N.8 Settling

Particulate organic matter is able to be settled within the WQ Module. Four settling models are available. These are able to be applied equally to both labile and refractory particulate organic matter to compute \(V_{settle}^{lorg}\) and \(V_{settle}^{rorg}\), respectively. The same settling model must be applied to both types of particulates, although the parameters ascribed to a model can be different for labile and refractory particulates. Once computed, the same settling rate is applied to each of labile particulate organic carbon, nitrogen and phosphorus.

N.8.1 None

In this model, particulate organic settling is set to zero and organic matter is simply advected by the hydrodynamic flow field.

N.8.2 Constant

In this model, \(V_{settle}^{lorg}\) and \(V_{settle}^{rorg}\) are set to constant values, and matter is settled at these velocities. These can be different velocities for labile and refractory particulate organics. A negative specification of this quantity corresponds to a downwards settling velocity.

N.8.3 Constant with density correction

In this model, \(V_{settle}^{lorg}\) and \(V_{settle}^{rorg}\) are set to constant values, and matter is settled at these velocities, but corrected for ambient water density effects, as per Equation (N.28).

\[\begin{equation} V_{sett\langle computed\rangle}^{org} = V_{settle}^{org} \times \frac{\mu_{20}\times\rho_w}{\mu\times\rho_{w20}} \tag{N.28} \end{equation}\]

\(V_{settle}^{org}\) is \(V_{settle}^{lorg}\) or \(V_{settle}^{rorg}\) at 20\(^o\)C, \(\mu\) and \(\rho_w\) are the ambient water dynamic viscosity (in Ns/m\(^2\)) and density (in kg/m\(^3\)), respectively, and \(\mu_{20}\) and \(\rho_{w20}\) are the dynamic viscosity and density of freshwater at 20\(^o\)C, respectively. A negative specification of \(V_{settle}^{org}\) corresponds to a downwards settling velocity.

N.8.4 Stokes

In this model, particulate organic settling is computed using the Stokes equation and particle diameter and density, as per Equations (N.29) and (N.30).

\[\begin{equation} V_{sett\langle computed\rangle}^{lorg} = -g \times d_{lorg}^2 \times \frac{\left(\rho_{lorg}-\rho_w\right)}{18\mu} \tag{N.29} \end{equation}\]

\[\begin{equation} V_{sett\langle computed\rangle}^{rorg} = -g \times d_{rorg}^2 \times \frac{\left(\rho_{rorg}-\rho_w\right)}{18\mu} \tag{N.30} \end{equation}\] \(g\) is acceleration due to gravity, \(d_{lorg}\) and \(d_{rorg}\) are conceptualised diameters of labile and refractory particulate organic matter respectively, \(\rho_{lorg}\) and \(\rho_{rorg}\) are labile and refractory particulate organic matter densities, respectively, and \(\rho_w\) and \(\mu\) are the ambient water density and dynamic viscosity, respectively.

Once the settling velocities for labile and refractory particulate organic matter have been computed, the relevant fluxes are calculated as follows.

\[\begin{equation} \left.\begin{aligned} \href{AppDiags.html#WQDiagPOCSedmtn}{F_{sedmtn\langle computed\rangle}^{POC}} =& \frac{\href{AppDiags.html#WQDiagPOMVVel}{V_{settle\langle computed \rangle}^{lorg}}}{dz} \times \left[ POC \right] \\ \\ \href{AppDiags.html#WQDiagPONSedmtn}{F_{sedmtn\langle computed\rangle}^{PON}} =& \frac{\href{AppDiags.html#WQDiagPOMVVel}{V_{settle\langle computed \rangle}^{lorg}}}{dz} \times \left[ PON \right] \\ \\ \href{AppDiags.html#WQDiagPOPSedmtn}{F_{sedmtn\langle computed\rangle}^{POP}} =& \frac{\href{AppDiags.html#WQDiagPOMVVel}{V_{settle\langle computed \rangle}^{lorg}}}{dz} \times \left[ POP \right] \end{aligned}\right\} \tag{N.31} \end{equation}\]

\[\begin{equation} \href{AppDiags.html#WQDiagRPOMSedmtn}{F_{sedmtn\langle computed\rangle}^{RPOM}} = \frac{\href{AppDiags.html#WQDiagRPOMVVel}{V_{settle\langle computed \rangle}^{rorg}}}{dz} \times \left[ RPOM \right] \tag{N.32} \end{equation}\] \(dz\) is the relevant cell thickness, and divides the flux to produce a per volume result for consistency with other corresponding diagnostics.

The limitations of this approach to modelling particulate organic matter settling are recognised. Future releases of the WQ Module will offer direct linkages between the TUFLOW FV ST Module and WQ Module, and treat particulate organics as sediment fractions that are transported using the advanced techniques and models offered by the ST Module.