Equilibrium settling-diffusion profile ($\varphi (z)={\varphi }_1(z/z_1{)}^{-W_s/K}$)

For downward settling velocity magnitude $W_s>0$ and eddy diffusivity ${\kappa }_T=Kz$, the total upward particle flux is $J=-W_s\varphi -Kz{\varphi }_z$. A stationary profile tending to zero at infinity has $J=0$, giving the displayed power law. The exponent compares settling with turbulent mixing. It describes a region above the bed; entrainment from the bed and viscous near-wall effects determine the reference concentration separately.