CMS-Flow:Equilibrium Bed load plus AD Suspended load

Transport Equation

The transport equation for the suspended load is given by

\begin{equation} \tag{1}

\frac{\partial (h C)}{\partial t} + \frac{\partial (u_j h C)}{\partial x_j} = \frac{\partial }{\partial x_j} \biggl[ \nu _s h \frac{\partial C}{\partial x_j} \biggr] + E_b - D_b 

\end{equation}

Bed Change Equation

If the advection-diffusion (A-D) equation is selected to simulate the sediment transport and mixing, the change in the water depth is calculated by the sediment continuity equation

\begin{equation} \tag{2}

(1 - p'_m) \frac{\partial \zeta}{\partial t} = \frac{\partial q_{b*j}}{\partial x_j} + \frac{\partial }{\partial x_j} \biggl[ D_s |q_{t*}| \frac{\partial \zeta}{\partial x_j} \biggr] + E_b - D_b

\end{equation}

where $p'_{m}$ is the sediment porosity, and $D_{s}$ is a bedslope coefficient.

Boundary Conditions

There are three types of boundary conditions in the sediment transport: Wet-dry, Outflow and Inflow.

1. Wet-dry interface.

The interface between wet and dry cells has a zero-flux boundary condition. Both the advective and diffusive fluxes are set to zero at the wet-dry interfaces. Note that avalanching may still occur between wet-dry cells.

2. Outflow Boundary Condition

Outflow boundaries are assigned a zero-gradient boundary condition and sediments are allowed to be transported freely out of the domain.

3. Inflow Boundary Condition

When flow is entering the domain, it is necessary to specify the sediment concentration. In CMS-Flow, the inflow sediment concentration is set to the equilibrium sediment concentation. For some cases, it is desired to reduce the amount of sediment entering from the boundary such as in locations where the sediment source is limited (i.e. coral reefs). The inflow equilibrium sediment concentration may be adjusted by multiplying by a loading scaling factor and is specified by the Advanced Card:

   NET_LOADING_FACTOR <white space> #

where # is the loading factor in dimensionless units.

References

Buttolph, A. M., C. W. Reed, N. C. Kraus, N. Ono, M. Larson, B. Camenen, H. Hanson, T. Wamsley, and A. K. Zundel. (2006). “Two-dimensional depth-averaged circulation model CMS-M2D: Version 3.0, Report 2: Sediment transport and morphology change.” Coastal and Hydraulics Laboratory Technical Report ERDC/CHL TR-06-9. Vicksburg, MS: U.S. Army Engineer Research and Development Center, U.S.A.

Camenen, B., and Larson, M. (2007). “A unified sediment transport formulation for coastal inlet application”. Technical Report ERDC-CHL CR-07-01. Vicksburg, MS: U.S. Army Engineer Research and Development Center, U.S.A

Soulsby, R. L. (1997). "Dynamics of marine sands, a manual for practical applications". H. R. Wallingford, UK: Thomas Telford.

Watanabe, A. (1987). “3-dimensional numerical model of beach evolution”. Proc. Coastal Sediments ’87, ASCE, 802-817.

Wu, W. (2004).“Depth-averaged 2-D numerical modeling of unsteady flow and nonuniform sediment transport in open channels”. J. Hydraulic Eng., ASCE, 135(10), 1013–1024.

van Rijn, L. C. (1985). “Flume experiments of sedimentation in channels by currents and waves.” Report S 347-II, Delft Hydraulics laboratory, Deflt, Netherlands.

Zhu, J. (1991). “A low diffusive and oscillation-free convection scheme”. Com. App. Num. Meth., 7, 225-232.

Zundel, A. K. (2000). “Surface-water modeling system reference manual”. Brigham Young University, Environmental Modeling Research Laboratory, Provo, UT.

External Links

• Aug 2006 Two-Dimensional Depth-Averaged Circulation Model CMS-M2D: Version 3.0, Report 2, Sediment Transport and Morphology Change [1]

• Aug 2008 CMS-Wave: A Nearshore Spectral Wave Processes Model for Coastal Inlets and Navigation Projects [2]

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CMS-Flow