= Source-volume length of a turbulent plume
{title2=$L_Q^{\mathrm{jet}}=Q_0/(c\sqrt{M_0}),\quad L_Q^{\mathrm{plume}}=(Q_0/C_Q)^{3/5}$}
= Source-volume lengths of a turbulent plume
{synonym}
Source <volume flux> is negligible only when entrained volume greatly exceeds it. In the <jet limit of the top-hat plume model>, this requires $z\gg Q_0/(c\sqrt{M_0})$. In a <pure plume> with $Q=C_Qz^{5/3}$, it requires $z\gg(Q_0/C_Q)^{3/5}$, where $C_Q=(3c/5)(9cF_0/20)^{1/3}$ for full-cross-section fluxes and $c=2\alpha_e\sqrt\pi$. These scales differ from the <jet length> which measures imposed momentum relative to buoyancy. Neglecting source volume does not automatically permit neglecting source momentum.
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