CMS-Flow:Equilibrium Bed load plus AD Suspended load

Transport Equation

The transport equation for the suspended load is given by

        ${\frac {\partial }{\partial t}}{\biggl (}{\frac {hC_{t}}{\beta _{t}}}{\biggr )}+{\frac {\partial (U_{j}hC_{t})}{\partial x_{j}}}={\frac {\partial }{\partial x_{j}}}{\biggl [}\nu _{s}h{\frac {\partial (r_{s}C_{t})}{\partial x_{j}}}{\biggr ]}+\alpha _{t}\omega _{s}(C_{t*}-C_{t})$

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

       $(1-p'_{m}){\frac {\partial \zeta }{\partial t}}=\alpha _{t}\omega _{s}(C_{t*}-C_{t})+{\frac {\partial }{\partial x_{j}}}{\biggl [}D_{s}|U|h(1-r_{s})C_{t}{\frac {\partial \zeta }{\partial x_{j}}}{\biggr ]}$

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

Boundary Conditions

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