Pure plume

A pure plume is a similarity regime in which the source supplies buoyancy flux but no dynamically persistent source volume or momentum flux. Its finite source region is represented by a plume virtual origin.

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

A line plume is invariant along one horizontal direction, so its integral fluxes are measured per unit span. A wall line plume entrains through one exposed edge and has width proportional to distance from its plume virtual origin.

A wall line plume is a one-sided line plume adjoining a solid wall. Under a top-hat pure-plume model, $d(bW)/ds=\alpha W$ because only its outer edge entrains ambient fluid.

In a triangular-profile wall line plume, axial velocity and reduced gravity decrease linearly from their wall values to zero across the plume width $b$. If the wall speed is $W$, its volume and kinematic momentum fluxes per unit span are $V=bW/2$ and $J=b{W}^2/3$.

A line plume of kinematic buoyancy flux $B_0$ rising through uniform buoyancy frequency $N$ has the dimensional height scaleIt measures the height over which ambient stratification removes an order-one fraction of the plume buoyancy before the plume reaches neutral buoyancy and spreads as a buoyant intrusion.

A plume virtual origin is the extrapolated point at which a similarity plume's width and volume flux vanish. It absorbs finite source geometry into a shift of the axial coordinate.