= Fixed-speed pure-plume merger and flux conservation
{title2=$b_p=b,\quad\pi b_p^2=\tfrac12\pi b_c^2$}
For a merged pair held at the original velocity and <reduced gravity>, <pure plume balance> requires the original individual radius, not the larger area-preserving radius. The required pure area is half the combined area. Shrinking to that area at unchanged velocity and <reduced gravity> would halve volume, momentum and <buoyancy fluxes>, contradicting conservation of the merged fluxes. A conservative merger must change its properties or begin away from pure balance.
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