows by multiplying the homogeneous equation by $\overline\eta$, integrating by parts and taking the real part. Such modes are damped even when the coupled velocity-vorticity system can exhibit <transient growth from non-normal modes>.
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