Radius growth of an axisymmetric pure plume
= Radius growth of an axisymmetric pure plume
{title2=$b(z)=b_s+6\alpha z/5$}
For pi-normalized top-hat fluxes, $b=Q/\sqrt M$. The pure <similarity solution> therefore has $b=(6\alpha/5)(z+z_0)$, so the radius grows linearly with slope $6\alpha/5$. The corresponding <plume virtual origin> is $-z_0$ and a finite source has $z_0=5b_s/(6\alpha)$. This law translates geometric plume-contact criteria into heights.