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Exact Material Circulation Surface in an Unsteady Viscous Vortex
An exact material circulation surface is derived for the source-bearing unsteady Kiknadze--Krasnov vortex. For a single distributed mode with $s>1$, the scaled radius $x=βr^2$ obeys $\frac{\mathrm D x}{\mathrm D t}=4νβ\big[(s-1)-x\big],$ so $x=s-1$ defines a material cylinder for any admissible time
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