= Extensional screening length of a slumping column
{title2=$\widehat z=\sqrt{h_0^3/(2\lambda a_0)}$}
For a uniform initial column, <annular return flow around a slumping column> competes with axial extensional <stress> over $\widehat z=\sqrt{h_0^3/(2\lambda a_0)}$. With $G=\Delta\rho g/(3\mu)$, choose <velocity> $\widehat w=G\widehat z^2$ and time $\widehat t=\widehat z/\widehat w$. Equivalently $\widehat z=R/\sqrt{\lambda\alpha_0}$, where $\phi=a^2/R^2$ and $\alpha(\phi)=2\sqrt\phi/(1-\sqrt\phi)^3$ in the leading thin-annulus model. This length describes the vertical range of the basal constraint: a much taller column has a localized basal <boundary layer>, while a much shorter column responds predominantly through extension.
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