Sediment Transport Module

Module framework:

Fundamental equations

Depth-averaged sediment concentration equation

(58)\[(\bar{c}H)_{t} + \nabla_{h} \cdot (\bar{c}H(\textbf{u}_{\alpha} + \bar{\textbf{u}}_2)) = \nabla_{h} \cdot (kH(\nabla_{h}\bar{c})) + P - D\]

Pick up function (van Rijn 1984):

(59)\[P = 0.015\frac{d_{50}}{a} \left( \frac{|\tau_b|-\tau_{cr}}{\tau_{cr}} \right)^{1.5} d_{*}^{-0.3} \omega_{f}, \ \ \ \ \ |\tau_b| > \tau_{cr}\]

Deposition rate (Cao 1999):

(60)\[D = \gamma \bar{c} \omega_{f} (1-\gamma\bar{c})^{m_o}\]

Bedload formula

Meyer-Peter and Muller (1948):

(61)\[q_b = \frac{8 [(\tau_b - \tau_{cr}^b) / \rho_{\omega}]^{3/2}}{g(s-1)}\]

Bed evolution equation

(62)\[\frac{dZ_{b}}{dt} = \frac{1}{1-n} (D-P-\nabla \cdot \overrightarrow{q}_b )\]

DETAILS

• Suspended Sediment Transport Equation (Non-cohesive)
• Suspended Sediment Transport Equation (Cohesive)
• Bedload Sediment Transport
• Morphological Evolution
• Hydrodynamic Correction for High Concentration Sediment
• Slope Limiting Methodology
• Non-erodible Bed
• Numerical Scheme for Sediment Transport
  • Space-differencing
  • Time stepping
  • Boundary conditions
• Ship Propeller Effects on Sediment Transport
  • Theory
  • Model configuration
  • Example

APPLICATIONS

• Ocean City Tsunami Inundation Map

• 2011 Tohoku-Oki tsunami impact in Crescent City harbor

  more results of Crescent City Case

References

Cao, Z., (1999). “Equilibrium Near-Bed Concentration of Suspended Sediment”. J. of Hydraulic Eng., 125 (12). DOI: 10.1061/(ASCE)0733-9429(1999)125:12(1270).

Meyer-Peter, E., and Muller, R., (1948). “Formulas for Bed-Load transport”. Hydraulic Eng. Reports: IAHSR 2nd meeting, Stockholm, Appendix 2. IAHSR.

van Rijn, L.C., (1984). “Sediment Pick-Up Functions”. J. of Hydraulic Eng., 110 (10). DOI: 10.1061/(ASCE)0733-9429(1984)110:10(1494).

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