Flux convergence in turbulent buoyancy mixing ($\mathcal{F}=d^4(G_z{)}^{3/2},F_{\mathrm{conv}}={\mathcal{F}}_z$)

In the area normalization $d^2$, the buoyancy-gradient mixing-length closure transports dense-fluid buoyancy downward with magnitude $\mathcal{F}=d^{2}K{G}_z=d^4(G_z{)}^{3/2}$. Its convergence in an upward coordinate is ${\mathcal{F}}_z$. Transport has units $L^4{T}^{-3}$ and convergence units $L^3{T}^{-3}$. Constant positive $G_z$ has nonzero transport and zero convergence; the two quantities cannot be identified.