Settling velocity in the NanoFASE model

If the particle density of suspended particulate matter (SPM) for a given size class, \(\rho _{spm,n}\), (kg/m3) (which includes the inflow of "new" SPM from erosion or other tributaries) is greater than the density of water \(\rho _{w}\) (kg/m3), then the settling of that sediment size class is triggered. The settling velocity \(W _{spm,n}\) for an individual SPM size class is calculated as:

\(w_{\text{SPM},n} = \begin{cases} \frac{\eta}{d_n} d_{*,n}^3 \left( 38.1 + 0.93d_{*,n}^{12/7} \right)^{-7/8} & \mbox{if } \rho_{\text{SPM},n} > \rho_{\text{w}} \\ 0 & \mbox{if } \rho_{\text{SPM},n} \leq \rho_{\text{w}} \end{cases}\)

where \(d_{*,n} = (\Delta g/\eta^2)^{1/3} d_n\) is an effective particle diameter (m), \(g\) is the gravitational acceleration (m/s2), \(d_n \)is the diameter (m) of the SPM particle in the size class, \(\eta \) is the kinematic viscosity (kg/m.s) of water, and \(\Delta = (\rho _{SPM,n/}\rho_{w} )-1\)



The calculated settling velocity is used to compute a settling rate constant \(k_{\text{settle}} = w_{\text{SPM},n} / D \)(/s), where \( D\) is the depth of the water column (m). On a timestep of length \(\delta t\), the mass of SPM in the size class lost to the bed sediment due to settling (kg) is thus

\(\mathbf{j}_{\text{SPM,dep},n} = \textbf{m}_{\text{SPM},n} k_{\text{settle},n} \delta t\)

where \(\mathbf{m}_{\text{SPM},n}\)(kg) is the mass of suspended sediment in the size class within the river reach being simulated. The deposited mass per unit area of the bed sediment (kg/m2) is given by 

\(\mathbf{M}_{\text{dep},n} = \mathbf{j}_{\text{SPM,dep},n} / l f_{\text{m}} W\)

where \(l\) is the linear reach length (m), \(W\) is the reach width (m) and\( f_(m)\) is a factor to account for meandering.

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Consult the NanoFASE Library to see abstracts of these deliverable reports:
NanoFASE Report D2.2 Spatial transport framework for NanoFASE model

Fentie, B., Yu, B., & Rose, C. W. (2004). Comparison of Seven Particle Settling Velocity Formulae for Erosion Modelling. Paper presented at the 13th International Soil Conservation Organisation Conference, Brisbane. 

Zhiyao, S., Tingting, W., Fumin, X., & Ruijie, L. (2008). A simple formula for predicting settling velocity of sediment particles. Water Science and Engineering, 1(1), 37-43.




  Sam Harrison

  Centre for Ecology and Hydrology (CEH)