Self-similar starting plume
= Self-similar starting plume
For constant kinematic <buoyancy flux> $f_0$ from a point source, <dimensional analysis> gives head height and radius proportional to $f_0^{1/4}t^{3/4}$, head velocity proportional to $f_0^{1/4}t^{-1/4}$, and head <reduced gravity> proportional to $f_0^{1/4}t^{-5/4}$. Dimensionless coefficients require the chosen <fluid entrainment> and head closures.