Axisymmetric pure plume
= Axisymmetric pure plume
For a top-hat axisymmetric pure plume of radius $r$, speed $U$, and reduced gravity $g'$, the conserved fluxes are $Q=\pi r^2U$, $M=\pi r^2U^2$, and $B=\pi r^2Ug'$. The <Batchelor entrainment hypothesis> gives $Q\propto B^{1/3}z^{5/3}$.