Unsteady Burgers-vortex core radius (${\delta }^2(t)=4\nu /\alpha +({\delta }_0^2-4\nu /\alpha )e^{-\alpha t}$)

An axisymmetric Gaussian Burgers vortex with constant circulation in axial strain $\alpha$ has core area parameter $s={\delta }^2$ satisfying $\dot{s}+\alpha s=4\nu$. Thus $s=4\nu /\alpha +(s_0-4\nu /\alpha )e^{-\alpha t}$, an attracting balance of transverse compression and viscous diffusion for every positive finite initial radius.