## Equilibrium Total load Transport model

The single-sized sediment transport model described in Sánchez and Wu (2011a) was extended to multiple-sized sediments within CMS by Sánchez and Wu (2011b). In this model, the sediment transport is separated into current- and wave-related transports. The transport due to currents includes the stirring effect of waves, and the wave-related transport includes the transport due to asymmetric oscillatory wave motion as well as steady contributions by Stokes drift, surface roller, and undertow. The current-related bed and suspended transports are combined into a single total-load transport equation, thus reducing the computational costs and simplifying the bed change computation. The 2DH transport equation for the current-related total load is

Equation 2-50 ??????

## Sediment Mass Balance Equation

The transport equation for the suspended load is given by

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

where $p'_m$ is the sediment porosity, and $D_s$ is a bedslope coefficient.

## 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.