Sediment Transport: Difference between revisions

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==Lund-CIRP==
As a user-specified option, CMS-M2D calculates sediment transport rates and resultant changes in water depth (bottom elevation) through gradients in thetransport rates. In CMS-M2D Version 3, three transport models are available:
Camenen and Larson (2005, 2007, and 2008) developed a general sediment transport formula for bed and suspended load under combined waves and currents.
# [[CMS-Flow:Equilibrium_Total_Load|Equilibrium total load formulation]]
# [[CMS-Flow:Equilibrium Bed load plus AD Suspended load|Equilibrium Bed Load plus Non-equilibrium Suspended Load]]
# [[CMS-Flow:Non-equilibrium Sediment Transport|Non-equilibrium Total Load ]]


=== Bed load===
CMS-Flow accounts for the two morphologic constraints of: (a) hard bottom(non-erodible substrate) and (b) bottom avalanching if the slope exceeds aspecified value. The approach taken to treat hard bottom allows for sand toaccumulate over the hard bottom if depositional conditions are present, and italso allows material overlying the hard substrate to erode while preservingsediment volume. Avalanching is invoked if the bottom slope between two cellsexceeds a specified critical slope. The avalanching algorithm applies an iterative approach to move material down slope until the critical slope is no longerexceeded, while conserving sediment volume. The transport rate formulas that can be applied in CMS-Flow are based on the shear stress concept, implying that bed roughness and resulting friction factors are key parameters to estimate when computing transport rates. A sediment transport formula is often developed (i.e., calibrated against data) based on specific equations for calculating bed roughness and associated shear stress. Thus, when calculating the transport rate in CMS-M2D with the threeimplemented formulas, slightly different approaches are taken to determine theshear stress. In the following sections, the methods are discussed for obtainingthe shear stress for each of the sediment transport formulas. Also, it is noted thatthe roughness and associated shear stresses within the sediment transportcalculations are different from those in the CMS-M2D hydrodynamiccalculations. The computed current field and properties of surface wavescalculated from a separate model are input to the roughness and shear stresscalculations for the sediment transport, but there is presently no feedback ofroughness or shear stress from the sediment transport component of the model tothe hydrodynamic or wave calculations.
The current-related bed load transport with wave stirring is given by
{{Equation|<math> \frac{q_{b}}{\sqrt{(s-1)gd^3}} = a_c \sqrt{\theta_c} \theta_{cw}\exp{ \biggl ( -b_c \frac{\theta_{cr}}{\theta_{cw}}} \biggr ) </math>|2=1}}


=== Suspended load ===
CMS-Flow calculates the current velocity in two horizontal coordinatedirections (u, v). If there is negligible contribution from the waves to thetransporting velocity (e.g., sinusoidal waves), the net transport is in the direction of the resulting current vector. Thus, waves will contribute to the mobilization and stirring of sediment, but a mean current is needed to produce a net transport.
The current-related suspended load transport with wave stirring is given by
{{Equation|<math> \frac{q_s}{\sqrt{ (s-1) g d^3 }} = U c_R \frac{\epsilon}{w_s} \biggl[ 1 - \exp{ \biggl( - \frac{w_s d}{\epsilon}} \biggr) \biggr] </math>|2=2}}


The reference sediment concentration is obtained from
{{Equation|<math> c_R = A_{cR}  \exp{ \biggl( - 4.5 \frac{\theta_{cr}}{\theta_{cw}}}  \biggr)  </math>|2=3}}
where the coefficient <math>A_{cR}</math> is given by
{{Equation|<math> A_{cR} = 3.5x10^3 \exp{ \bigl( - 0.3 d_{*} } \bigr)  </math>|2=4}}
with <math> d_{*} = d \sqrt{(s-1) g \nu^{-2}} </math> being the dimensionless grain size and <math> \nu </math> the kinematic viscosity of water.
The sediment mixing coefficient is calculated as
{{Equation|<math> \epsilon = h \biggl( \frac{k_b^3 D_b + k_c^3 D_c + k_w^3 D_w}{\rho} \biggr)^{1/3}  </math>|2=5}}
== van Rijn ==
== Watanabe ==
The equilibrium total load sediment transport rate of Watanabe (1987) is given by
{{Equation|<math> q_{t*} = A \biggl[ \frac{(\tau_{b,max} - \tau_{cr}) U_c }{\rho g } \biggr]  </math>|2=6}}
where <math> \tau_{b,max} </math> is the maximum shear stress, <math> \tau_{cr} </math> is the critical shear stress of incipient motion, and <math> A </math> is an empirical coefficient typically ranging from 0.1 to 2.
The critical shear stress is determined using
{{Equation|<math> \tau_{cr} = (\rho_s - \rho) g d \phi_{cr} </math>|2=6}}
In the case of currents only the bed shear stress is determined as <math> \tau_{c} = \frac{1}{8}\rho g f_c U_c^2 </math> where <math> f_c </math> is the current friction factor. The friction factor is calculated as <math> f_c = 0.24log^{-2}(12h/k_{sd}) </math> where <math> k_{sd} </math> is the Nikuradse equivalent sand roughness obtained from <math> k_{sd} = 2.5d_{50} </math>.
If waves are present, the maximum bed shear stress \tau_{b,max} is calculated based on Soulsby (1997)
{{Equation|<math> \tau_{max} = \sqrt{(\tau_m + \tau_w \cos{\phi})^2 } + (\tau_w \sin{\phi})^2</math>|2=6}}
== Soulsby-van Rijn ==
The equilibrium sediment concentration is calculated as (Soulsby 1997)
{{Equation|<math> C_{*} = \frac{A_{sb}+A_{ss}}{h} \biggl[ \biggl( U_c^2 + 0.018 \frac{U_{rms}^2}{C_d} \biggr)^{0.5} - u_{cr} \biggr]^{2.4}  </math>|2=7}}


----
----
{| border="1"
[[CMS#Documentation Portal | Documentation Portal ]]
! Symbol !! Description !! Units
|-
|<math> q_{bc} </math> || Bed load transport rate || m<sup>3</sup>/s
|-
|<math> s </math> ||  Relative density || -
|-
|<math> \theta_{c}  </math> || Shields parameter due to currents || -
|-
|<math> \theta_{cw} </math> ||  Shields parameter due to waves and currents || -
|-
|<math> \theta_{cw}</math> ||  Critical shields parameter  || -
|-
|<math> a_c </math> || Empirical coefficient || -
|-
|<math> b_c </math> || Empirical coefficient || -
|-
|<math> U_c </math> || Current magnitude || m/s
|}
 
== References ==
* Camenen, B., and Larson, M. (2005). "A bed load sediment transport formula for the nearshore," Estuarine, Coastal and Shelf Science, 63, 249-260.
* Camenen, B., and Larson, M., (2008). "A General Formula for Non-Cohesive  Suspended Sediment Transport," Journal of Coastal Research, 24(3), 615-627. 
* Soulsby, D.H. (1997). "Dynamics of marine sands. A manual for practical applications," Thomas Telford Publications, London, England, 249 p.
* Watanabe, A. (1987). "3-dimensional numerical model of beach evolution," Proceedings Coastal Sediments '87, ASCE, 802-817.

Latest revision as of 18:04, 23 February 2015

As a user-specified option, CMS-M2D calculates sediment transport rates and resultant changes in water depth (bottom elevation) through gradients in thetransport rates. In CMS-M2D Version 3, three transport models are available:

  1. Equilibrium total load formulation
  2. Equilibrium Bed Load plus Non-equilibrium Suspended Load
  3. Non-equilibrium Total Load

CMS-Flow accounts for the two morphologic constraints of: (a) hard bottom(non-erodible substrate) and (b) bottom avalanching if the slope exceeds aspecified value. The approach taken to treat hard bottom allows for sand toaccumulate over the hard bottom if depositional conditions are present, and italso allows material overlying the hard substrate to erode while preservingsediment volume. Avalanching is invoked if the bottom slope between two cellsexceeds a specified critical slope. The avalanching algorithm applies an iterative approach to move material down slope until the critical slope is no longerexceeded, while conserving sediment volume. The transport rate formulas that can be applied in CMS-Flow are based on the shear stress concept, implying that bed roughness and resulting friction factors are key parameters to estimate when computing transport rates. A sediment transport formula is often developed (i.e., calibrated against data) based on specific equations for calculating bed roughness and associated shear stress. Thus, when calculating the transport rate in CMS-M2D with the threeimplemented formulas, slightly different approaches are taken to determine theshear stress. In the following sections, the methods are discussed for obtainingthe shear stress for each of the sediment transport formulas. Also, it is noted thatthe roughness and associated shear stresses within the sediment transportcalculations are different from those in the CMS-M2D hydrodynamiccalculations. The computed current field and properties of surface wavescalculated from a separate model are input to the roughness and shear stresscalculations for the sediment transport, but there is presently no feedback ofroughness or shear stress from the sediment transport component of the model tothe hydrodynamic or wave calculations.

CMS-Flow calculates the current velocity in two horizontal coordinatedirections (u, v). If there is negligible contribution from the waves to thetransporting velocity (e.g., sinusoidal waves), the net transport is in the direction of the resulting current vector. Thus, waves will contribute to the mobilization and stirring of sediment, but a mean current is needed to produce a net transport.


Documentation Portal

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