Sediment transport saturation

The equilibrium sediment flux is the transport supported locally by a prescribed bed shear stress. A common idealization is $q_{\mathrm{sat}}={\varphi }_b\chi (\tau -{\tau }_{\mathrm{th}}{)}_{+}^{\gamma }$. Linearization above the sediment entrainment threshold requires perturbations small compared with the positive excess stress.

The saturation length measures downstream relaxation of a transported grain population toward its equilibrium sediment transport flux. The elementary steady relaxation law is $L_{\mathrm{sat}}{q}_x=q_{\mathrm{sat}}-q$; it introduces a phase lag between forcing and actual transport.