= Local sound-speed criterion for circular condensate stirring
{title2=$D/R>\omega_r/\sqrt{\omega_r^2+2\Omega^2}$}
In a parabolic condensate in the <Thomas–Fermi approximation for a condensate>, the local sound <speed> is $c(D)=\omega_r\sqrt{R^2-D^2}/\sqrt2$. Equating it to the obstacle <speed> $\Omega D$ gives the displayed threshold. This is the stipulated local <phonon> estimate; a finite strongly depleting obstacle can modify flow and nucleate <vortices>, so the inequality is not a universal exact onset law for every stirring experiment.
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