Vertical Diffusion Coefficient

The vertical diffusion coefficient is required for determining the suspended-load correction factor. The vertical sediment diffusion coefficient is assumed to be related to the turbulent eddy viscosity as

$//<![CDATA[ \begin{array}{l}\varepsilon _{vk}=\frac{\nu _{tv}}{\sigma _{sk}}\end{array} //]]>$

where

$//<![CDATA[ \begin{array}{l}ε_{vk } = \text{vertical sediment diffusion coefficient (diffusivity) }[L^2/T]\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}ν_{tv } = \text{vertical turbulent eddy viscosity (diffusivity) }[L^2/T]\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}σ_{sk } = \text{Schmidt number [ - ]}\end{array} //]]>$

The vertical turbulent eddy viscosity is computed as

$//<![CDATA[ \begin{array}{l}ν_{tv} = c_{Mv}u_*h\end{array} //]]>$

where

$//<![CDATA[ \begin{array}{l}c_{Mv } = \text{empirical coefficient ( ≈ κ/6) [ - ]}\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}u_{* } = \text{total bed shear velocity }[L/T]\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}h_{} = \text{water depth }[L]\end{array} //]]>$