Model help:Sedflux: Difference between revisions

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1) Log in to the wiki
1) Log in to the wiki
2) Create a new page for each model, by using the following URL:
2) Create a new page for each model, by using the following URL:
   * http://csdms.colorado.edu/wiki/Model help:<modelname>
   * https://csdms.colorado.edu/wiki/Model help:<modelname>
   * Replace <modelname> with the name of a model
   * Replace <modelname> with the name of a model
3) Than follow the link "edit this page"
3) Than follow the link "edit this page"
Line 135: Line 135:
|-
|-
|SeaFloorDepth file
|SeaFloorDepth file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorSlope file
|SeaFloorSlope file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorElevation file
|SeaFloorElevation file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloor Thickness file
|SeaFloor Thickness file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorGrain file
|SeaFloorGrain file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorAge file
|SeaFloorAge file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorSand file
|SeaFloorSand file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorSilt file
|SeaFloorSilt file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorClay file
|SeaFloorClay file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorMud file
|SeaFloorMud file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorFacies file
|SeaFloorFacies file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorDensity file
|SeaFloorDensity file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorPorosity file
|SeaFloorPorosity file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorPermeability file
|SeaFloorPermeability file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorBasement file
|SeaFloorBasement file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|SeaFloorRiver_mouth file
|SeaFloorRiver_mouth file
|output file prefix for variable
|output file prefix for variable, in NetCDF format
| -
| -
|-
|-
|}
|}
= Output Gubes =
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0"  cellpadding="0" style="margin:0em 0em 0em 0;"
|-
!Parameter!!Description!!Unit
|-valign="top"
|width="20%"|Output directory
|width="60%"|path to output cube files
|width="20%"| -
|-
|Interval between output files
|
| -
|-
|Age file
|output file prefix for variable, in NetCDF format
| -
|-
|Facies file
|output file prefix for variable, in NetCDF format
| -
|-
|Pressure file
|output file prefix for variable, in NetCDF format
| -
|-
|Density file
|output file prefix for variable, in NetCDF format
| -
|-
|Grain_density file
|output file prefix for variable, in NetCDF format
| -
|-
|Max_density file
|output file prefix for variable, in NetCDF format
| -
|-
|Grain file
|output file prefix for variable, in NetCDF format
| -
|-
|Grain_in_meters file
|output file prefix for variable, in NetCDF format
| -
|-
|Sand file
|output file prefix for variable, in NetCDF format
| -
|-
|Silt file
|output file prefix for variable, in NetCDF format
| -
|-
|Clay file
|output file prefix for variable, in NetCDF format
| -
|-
|Mud file
|output file prefix for variable, in NetCDF format
| -
|-
|Velocity file
|output file prefix for variable, in NetCDF format
| -
|-
|Viscosity file
|output file prefix for variable, in NetCDF format
| -
|-
|Relative_density file
|output file prefix for variable, in NetCDF format
| -
|-
|Porosity file
|output file prefix for variable, in NetCDF format
| -
|-
|Porosity_min file
|output file prefix for variable, in NetCDF format
| -
|-
|Porosity_max file
|output file prefix for variable, in NetCDF format
| -
|-
|Pi file
|output file prefix for variable, in NetCDF format
| -
|-
|Permeability file
|output file prefix for variable, in NetCDF format
| -
|-
|Void_ratio file
|output file prefix for variable, in NetCDF format
| -
|-
|Void_ratio_min file
|output file prefix for variable, in NetCDF format
| -
|-
|Void_ratio_max file
|output file prefix for variable, in NetCDF format
| -
|-
|Friction_angle file
|output file prefix for variable, in NetCDF format
| -
|-
|Consolidation file
|output file prefix for variable, in NetCDF format
| -
|-
|Yield_strength file
|output file prefix for variable, in NetCDF format
| -
|-
|Dynamic_viscosity file
|output file prefix for variable, in NetCDF format
| -
|-
|Mv file
|output file prefix for variable, in NetCDF format
| -
|-
|Hydraulic_con file
|output file prefix for variable, in NetCDF format
| -
|-
|Shear_strength file
|output file prefix for variable, in NetCDF format
| -
|-
|Cohesion file
|output file prefix for variable, in NetCDF format
| -
|-
|Consolidation_rate file
|output file prefix for variable, in NetCDF format
| -
|-
|Excess_pressure file
|output file prefix for variable, in NetCDF format
| -
|-
|Relative_pressure file
|output file prefix for variable, in NetCDF format
| -
|-
|Fraction file
|output file prefix for variable, in NetCDF format
| -
|-
|}
= About =
= About =
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0"  cellpadding="0" style="margin:0em 0em 0em 0;"
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0"  cellpadding="0" style="margin:0em 0em 0em 0;"
Line 225: Line 381:
1) Water discharge
1) Water discharge
::::{|
::::{|
|width=500px|<math>Q_{0}=u_{0}b_{0}h_{0}  </math>
|width=800px|<math>Q_{0}=u_{0}b_{0}h_{0}  </math>
|width=50p=x align="right"|(1)
|width=50p=x align="right"|(1)
|}
|}
2) Mean suspended load entering the ocean basin
2) Mean suspended load entering the ocean basin
::::{|
::::{|
|width=500px|<math>Q_{s0}= Q_{0} \sum\limits_{i=1}^N Cs_{i}  </math>
|width=800px|<math>Q_{s0}= Q_{0} \sum\limits_{i=1}^N Cs_{i}  </math>
|width=50p=x align="right"|(2)
|width=50p=x align="right"|(2)
|}
|}
3) Bedload equation by Bagnold (1966)
3) Bedload equation by Bagnold (1966)
::::{|
::::{|
|width=500px|<math>Q_{b}={\frac{\rho _{s}}{\rho _{s} - \rho}}{\frac{\rho g Q_{0}^ \beta s e_{b}}{g tan f}}  </math>
|width=800px|<math>Q_{b}={\frac{\rho _{s}}{\rho _{s} - \rho}}{\frac{\rho g Q_{0}^ \beta s e_{b}}{g tan f}}  </math>
|width=50p=x align="right"|(3)
|width=50p=x align="right"|(3)
|}
|}
* Channel avulsion (using Avulsion model)
* Channel avulsion (using Avulsion model)
::::{|
::::{|
|width=500px|<math>\Theta _{n+1}=\Theta_{n} + X_{n}  </math>
|width=800px|<math>\Theta _{n+1}=\Theta_{n} + X_{n}  </math>
|width=50p=x align="right"|(4)
|width=50p=x align="right"|(4)
|}
|}
* Bedload dumpling (not hyperpycnal flow)
* Bedload dumping (not hyperpycnal flow)
::::{|
::::{|
|width=500px|<math>D={\frac{Q_{b}}{W_{d}L \rho}}  </math>
|width=800px|<math>D={\frac{Q_{b}}{W_{d}L \rho}}  </math>
|width=50p=x align="right"|(5)
|width=50p=x align="right"|(5)
|}
|}
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1) Advection-diffusion equation
1) Advection-diffusion equation
::::{|
::::{|
|width=500px|<math> {\frac{\partial u I}{\partial x}} + {\frac{\partial v I}{\partial y}} + \lambda I = {\frac{\partial}{\partial y}} \left ( K {\frac{\partial I}{\partial y}} + {\frac{\partial}{\partial x}} \left (K {\frac{\partial I}{\parital x}}\right )  </math>
|width=800px|<math> {\frac{\partial u I}{\partial x}} + {\frac{\partial v I}{\partial y}} + \lambda I = {\frac{\partial}{\partial y}} \left ( K {\frac{\partial I}{\partial y}}\right ) + {\frac{\partial}{\partial x}} \left (K {\frac{\partial I}{\partial x}}\right )  </math>
|width=50p=x align="right"|(6)
|width=50p=x align="right"|(6)
|}
|}
2) Froude number
2) Froude number
::::{|
::::{|
|width=500px|<math> Fr = {\frac{u_{0}}{\sqrt{g h_{0}}}} </math>
|width=800px|<math> Fr = {\frac{u_{0}}{\sqrt{g h_{0}}}} </math>
|width=50p=x align="right"|(7)
|width=50p=x align="right"|(7)
|}
|}
3) Plume's centerline
3) Plume's centerline
::::{|
::::{|
|width=500px|<math> {\frac{x}{b_{0}}}=1.53 + 0.90 \left ({\frac{u_{0}}{v_{0}}}\right ) \left ({\frac{y}{b_{0}}}\right )^\left (0.37\right )</math>
|width=800px|<math> {\frac{x}{b_{0}}}=1.53 + 0.90 \left ({\frac{u_{0}}{v_{0}}}\right ) \left ({\frac{y}{b_{0}}}\right )^\left (0.37\right )</math>
|width=50p=x align="right"|(8)
|width=50p=x align="right"|(8)
|}
|}
4) Non-conservative concentration along and surrounding the centerline position
4) Non-conservative concentration along and surrounding the centerline position
::::{|
::::{|
|width=500px|<math> C\left (x,y\right ) = C_{0}exp\left (-\lambda t \right ) \sqrt{{\frac{b_{0}}{\sqrt{\pi}C_{1} x}}} exp [-\left ({\frac{y}{\sqrt{2} C_{1} x}}\right )^2] </math>
|width=800px|<math> C\left (x,y\right ) = C_{0}exp\left (-\lambda t \right ) \sqrt{{\frac{b_{0}}{\sqrt{\pi}C_{1} x}}} exp [-\left ({\frac{y}{\sqrt{2} C_{1} x}}\right )^2] </math>
|width=50p=x align="right"|(9)
|width=50p=x align="right"|(9)
|}
|}
::::{|
::::{|
|width=500px|<math> t\left (x,y\right ) = {\frac{u_{0} + u_{c}\left (x\right ) + 7u\left (x,y\right )}{9}} </math>
|width=800px|<math> t\left (x,y\right ) = {\frac{u_{0} + u_{c}\left (x\right ) + 7u\left (x,y\right )}{9}} </math>
|width=50p=x align="right"|(10)
|width=50p=x align="right"|(10)
|}
|}
::::{|
::::{|
|width=500px|<math> u_{c}\left (x\right ) = u_{0} \sqrt{{\frac{b_{0}}{\sqrt{\pi} C_{1} x}}} </math>
|width=800px|<math> u_{c}\left (x\right ) = u_{0} \sqrt{{\frac{b_{0}}{\sqrt{\pi} C_{1} x}}} </math>
|width=50p=x align="right"|(11)
|width=50p=x align="right"|(11)
|}
|}
::::{|
::::{|
|width=500px|<math> u\left (x,y\right ) = u_{0} \sqrt{{\frac{b_{0}}{\sqrt{\pi} C_{1} x }}} exp [-\left ({\frac{y}{\sqrt{2} C_{1} x}}\right )^2] </math>
|width=800px|<math> u\left (x,y\right ) = u_{0} \sqrt{{\frac{b_{0}}{\sqrt{\pi} C_{1} x }}} exp [-\left ({\frac{y}{\sqrt{2} C_{1} x}}\right )^2] </math>
|width=50p=x align="right"|(12)
|width=50p=x align="right"|(12)
|}
|}
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1) Amount of bottom sediments that can be reworked by resuspension and diffusion
1) Amount of bottom sediments that can be reworked by resuspension and diffusion
::::{|
::::{|
|width=500px|<math> q_{s} = k\left (t,z,D\right ) \bigtriangledown z = k \left ( {\frac{\partial z}{\partial x}}\hat{i} + {\frac{\partial z}{\partial y}} \hat{j} \right )  </math>
|width=800px|<math> q_{s} = k\left (t,z,D\right ) \bigtriangledown z = k \left ( {\frac{\partial z}{\partial x}}\hat{i} + {\frac{\partial z}{\partial y}} \hat{j} \right )  </math>
|width=50p=x align="right"|(13)
|width=50p=x align="right"|(13)
|}
|}
2) Amount and direction of transport of the ith grain size
2) Amount and direction of transport of the ith grain size
::::{|
::::{|
|width=500px|<math> q_{si} = \beta _{i} q_{s}  </math>
|width=800px|<math> q_{si} = \beta _{i} q_{s}  </math>
|width=50p=x align="right"|(14)
|width=50p=x align="right"|(14)
|}
|}
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1) Stability of a possible failure plane
1) Stability of a possible failure plane
::::{|
::::{|
|width=500px|<math> F_{total} = {\frac{ \sum\limits_{i=0}^N[b_{i}\left ( c_{i} + \left ( {\frac{W_{i}}{b_{i}}} - u_{i} \right ) tan \phi _{i} \right ) {\frac{sec \alpha _{i}}{1 + {\frac{tan \alpha _{i} tan \phi _{i}}{F_{total}}}}}]}{\sum\limits_{i=0}^N W_{i} sin \alpha _{i}}}  </math>
|width=800px|<math> F_{total} = {\frac{ \sum\limits_{i=0}^N[b_{i}\left ( c_{i} + \left ( {\frac{W_{i}}{b_{i}}} - u_{i} \right ) tan \phi _{i} \right ) {\frac{sec \alpha _{i}}{1 + {\frac{tan \alpha _{i} tan \phi _{i}}{F_{total}}}}}]}{\sum\limits_{i=0}^N W_{i} sin \alpha _{i}}}  </math>
|width=50p=x align="right"|(15)
|width=50p=x align="right"|(15)
|}
|}
2) excess pore pressure using Gibson's graphical approximation (1958)
2) excess pore pressure using Gibson's graphical approximation (1958)
::::{|
::::{|
|width=500px|<math> u_{i} = {\frac{\gamma' z_{i}}{a_{i}}}  </math>
|width=800px|<math> u_{i} = {\frac{\gamma' z_{i}}{a_{i}}}  </math>
|width=50p=x align="right"|(16)
|width=50p=x align="right"|(16)
|}
|}
::::{|
::::{|
|width=500px|<math> a \equiv 6.4 \left ( 1 - {\frac{T}{16}} \right )^\left (17\right ) + 1  </math>
|width=800px|<math> a \equiv 6.4 \left ( 1 - {\frac{T}{16}} \right )^\left (17\right ) + 1  </math>
|width=50p=x align="right"|(17)
|width=50p=x align="right"|(17)
|}
|}
::::{|
::::{|
|width=500px|<math> T \equiv {\frac{m^2 t}{c_{v}}}  </math>
|width=800px|<math> T \equiv {\frac{m^2 t}{c_{v}}}  </math>
|width=50p=x align="right"|(18)
|width=50p=x align="right"|(18)
|}
|}
* River mouth turbidity currents
* River mouth turbidity currents
::::{|
::::{|
|width=500px|<math> {\frac{\partial u}{\partial t}} = g_{0} sin \alpha C - {\frac{E + C_{d}}{h}}u^2 - g_{0} \left ({\frac{e^C - 1}{e - 1}}\right ) cos \alpha C tan \gamma  </math>
|width=800px|<math> {\frac{\partial u}{\partial t}} = g_{0} sin \alpha C - {\frac{E + C_{d}}{h}}u^2 - g_{0} \left ({\frac{e^C - 1}{e - 1}}\right ) cos \alpha C tan \gamma  </math>
|width=50p=x align="right"|(19)
|width=50p=x align="right"|(19)
|}
|}
::::{|
::::{|
|width=500px|<math> C = \sum\limits_{i=1}^N C_{i} = {\frac{\rho _{f} - \rho}{\rho _{s} - \rho}} </math>
|width=800px|<math> C = \sum\limits_{i=1}^N C_{i} = {\frac{\rho _{f} - \rho}{\rho _{s} - \rho}} </math>
|width=50p=x align="right"|(20)
|width=50p=x align="right"|(20)
|}
|}
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1) one dimensional steady-state turbidity current model INFLO
1) one dimensional steady-state turbidity current model INFLO
::::{|
::::{|
|width=500px|<math> {\frac{\partial Q}{\partial x}} = E u W </math>
|width=800px|<math> {\frac{\partial Q}{\partial x}} = E u W </math>
|width=50p=x align="right"|(21)
|width=50p=x align="right"|(21)
|}
|}
Continuity equation for the ith grain size of the flow's suspeneded load
Continuity equation for the ith grain size of the flow's suspeneded load
::::{|
::::{|
|width=500px|<math> {\frac{\partial J_{i}}{\partial x}} = E_{Ri} - D_{Ri}</math>
|width=800px|<math> {\frac{\partial J_{i}}{\partial x}} = E_{Ri} - D_{Ri}</math>
|width=50p=x align="right"|(22)
|width=50p=x align="right"|(22)
|}
|}
The rate of erosion of the ith grain size of the seafloor by the current
The rate of erosion of the ith grain size of the seafloor by the current
::::{|
::::{|
|width=500px|<math> E_{R} = \left ({\frac{C_{D} \rho _{f} u^2 - \delta _{b}}{\delta _{a}}} \right ) {\frac{\varphi _{i} W}{day}} </math>
|width=800px|<math> E_{R} = \left ({\frac{C_{D} \rho _{f} u^2 - \delta _{b}}{\delta _{a}}} \right ) {\frac{\varphi _{i} W}{day}} </math>
|width=50p=x align="right"|(23)
|width=50p=x align="right"|(23)
|}
|}
Rate of deposition of the ith grain size in the flow
Rate of deposition of the ith grain size in the flow
::::{|
::::{|
|width=500px|<math> D_{Ri} = \left\{\begin{matrix} 0 & if u > u_{cr} \\ {\frac{\lambda _{i} J_{i}}{u}} \left ( 1 - {\frac{u^2}{u_{cr}^2}}\right ) & if u <= u_{cr} \end{matrix}\right. </math>
|width=800px|<math> D_{Ri} = \left\{\begin{matrix} 0 & if u > u_{cr} \\ {\frac{\lambda _{i} J_{i}}{u}} \left ( 1 - {\frac{u^2}{u_{cr}^2}}\right ) & if u <= u_{cr} \end{matrix}\right. </math>
|width=50p=x align="right"|(24)
|width=50p=x align="right"|(24)
|}
|}
Critical velocity for deposition
Critical velocity for deposition
::::{|
::::{|
|width=500px|<math> u_{cr} = {\frac{w_{s}}{\sqrt{C_{D}}}} </math>
|width=800px|<math> u_{cr} = {\frac{w_{s}}{\sqrt{C_{D}}}} </math>
|width=50p=x align="right"|(25)
|width=50p=x align="right"|(25)
|}
|}
Line 349: Line 505:
Governing equation
Governing equation
::::{|
::::{|
|width=500px|<math> {\frac{\partial h}{\partial t}} + {\frac{\partial}{\partial x}} \left (u h_{f} \right ) = E_{w} u </math>
|width=800px|<math> {\frac{\partial h}{\partial t}} + {\frac{\partial}{\partial x}} \left (u h_{f} \right ) = E_{w} u </math>
|width=50p=x align="right"|(26)
|width=50p=x align="right"|(26)
|}
|}
::::{|
::::{|
|width=500px|<math> {\frac{\partial}{\partial t}} \left (u h_{f} \right ) + {\frac{\partial}{\partial x}}\left (u^2 h_{f}\right ) = -{\frac{\left ( \rho _{s} - \rho _{w} \right ) g}{2 \rho_{w}}}{\frac{\partial}{\partial x}} \left (Ch_{f}^2 \right ) + {\frac{\left (\rho _{s} - \rho _{w} \right ) g h_{f} C S}{\rho_{w}}} - C_{d} \left ( 1 + \alpha \right ) u^2 </math>
|width=800px|<math> {\frac{\partial}{\partial t}} \left (u h_{f} \right ) + {\frac{\partial}{\partial x}}\left (u^2 h_{f}\right ) = -{\frac{\left ( \rho _{s} - \rho _{w} \right ) g}{2 \rho_{w}}}{\frac{\partial}{\partial x}} \left (Ch_{f}^2 \right ) + {\frac{\left (\rho _{s} - \rho _{w} \right ) g h_{f} C S}{\rho_{w}}} - C_{d} \left ( 1 + \alpha \right ) u^2 </math>
|width=50p=x align="right"|(27)
|width=50p=x align="right"|(27)
|}
|}
::::{|
::::{|
|width=500px|<math> {\frac{\partial}{\partial t}} \left ( Ch_{f} \right ) + {\frac{\partial}{\partial x}}\left ( u Ch_{f}\right ) = - F_{d} + F </math>
|width=800px|<math> {\frac{\partial}{\partial t}} \left ( Ch_{f} \right ) + {\frac{\partial}{\partial x}}\left ( u Ch_{f}\right ) = - F_{d} + F </math>
|width=50p=x align="right"|(28)
|width=50p=x align="right"|(28)
|}
|}
::::{|
::::{|
|width=500px|<math> E_{w} = {\frac{0.00153}{0.0204 + Ri}} </math>
|width=800px|<math> E_{w} = {\frac{0.00153}{0.0204 + Ri}} </math>
|width=50p=x align="right"|(29)
|width=50p=x align="right"|(29)
|}
|}
::::{|
::::{|
|width=500px|<math> Ri = {\frac{\left (\rho_{s} - \rho_{w}\right ) g h_{f}C}{\rho_{w}u^2}} </math>
|width=800px|<math> Ri = {\frac{\left (\rho_{s} - \rho_{w}\right ) g h_{f}C}{\rho_{w}u^2}} </math>
|width=50p=x align="right"|(30)
|width=50p=x align="right"|(30)
|}
|}
::::{|
::::{|
|width=500px|<math> F_{d} = \left\{\begin{matrix} w_{s} C \left (2 - 1/p_{z} \right ) & p_{z} < 0.5 // 0 & p_{z} >= 0.5 \end{matrix}\right.</math>
|width=800px|<math> F_{d} = \left\{\begin{matrix} w_{s} C \left (2 - 1/p_{z} \right ) & p_{z} < 0.5 // 0 & p_{z} >= 0.5 \end{matrix}\right.</math>
|width=50p=x align="right"|(31)
|width=50p=x align="right"|(31)
|}
|}
::::{|
::::{|
|width=500px|<math> F_{e} = \left ( \left (C_{d} \rho_{f} u^2 - b \right ) / \left ( a 86400 \right ) \right ) </math>
|width=800px|<math> F_{e} = \left ( \left (C_{d} \rho_{f} u^2 - b \right ) / \left ( a 86400 \right ) \right ) </math>
|width=50p=x align="right"|(32)
|width=50p=x align="right"|(32)
|}
|}
::::{|
::::{|
|width=500px|<math> |log p_{z}|^\left (1/4 \right ) \cong 0.124 log_{2} Z_{0} + 1.2 </math>
|width=800px|<math> |log p_{z}|^\left (1/4 \right ) \cong 0.124 log_{2} Z_{0} + 1.2 </math>
|width=50p=x align="right"|(33)
|width=50p=x align="right"|(33)
|}
|}
::::{|
::::{|
|width=500px|<math> Z_{0} \equiv w_{s}/ \left (\kappa u_{*} \right ) </math>
|width=800px|<math> Z_{0} \equiv w_{s}/ \left (\kappa u_{*} \right ) </math>
|width=50p=x align="right"|(34)
|width=50p=x align="right"|(34)
|}
|}
Line 387: Line 543:
1) Depth-averaged debris flow equations (Continuity)
1) Depth-averaged debris flow equations (Continuity)
::::{|
::::{|
|width=500px|<math> {\frac{\partial D}{\partial t}} + {\frac{\partial}{\partial x}} [U_{p}D_{p} + {\frac{2}{3}}U_{p}D_{s}] = 0 </math>
|width=800px|<math> {\frac{\partial D}{\partial t}} + {\frac{\partial}{\partial x}} [U_{p}D_{p} + {\frac{2}{3}}U_{p}D_{s}] = 0 </math>
|width=50p=x align="right"|(35)
|width=50p=x align="right"|(35)
|}
|}
2) Depth-averaged debris flow equations (Momentum (shear layer))
2) Depth-averaged debris flow equations (Momentum (shear layer))
::::{|
::::{|
|width=500px|<math> {\frac{2}{3}} {\frac{\partial}{\partial t}} \left (U_{p}U_{s} \right ) - U_{p} {\frac{\partial D_{s}}{\partial t}} + {\frac{8}{15}}{\frac{\partial}{\partial x}} \left ( U_{p}^2 D_{s} \right ) {\frac{2}{3}} U_{p} {\frac{\partial}{\partial x}} \left (U_{p} D_{s} \right ) = D_{s} g \left ( 1 - {\frac{\rho_{w}}{\rho_{\rho_{m}}}}\right ) S - D_{s} g {\frac{\partial D}{\partial x}} - 2 {\frac{\mu U_{p}}{\rho_{m} D_{s}}} </math>
|width=800px|<math> {\frac{2}{3}} {\frac{\partial}{\partial t}} \left (U_{p}U_{s} \right ) - U_{p} {\frac{\partial D_{s}}{\partial t}} + {\frac{8}{15}}{\frac{\partial}{\partial x}} \left ( U_{p}^2 D_{s} \right ) {\frac{2}{3}} U_{p} {\frac{\partial}{\partial x}} \left (U_{p} D_{s} \right ) = D_{s} g \left ( 1 - {\frac{\rho_{w}}{\rho_{\rho_{m}}}}\right ) S - D_{s} g {\frac{\partial D}{\partial x}} - 2 {\frac{\mu U_{p}}{\rho_{m} D_{s}}} </math>
|width=50p=x align="right"|(36)
|width=50p=x align="right"|(36)
|}
|}
3) Depth-averaged debris flow equations (Momentum (plug flow layer))
3) Depth-averaged debris flow equations (Momentum (plug flow layer))
::::{|
::::{|
|width=500px|<math> {\frac{\partial}{\partial t}} \left ( U_{p} D_{p}\right ) + {\frac{\partial}{\partial x}} \left (U_{p}^2 D_{p} \right ) + U_{p}{\frac{\partial D_{s}}{\partial t}} + {\frac{2}{3}}U_{p}{\frac{\partial}{\partial x}} \left (U_{p} D_{s} \right ) = D_{p} g \left ( 1 - {\frac{\rho_{w}}{\rho_{m}}} \right ) S - D_{p} g {\frac{\partial D}{\partial x}} - {\frac{\tau_{y}}{\rho_{m}}}</math>
|width=800px|<math> {\frac{\partial}{\partial t}} \left ( U_{p} D_{p}\right ) + {\frac{\partial}{\partial x}} \left (U_{p}^2 D_{p} \right ) + U_{p}{\frac{\partial D_{s}}{\partial t}} + {\frac{2}{3}}U_{p}{\frac{\partial}{\partial x}} \left (U_{p} D_{s} \right ) = D_{p} g \left ( 1 - {\frac{\rho_{w}}{\rho_{m}}} \right ) S - D_{p} g {\frac{\partial D}{\partial x}} - {\frac{\tau_{y}}{\rho_{m}}}</math>
|width=50p=x align="right"|(37)
|width=50p=x align="right"|(37)
|}
|}
Line 403: Line 559:
1) Isostatic subsidence
1) Isostatic subsidence
::::{|
::::{|
|width=500px|<math> w \left (x\right ) = {\frac{p\left (x\right ) \alpha ^3}{8D}}exp \left( -{\frac{|x|}{\alpha}}\right ) + sin \left ({\frac{|x|}{\alpha}}\right ) \right ) </math>
|width=800px|<math> w \left (x\right ) = {\frac{p\left (x\right ) \alpha ^3}{8D}}exp \left( -{\frac{|x|}{\alpha}}\right ) + sin \left ({\frac{|x|}{\alpha}}\right ) </math>
|width=50p=x align="right"|(38)
|width=50p=x align="right"|(38)
|}
|}
::::{|
::::{|
|width=500px|<math> \alpha \equiv ^4 \sqrt{{\frac{4D}{\rho_{m}g}}} </math>
|width=800px|<math> \alpha \equiv ^4 \sqrt{{\frac{4D}{\rho_{m}g}}} </math>
|width=50p=x align="right"|(39)
|width=50p=x align="right"|(39)
|}
|}
::::{|
::::{|
|width=500px|<math> W \left (x\right ) = \sum\limits_{i=-\propto}^\left (\propto\right ) w \left ( x - x_{i} \right ) </math>
|width=800px|<math> W \left (x\right ) = \sum\limits_{i=-\propto}^\left (\propto\right ) w \left ( x - x_{i} \right ) </math>
|width=50p=x align="right"|(40)
|width=50p=x align="right"|(40)
|}
|}
* Compaction
* Compaction
::::{|
::::{|
|width=500px|<math> {\frac{\partial \phi}{\partial \delta}} = - c \left ( \phi - \phi_{0}\right ) </math>
|width=800px|<math> {\frac{\partial \phi}{\partial \delta}} = - c \left ( \phi - \phi_{0}\right ) </math>
|width=50p=x align="right"|(41)
|width=50p=x align="right"|(41)
|}
|}
* Subaerial erosion and deposition by river
* Subaerial erosion and deposition by river
::::{|
::::{|
|width=500px|<math> {\frac{\partial \eta}{\partial t}} = \nu {\frac{\partial ^2 \eta}{\partial x^2}} </math>
|width=800px|<math> {\frac{\partial \eta}{\partial t}} = \nu {\frac{\partial ^2 \eta}{\partial x^2}} </math>
|width=50p=x align="right"|(42)
|width=50p=x align="right"|(42)
|}
|}
Diffusion coefficient
Diffusion coefficient
::::{|
::::{|
|width=500px|<math> \nu \equiv {\frac{-8 <q> A \sqrt{c_{f}}}{C_{0}\left ( s - 1 \right )}} </math>
|width=800px|<math> \nu \equiv {\frac{-8 <q> A \sqrt{c_{f}}}{C_{0}\left ( s - 1 \right )}} </math>
|width=50p=x align="right"|(43)
|width=50p=x align="right"|(43)
|}
|}
Line 432: Line 588:
1) Closure depth
1) Closure depth
::::{|
::::{|
|width=500px|<math> h_{c} = 2.28 H_{ss} - 6.85 \left ({\frac{H_{ss}^2}{g T^2}}\right ) </math>
|width=800px|<math> h_{c} = 2.28 H_{ss} - 6.85 \left ({\frac{H_{ss}^2}{g T^2}}\right ) </math>
|width=50p=x align="right"|(44)
|width=50p=x align="right"|(44)
|}
|}
2) Sediment flux for the outer shelf (depth greater than h<sub>c</sub>)
2) Sediment flux for the outer shelf (depth greater than h<sub>c</sub>)
::::{|
::::{|
|width=500px|<math> q_{s} = {\frac{16}{3\pi}}{\frac{\rho}{\rho_{s} - \rho}}{\frac{C_{fs}\varepsilon _{ss}}{g}}I_{s}{\frac{U_{om}^3}{w_{s}}}\left ( v_{0} + {\frac{U_{om}^2}{5 w_{s}}}{\frac{\partial h}{\partial x}}\right ) </math>
|width=800px|<math> q_{s} = {\frac{16}{3\pi}}{\frac{\rho}{\rho_{s} - \rho}}{\frac{C_{fs}\varepsilon _{ss}}{g}}I_{s}{\frac{U_{om}^3}{w_{s}}}\left ( v_{0} + {\frac{U_{om}^2}{5 w_{s}}}{\frac{\partial h}{\partial x}}\right ) </math>
|width=50p=x align="right"|(45)
|width=50p=x align="right"|(45)
|}
|}
3) Equation for shoaling waves
3) Equation for shoaling waves
::::{|
::::{|
|width=500px|<math> U_{om} \left (h\right ) = {\frac{\gamma b}{2}} \sqrt{g b_{b}} \left ({\frac{h}{h_{b}}}\right )^\left ({\frac{-3}{4}}\right ) </math>
|width=800px|<math> U_{om} \left (h\right ) = {\frac{\gamma b}{2}} \sqrt{g b_{b}} \left ({\frac{h}{h_{b}}}\right )^\left ({\frac{-3}{4}}\right ) </math>
|width=50p=x align="right"|(46)
|width=50p=x align="right"|(46)
|}
|}
4) Komar's (1998) equation for the threshold of sediment motion
4) Komar's (1998) equation for the threshold of sediment motion
::::{|
::::{|
|width=500px|<math> {\frac{\rho u_{t}^2}{\left ( \rho_{s} - \rho \right ) g d}} =  \left\{\begin{matrix} 0.21 \left ({\frac{d_{0}}{d}}\right )^ \left ({\frac{1}{2}}\right ) & for D <= 0.5 mm // 0.46 \pi \left ({\frac{d_{0}}{d}}\right )^\left ({\frac{1}{4}}\right ) & for D > 0.5 mm \end{matrix}\right.</math>
|width=800px|<math> {\frac{\rho u_{t}^2}{\left ( \rho_{s} - \rho \right ) g d}} =  \left\{\begin{matrix} 0.21 \left ({\frac{d_{0}}{d}}\right )^ \left ({\frac{1}{2}}\right ) & for D <= 0.5 mm \\ 0.46 \pi \left ({\frac{d_{0}}{d}}\right )^\left ({\frac{1}{4}}\right ) & for D > 0.5 mm \end{matrix}\right.</math>
|width=50p=x align="right"|(47)
|width=50p=x align="right"|(47)
|}
|}
5) Near-bottom threshold velocity
5) Near-bottom threshold velocity
::::{|
::::{|
|width=500px|<math> u_{t} = {\frac{\pi d_{0}}{T}} = {\frac{\pi H}{T sinh \left (2 \pi h / L \right )}} </math>
|width=800px|<math> u_{t} = {\frac{\pi d_{0}}{T}} = {\frac{\pi H}{T sinh \left (2 \pi h / L \right )}} </math>
|width=50p=x align="right"|(48)
|width=50p=x align="right"|(48)
|}
|}
6) Sediment flux within the near-shore zone (depth less than h<sub>c</sub>)
6) Sediment flux within the near-shore zone (depth less than h<sub>c</sub>)
::::{|
::::{|
|width=500px|<math> q_{s} = k_{c} \underline{x}^ \left ( 1 - m \right ) {\frac{dh}{dx}} </math>
|width=800px|<math> q_{s} = k_{c} \underline{x}^ \left ( 1 - m \right ) {\frac{dh}{dx}} </math>
|width=50p=x align="right"|(49)
|width=50p=x align="right"|(49)
|}
* Flexure of the lithosphere
1) Deflection of Earth's crust
::::{|
|width=800px|<math>w \left (\lambda r \right ) = {\frac{q \lambda}{2 \pi \rho_{d}g}} Kei \left (\lambda r \right )  </math>
|width=50p=x align="right"|(50)
|}
2) Flexural parameter
::::{|
|width=800px|<math> \lambda = \left ({\frac{D}{\rho_{d}g}}\right )^ \left ({\frac{-1}{4}}\right )  </math>
|width=50p=x align="right"|(51)
|}
3) Time delay between the addition of load and the lithosphere's response
::::{|
|width=800px|<math> w \left (t \right ) = w_{0} \left ( 1 - exp \left (- t / t_{0} \right ) \right )  </math>
|width=50p=x align="right"|(52)
|}
|}
<div class="NavFrame collapsed" style="text-align:left">
  <div class="NavHead">Nomenclature</div>
  <div class="NavContent">
{| {{Prettytable}} class="wikitable sortable"
!Symbol!!Description!!Unit
|-
|Q<sub>0</sub> (in River dynamics)
|water discharge from the river
| L<sup>3</sup> / T
|-
|u<sub>0</sub> (in River dynamics)
|mean river mouth flow velocity
| L / T
|-
|b<sub>0</sub> (in River dynamics)
|channel width
| L
|-
|h<sub>0</sub> (in River dynamics)
|channel depth
| L
|-
|Q<sub>s0</sub> (in River dynamics)
|mean suspended suspended load leaving the river
| M / L
|-
|Cs<sub>i</sub> (in River dynamics)
|concentration of the ith grain size size
| M / L<sup>3</sup>
|-
|Q<sub>b</sub> (in River dynamics)
|bedload flux from river mouth
| M / T
|-
|Q<sub>c</sub> (in River dynamics)
|critical discharge below which no bedload transport occurs
| M / T
|-
|ρ<sub>s</sub> (in River dynamics)
|grain density
| M / L<sup>3</sup>
|-
|fluid density (in River dynamics)
| M / L<sup>3</sup>
|-
|g
|acceleration due to gravity
| l / t<sup>2</sup>
|-
|β (in River dynamics)
|bedload rating term
| -
|-
|s (in River dynamics)
|slope of the riverbed
| -
|-
|e<sub>b</sub> (in River dynamics)
|bedload efficiency
| -
|-
|f (in River dynamics)
|angle of repose of river bed sediment
| -
|-
|X (In avulsion)
| river distributary
| -
|-
|Θ (In avulsion)
| anglar position of X distributary
| -
|-
|D (in bedload dumping)
| depth of bedload dumped at river mouth
| L
|-
|x
| longitudinal or axial direction
| -
|-
|y
| lateral direction
| -
|-
|u (in river plumes)
| longitudinal velocity (in the x direction)
| L / T
|-
|v (in river plumes)
| lateral velocity (in the y direction)
| L / T
|-
|I (in river plumes)
| sediment inventory of the plume
| -
|-
|λ (in river plumes)
| removal rate constant for a grain size (take marine flocculation into account)
| 1 / T
|-
|K (in river plumes)
| sediment diffusivity driven by turbulence (assumed equal to the turbulent diffusivity and the eddy viscosity)
| L<sup>2</sup> / T
|-
|Fr
| Froude number
| -
|-
|v<sub>0</sub> (in river plumes)
| ambient coastal current velocity
| L / T
|-
|C<sub>1</sub> (in river plumes)
| empirically derived constant and found to be 0.109
| -
|-
|C<sub>0</sub> (in river plumes)
| plume concentration at the river mouth
| M / L<sup>3</sup>
|-
|q<sub>s</sub>  (in diffusion of seafloor sediments)
| amount of bottom sediments that can be reworked by resuspension and diffusion (resuspended sediment)
| M / L
|-
|k  (in diffusion of seafloor sediments)
| diffusion coefficient
| -
|-
|t
| time
| T
|-
|z  (in diffusion of seafloor sediments)
| water depth
| L
|-
|D (in diffusion of seafloor sediments)
| grain size
| L
|-
|β<sub>i</sub>  (in diffusion of seafloor sediments)
| user-defined index (between 0 and 1), reflect the ability of resuspension to move the ith grain size
| -
|-
|b (in Sediment failure)
| width of a slice in a failure
| L
|-
|c (in Sediment failure)
| sediment cohesion
| M / T<sup>2</sup>
|-
|W (in Sediment failure)
| linear weight of the sediment
| M / T<sup>2</sup>
|-
|u (in Sediment failure)
| excess pore pressure
| M / (L T<sup>2</sup>)
|-
|φ (in Sediment failure)
| sediment friction angle
| -
|-
|α (slope of failure surface)
| slope of the failure surface
| -
|-
|F<sub>total</sub> (slope of failure surface)
| factor of safety for a sediment failure
| -
|-
|γ' (slope of failure surface)
| submerged density of sediment, equals to (γ - γ<sub>f</sub>)g
| M / L<sup>3</sup>
|-
|z
| depth of the failure plane with respect to the seafloor
| L
|-
|l
| sedimentation rate
| M / T
|-
|C<sub>v</sub> (in River mouth turbidity currents )
| consolidation coefficient for the sediment
| -
|-
|g<sub>0</sub> (in River mouth turbidity currents )
| reduced gravity
| L / T<sup>2</sup>
|-
|u (in River mouth turbidity currents)
| downslope velocity
| L / T
|-
|α (in River mouth turbidity currents)
| seafloor slope
| -
|-
|E (in River mouth turbidity currents)
| entrainment coefficient that controls the rate seawater dilutes the gravity flow
| -
|-
|C<sub>D</sub> (in River mouth turbidity currents)
| drag coefficient
| -
|-
|h (in River mouth turbidity currents)
| height of the flow
| L
|-
|ρ (in River mouth turbidity currents)
| ambient fluid density
| M / L<sup>3</sup>
|-
|ρ<sub>f</sub> (in River mouth turbidity currents)
| density of the flow
| M / L<sup>3</sup>
|-
|ρ<sub>s</sub> (in River mouth turbidity currents)
| grain density
| M / L<sup>3</sup>
|-
|C (in River mouth turbidity currents)
| vertically averaged flow concentration
| -
|-
|C<sub>i</sub> (in River mouth turbidity currents)
| volume concentration of the ith grain size in the flow
| M / L<sup>3</sup>
|-
|n (in River mouth turbidity currents)
| number of discrete grain sizes carried by the flow
| -
|-
|W (in River mouth turbidity currents)
| flow width
| L
|-
|Q (in River mouth turbidity currents)
| volume discharge between flow elements
| L<sup>3</sup> / T
|-
|J<sub>i</sub> (in River mouth turbidity currents)
| flux of ith grain size between elements
| L<sup>3</sup> / T
|-
|E<sub>Ri</sub> (in River mouth turbidity currents)
| rate of erosion of the ith grain size
| L / T
|-
|day (in River mouth turbidity currents)
| 86400 s
| T
|-
|δ<sub>a</sub> (in River mouth turbidity currents)
| gradient of shear strength in seafloor sediment
| M / (LT<sup>2</sup>)
|-
|δ<sub>b</sub> (in River mouth turbidity currents)
| shear strength of the sediment at the seafloor
| M / (L<sup>1</sup> T<sup>2</sup>)
|-
|D<sub>Ri</sub> (in River mouth turbidity currents)
| rate of deposition of the ith grain size
| L / T
|-
|u<sub>cr</sub> (in River mouth turbidity currents)
| critical velocity for deposition
| L / T
|-
|h<sub>f</sub> (in River mouth turbidity currents)
| flow thickness
| L
|-
|E<sub>w</sub> (in River mouth turbidity currents)
| water entrainment coefficient
| -
|-
|S (in River mouth turbidity currents)
| bottom slope gradient
| -
|-
|C<sub>d</sub> (in River mouth turbidity currents)
| drag coefficient, equals to 0.004
| -
|-
| α(in River mouth turbidity currents)
| ratio of the drag force at the upper flow surface to that at the bed, equals to 0.43
| -
|-
| F<sub>d</sub>(in River mouth turbidity currents)
| flux of sediment deposition
| -
|-
| F<sub>d</sub>(in River mouth turbidity currents)
| flux of sediment erosion
| -
|-
| Ri(in River mouth turbidity currents)
| Richardson number from Fukishima et al. (1985)
| -
|-
| w<sub>s</sub>(in River mouth turbidity currents)
| particle settling velocity
| L / T
|-
| ρ<sub>f</sub>(in River mouth turbidity currents)
| flow density
| M / L<sup>3</sup>
|-
| a(in River mouth turbidity currents)
| increasing rate of shear strength with burial depth, equals to 3.5
| -
|-
| b(in River mouth turbidity currents)
| shear strength at the bed, equals to 0.2
| -
|-
| Z<sub>0</sub>(in River mouth turbidity currents)
| Rouse number
| -
|-
| κ (in River mouth turbidity currents)
| von Karman constant, equals to 0.4
| -
|-
| u<sub>*</sub> (in River mouth turbidity currents)
| shear velocity of the flow
| l / t
|-
| D (in Debris flows)
| total depth of the debris flow (D<sub>p</sub> + D<sub>s</sub>)
| L
|-
| D<sub>p</sub> (in Debris flows)
| depth of the upper plug zone
| L
|-
| U<sub>p</sub> (in Debris flows)
| layer-averaged velocity of the upper plug zone
| L / T
|-
| D<sub>s</sub> (in Debris flows)
| depth of the lower shear layer
| L
|-
| U<sub>s</sub> (in Debris flows)
| layer-averaged veolocity of the lower shear layer
| L / T
|-
| ρ<sub>m</sub> (in Debris flows)
| density of the mud flow
| M / L<sup>3</sup>
|-
| τ<sub>y</sub> (in Debris flows)
| yield strength
| -
|-
| μ (in Debris flows)
| kinematic viscosity
| -
|-
| w (in Subsidence)
| displacement of crust due to sediment loading
| L
|-
| D (in Subsidence)
| flexural rigidity of the earth's crust
| M L<sup>2</sup> / T<sup>2</sup>
|-
| ρ<sub>m</sub> (in Subsidence)
| density of the overlying sediment
| M / L<sup>3</sup>
|-
| φ (in Compaction)
| porosity of sediment
| -
|-
| φ<sub>0</sub> (in Compaction)
| porosity of sediment in its closest packed arrangement (due only to mechanical compaction)
| -
|-
| δ (in Compaction)
| sediment load
| -
|-
| c (in Compaction)
| empirical constant for compaction
| L T<sup>2</sup> / M
|-
| η (in Subaerial erosion and deposition by rivers)
| height of the bed
| L
|-
| ν (in Subaerial erosion and deposition by rivers)
| diffusion coefficient
| -
|-
| <q> (in Subaerial erosion and deposition by rivers)
| long-term average water discharge
| L<sup>3</sup> / T
|-
| c<sub>f</sub> (in Subaerial erosion and deposition by rivers)
| drag coefficient
| -
|-
| C<sub>0</sub> (in Subaerial erosion and deposition by rivers)
| sediment concentration of the bed
| M / L<sup>3</sup>
|-
| s (in Subaerial erosion and deposition by rivers)
| sediment specific gravity
| -
|-
| A (in Subaerial erosion and deposition by rivers)
| river-type dependent constant (user-defined and takes on one of the two values depending on the river type: 1 for meandering river, (ε/(1+ε))<sup>3/2</sup> for braided river)
| -
|-
| ε (in Subaerial erosion and deposition by rivers)
|  typically about 0.4 for gravel bed rivers (Parker, 1978)
| -
|-
| τ (in Subaerial erosion and deposition by rivers)
| shear stress in the center of a braided channel, equals to (1+ε)τ<sub>c</sub>
| -
|-
| τ<sub>c</sub> (in Subaerial erosion and deposition by rivers)
| critical shear stress needed for band erosion
| -
|-
| h<sub>c</sub> (in Cross-shore transport due to ocean storms)
| closure depth
| L
|-
| H<sub>ss</sub> (in Cross-shore transport due to ocean storms)
| height of the storm wave that is exceeded only 12h each year
| L
|-
| T (in Cross-shore transport due to ocean storms)
| period of the storm wave that is exceeded only 12h each year
| T
|-
| q<sub>s</sub> (in Cross-shore transport due to ocean storms)
| sediment flux at each position along the outer shelf profile
| M / T
|-
| C<sub>fs</sub> (in Cross-shore transport due to ocean storms)
| constant drag coefficient
| -
|-
| ε<sub>ss</sub> (in Cross-shore transport due to ocean storms)
| efficiency of suspended sediment transport
| -
|-
| I<sub>s</sub> (in Cross-shore transport due to ocean storms)
| time fraction (intermittency) of ocean storms
| -
|-
| U<sub>om</sub> (in Cross-shore transport due to ocean storms)
| near-bed velocity due to waves
| L / T
|-
| h (in Cross-shore transport due to ocean storms)
| local water depth
| L
|-
| γ<sub>b</sub> (in Cross-shore transport due to ocean storms)
| ratio of wave height to water depth where wave will break, assumed to be 0.6
| -
|-
| h<sub>b</sub> (in Cross-shore transport due to ocean storms)
|  water depth where wave will break
| L
|-
| D (in Cross-shore transport due to ocean storms)
|  grain size
| L
|-
| u<sub>t</sub> (in Cross-shore transport due to ocean storms)
|  near-bottom threshold velocity
| L / T
|-
| d<sub>0</sub> (in Cross-shore transport due to ocean storms)
|  orbital diameter of the wave motion
| L
|-
| H (in Cross-shore transport due to ocean storms)
|  wave height
| L
|-
| T (in Cross-shore transport due to ocean storms)
| wave period
| T
|-
| L (in Cross-shore transport due to ocean storms)
|  wave length
| L
|-
| x (in Cross-shore transport due to ocean storms)
|  offshore position normalized by the position of near-shore boundary
| -
|-
| m (in Cross-shore transport due to ocean storms)
|  diffusion coefficient within this specific x-dependence to ensure the equilibrim profile will be a Bruun profile, m equals to 2/3
| -
|-
|w (in Flexure of the lithosphere)
| deflection of earth's crust
| -
|-
|λ (in Flexure of the lithosphere)
| flexural parameter
| -
|-
|r (in Flexure of the lithosphere)
| distance from the point load
| -
|-
|q (in Flexure of the lithosphere)
| point load
| -
|-
|Kei (in Flexure of the lithosphere)
| Kelvin function
| -
|-
|ρ<sub>d</sub> (in Flexure of the lithosphere)
| density of the asthenosphere
| M / L<sup>3</sup>
|-
|D (in Flexure of the lithosphere)
| flexural rigidity of the earth's crust
| -
|-
|w<sub>0</sub> (in Flexure of the lithosphere)
| equilibrium deflection
| -
|-
|t<sub>0</sub> (in Flexure of the lithosphere)
| response time associated with mantle viscosity
| -
|-
|}
  </div>
</div>


==Notes==
==Notes==
<span class="remove_this_tag">Any notes, comments, you want to share with the user</span>
See the reference Syvitski and Hutton (2001) and Hutton and Syvitski (2008).
 
<span class="remove_this_tag">Numerical scheme</span>
 


==Examples==
==Examples==
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<span class="remove_this_tag">Follow the next steps to include images / movies of simulations:</span>
<span class="remove_this_tag">Follow the next steps to include images / movies of simulations:</span>
* <span class="remove_this_tag">Upload file: http://csdms.colorado.edu/wiki/Special:Upload</span>
* <span class="remove_this_tag">Upload file: https://csdms.colorado.edu/wiki/Special:Upload</span>
* <span class="remove_this_tag">Create link to the file on your page: <nowiki>[[Image:<file name>]]</nowiki>.</span>
* <span class="remove_this_tag">Create link to the file on your page: <nowiki>[[Image:<file name>]]</nowiki>.</span>


Line 477: Line 1,196:


==Developer(s)==
==Developer(s)==
<span class="remove_this_tag">Name of the module developer(s)</span>
[[User:Huttone|Eric Hutton]]


==References==
==References==
<span class="remove_this_tag">Key papers</span>
* Hutton, E. W. H. and Syvitski, J. P. M., 2008. Sedflux 2.0: An advanced process-response model that generates three-dimensional stratigraphy. Computer & Geosciences, 34, 1319~1337, Doi: [[http://dx.doi.org/10.1016/j.cageo.2008.02.013 10.1016/j.cageo.2008.02.013]].
* Syvitski, J. P. M. and Hutton, E. W. H., 2001. 2D SEDFLUX 1.0C: an advanced process-response numerical model for the fill of marine sedimentary basins. Computer & Geosciences, 27, 731~753, Doi: [[http://dx.doi.org/10.1016/S0098-3004(00)00139-4 10.1016/S0098-3004(00)00139-4]].


==Links==
==Links==
<span class="remove_this_tag">Any link, eg. to the model questionnaire, etc.</span>
* [[Model:Sedflux]]


[[Category:Modules]] [[Category:Utility components]]
[[Category:Modules]]

Latest revision as of 17:16, 19 February 2018

The CSDMS Help System

Sedflux

SEDFLUX is a basin-fill model, written in ANSI-standard C, able to simulate the delivery of sediment and their accumulation over time scales of tens of thousands of years. It simulates the dynamics of strata formation of continental margins fuse information from the atmosphere, ocean and regional geology, and it can provide information for areas and times for which actual measurements are not available, or for when purely statistical estimates are not adequate by themselves.

Model introduction

Sedflux combines individual process-response models into one fully interactive model, delivering a multi-sized sediment load onto and across a continental margin. The model allows for the deposit to compact, to undergo tectonic processes and isostatic subsidence from the sediment load. The new version, Sedflux 2.0 introduces a series of new process models, and is able to operate in one of two models to track the evolution of stratigraphy in either 2D or 3D. Additions to the 2D mode include the addition of models that simulate (1) erosion and deposition of sediment along a riverbed, (2) cross-shore transport due to ocean waves, and (3) turbidity currents and hyperpycnal flows. New processes in the 3D mode include (1) river channel avulsion, (2) two-dimensional diffusion due to ocean storms, and (3) two-dimensional flexure due to sediment loading. The spatial resolution of the architecture is typically 1–25 cm in the vertical and 10–100 m in the horizontal when operating in 2D mode. In 3D mode, the horizontal resolution usually extends to kilometers. In addition to fixed time steps (from days to hundreds of years), Sedflux 2.0 offers event-based time stepping as a way to conduct long-term simulations while still modeling low-frequency but high-energy events.

Model parameters

Parameter Description Unit
Input directory path to input files -
Site prefix site prefix for Input/Output files -
Case prefix case prefix for Input/Output files -
Parameter Description Unit
Water discharge port use the water discharge provides port -
Erosion port Use the erosion provides port -
Parameter Description Unit
Run duration simulation run time years
Grid resolution in x-direction m
Grid resolution in y-direction m
Grid resolution in z-direction m
Parameter Description Unit
Avulsion standard deviation degrees
Minimum river angle degrees
Maximum river angle degrees
Row position of river hinge point -
Column position of river hinge point -
Velocity of coastal current m / s
Suspended load concentration pre-grain suspended sediment concentration -
Distance to dump bedload -
Bed load flux bed load flux at river mouth kg / s
Parameter Description Unit
Output directory path to output grid files -
Interval between output files -
SeaFloorDepth file output file prefix for variable, in NetCDF format -
SeaFloorSlope file output file prefix for variable, in NetCDF format -
SeaFloorElevation file output file prefix for variable, in NetCDF format -
SeaFloor Thickness file output file prefix for variable, in NetCDF format -
SeaFloorGrain file output file prefix for variable, in NetCDF format -
SeaFloorAge file output file prefix for variable, in NetCDF format -
SeaFloorSand file output file prefix for variable, in NetCDF format -
SeaFloorSilt file output file prefix for variable, in NetCDF format -
SeaFloorClay file output file prefix for variable, in NetCDF format -
SeaFloorMud file output file prefix for variable, in NetCDF format -
SeaFloorFacies file output file prefix for variable, in NetCDF format -
SeaFloorDensity file output file prefix for variable, in NetCDF format -
SeaFloorPorosity file output file prefix for variable, in NetCDF format -
SeaFloorPermeability file output file prefix for variable, in NetCDF format -
SeaFloorBasement file output file prefix for variable, in NetCDF format -
SeaFloorRiver_mouth file output file prefix for variable, in NetCDF format -
Parameter Description Unit
Output directory path to output cube files -
Interval between output files -
Age file output file prefix for variable, in NetCDF format -
Facies file output file prefix for variable, in NetCDF format -
Pressure file output file prefix for variable, in NetCDF format -
Density file output file prefix for variable, in NetCDF format -
Grain_density file output file prefix for variable, in NetCDF format -
Max_density file output file prefix for variable, in NetCDF format -
Grain file output file prefix for variable, in NetCDF format -
Grain_in_meters file output file prefix for variable, in NetCDF format -
Sand file output file prefix for variable, in NetCDF format -
Silt file output file prefix for variable, in NetCDF format -
Clay file output file prefix for variable, in NetCDF format -
Mud file output file prefix for variable, in NetCDF format -
Velocity file output file prefix for variable, in NetCDF format -
Viscosity file output file prefix for variable, in NetCDF format -
Relative_density file output file prefix for variable, in NetCDF format -
Porosity file output file prefix for variable, in NetCDF format -
Porosity_min file output file prefix for variable, in NetCDF format -
Porosity_max file output file prefix for variable, in NetCDF format -
Pi file output file prefix for variable, in NetCDF format -
Permeability file output file prefix for variable, in NetCDF format -
Void_ratio file output file prefix for variable, in NetCDF format -
Void_ratio_min file output file prefix for variable, in NetCDF format -
Void_ratio_max file output file prefix for variable, in NetCDF format -
Friction_angle file output file prefix for variable, in NetCDF format -
Consolidation file output file prefix for variable, in NetCDF format -
Yield_strength file output file prefix for variable, in NetCDF format -
Dynamic_viscosity file output file prefix for variable, in NetCDF format -
Mv file output file prefix for variable, in NetCDF format -
Hydraulic_con file output file prefix for variable, in NetCDF format -
Shear_strength file output file prefix for variable, in NetCDF format -
Cohesion file output file prefix for variable, in NetCDF format -
Consolidation_rate file output file prefix for variable, in NetCDF format -
Excess_pressure file output file prefix for variable, in NetCDF format -
Relative_pressure file output file prefix for variable, in NetCDF format -
Fraction file output file prefix for variable, in NetCDF format -
Parameter Description Unit
Model name name of the model -
Author name name of the model author m

Uses ports

This will be something that the CSDMS facility will add

Provides ports

This will be something that the CSDMS facility will add

Main equations

  • River dynamics (using HydroTrend model)

1) Water discharge

[math]\displaystyle{ Q_{0}=u_{0}b_{0}h_{0} }[/math] (1)

2) Mean suspended load entering the ocean basin

[math]\displaystyle{ Q_{s0}= Q_{0} \sum\limits_{i=1}^N Cs_{i} }[/math] (2)

3) Bedload equation by Bagnold (1966)

[math]\displaystyle{ Q_{b}={\frac{\rho _{s}}{\rho _{s} - \rho}}{\frac{\rho g Q_{0}^ \beta s e_{b}}{g tan f}} }[/math] (3)
  • Channel avulsion (using Avulsion model)
[math]\displaystyle{ \Theta _{n+1}=\Theta_{n} + X_{n} }[/math] (4)
  • Bedload dumping (not hyperpycnal flow)
[math]\displaystyle{ D={\frac{Q_{b}}{W_{d}L \rho}} }[/math] (5)
  • River plumes

1) Advection-diffusion equation

[math]\displaystyle{ {\frac{\partial u I}{\partial x}} + {\frac{\partial v I}{\partial y}} + \lambda I = {\frac{\partial}{\partial y}} \left ( K {\frac{\partial I}{\partial y}}\right ) + {\frac{\partial}{\partial x}} \left (K {\frac{\partial I}{\partial x}}\right ) }[/math] (6)

2) Froude number

[math]\displaystyle{ Fr = {\frac{u_{0}}{\sqrt{g h_{0}}}} }[/math] (7)

3) Plume's centerline

[math]\displaystyle{ {\frac{x}{b_{0}}}=1.53 + 0.90 \left ({\frac{u_{0}}{v_{0}}}\right ) \left ({\frac{y}{b_{0}}}\right )^\left (0.37\right ) }[/math] (8)

4) Non-conservative concentration along and surrounding the centerline position

[math]\displaystyle{ C\left (x,y\right ) = C_{0}exp\left (-\lambda t \right ) \sqrt{{\frac{b_{0}}{\sqrt{\pi}C_{1} x}}} exp [-\left ({\frac{y}{\sqrt{2} C_{1} x}}\right )^2] }[/math] (9)
[math]\displaystyle{ t\left (x,y\right ) = {\frac{u_{0} + u_{c}\left (x\right ) + 7u\left (x,y\right )}{9}} }[/math] (10)
[math]\displaystyle{ u_{c}\left (x\right ) = u_{0} \sqrt{{\frac{b_{0}}{\sqrt{\pi} C_{1} x}}} }[/math] (11)
[math]\displaystyle{ u\left (x,y\right ) = u_{0} \sqrt{{\frac{b_{0}}{\sqrt{\pi} C_{1} x }}} exp [-\left ({\frac{y}{\sqrt{2} C_{1} x}}\right )^2] }[/math] (12)
  • Diffusion of seafloor sediments

1) Amount of bottom sediments that can be reworked by resuspension and diffusion

[math]\displaystyle{ q_{s} = k\left (t,z,D\right ) \bigtriangledown z = k \left ( {\frac{\partial z}{\partial x}}\hat{i} + {\frac{\partial z}{\partial y}} \hat{j} \right ) }[/math] (13)

2) Amount and direction of transport of the ith grain size

[math]\displaystyle{ q_{si} = \beta _{i} q_{s} }[/math] (14)
  • Sediment failure

1) Stability of a possible failure plane

[math]\displaystyle{ F_{total} = {\frac{ \sum\limits_{i=0}^N[b_{i}\left ( c_{i} + \left ( {\frac{W_{i}}{b_{i}}} - u_{i} \right ) tan \phi _{i} \right ) {\frac{sec \alpha _{i}}{1 + {\frac{tan \alpha _{i} tan \phi _{i}}{F_{total}}}}}]}{\sum\limits_{i=0}^N W_{i} sin \alpha _{i}}} }[/math] (15)

2) excess pore pressure using Gibson's graphical approximation (1958)

[math]\displaystyle{ u_{i} = {\frac{\gamma' z_{i}}{a_{i}}} }[/math] (16)
[math]\displaystyle{ a \equiv 6.4 \left ( 1 - {\frac{T}{16}} \right )^\left (17\right ) + 1 }[/math] (17)
[math]\displaystyle{ T \equiv {\frac{m^2 t}{c_{v}}} }[/math] (18)
  • River mouth turbidity currents
[math]\displaystyle{ {\frac{\partial u}{\partial t}} = g_{0} sin \alpha C - {\frac{E + C_{d}}{h}}u^2 - g_{0} \left ({\frac{e^C - 1}{e - 1}}\right ) cos \alpha C tan \gamma }[/math] (19)
[math]\displaystyle{ C = \sum\limits_{i=1}^N C_{i} = {\frac{\rho _{f} - \rho}{\rho _{s} - \rho}} }[/math] (20)

Fluid continuity equation 1) one dimensional steady-state turbidity current model INFLO

[math]\displaystyle{ {\frac{\partial Q}{\partial x}} = E u W }[/math] (21)

Continuity equation for the ith grain size of the flow's suspeneded load

[math]\displaystyle{ {\frac{\partial J_{i}}{\partial x}} = E_{Ri} - D_{Ri} }[/math] (22)

The rate of erosion of the ith grain size of the seafloor by the current

[math]\displaystyle{ E_{R} = \left ({\frac{C_{D} \rho _{f} u^2 - \delta _{b}}{\delta _{a}}} \right ) {\frac{\varphi _{i} W}{day}} }[/math] (23)

Rate of deposition of the ith grain size in the flow

[math]\displaystyle{ D_{Ri} = \left\{\begin{matrix} 0 & if u \gt u_{cr} \\ {\frac{\lambda _{i} J_{i}}{u}} \left ( 1 - {\frac{u^2}{u_{cr}^2}}\right ) & if u \lt = u_{cr} \end{matrix}\right. }[/math] (24)

Critical velocity for deposition

[math]\displaystyle{ u_{cr} = {\frac{w_{s}}{\sqrt{C_{D}}}} }[/math] (25)

2) turbidity current model Sakura Governing equation

[math]\displaystyle{ {\frac{\partial h}{\partial t}} + {\frac{\partial}{\partial x}} \left (u h_{f} \right ) = E_{w} u }[/math] (26)
[math]\displaystyle{ {\frac{\partial}{\partial t}} \left (u h_{f} \right ) + {\frac{\partial}{\partial x}}\left (u^2 h_{f}\right ) = -{\frac{\left ( \rho _{s} - \rho _{w} \right ) g}{2 \rho_{w}}}{\frac{\partial}{\partial x}} \left (Ch_{f}^2 \right ) + {\frac{\left (\rho _{s} - \rho _{w} \right ) g h_{f} C S}{\rho_{w}}} - C_{d} \left ( 1 + \alpha \right ) u^2 }[/math] (27)
[math]\displaystyle{ {\frac{\partial}{\partial t}} \left ( Ch_{f} \right ) + {\frac{\partial}{\partial x}}\left ( u Ch_{f}\right ) = - F_{d} + F }[/math] (28)
[math]\displaystyle{ E_{w} = {\frac{0.00153}{0.0204 + Ri}} }[/math] (29)
[math]\displaystyle{ Ri = {\frac{\left (\rho_{s} - \rho_{w}\right ) g h_{f}C}{\rho_{w}u^2}} }[/math] (30)
[math]\displaystyle{ F_{d} = \left\{\begin{matrix} w_{s} C \left (2 - 1/p_{z} \right ) & p_{z} \lt 0.5 // 0 & p_{z} \gt = 0.5 \end{matrix}\right. }[/math] (31)
[math]\displaystyle{ F_{e} = \left ( \left (C_{d} \rho_{f} u^2 - b \right ) / \left ( a 86400 \right ) \right ) }[/math] (32)
[math]\displaystyle{ |log p_{z}|^\left (1/4 \right ) \cong 0.124 log_{2} Z_{0} + 1.2 }[/math] (33)
[math]\displaystyle{ Z_{0} \equiv w_{s}/ \left (\kappa u_{*} \right ) }[/math] (34)
  • Debris flows

1) Depth-averaged debris flow equations (Continuity)

[math]\displaystyle{ {\frac{\partial D}{\partial t}} + {\frac{\partial}{\partial x}} [U_{p}D_{p} + {\frac{2}{3}}U_{p}D_{s}] = 0 }[/math] (35)

2) Depth-averaged debris flow equations (Momentum (shear layer))

[math]\displaystyle{ {\frac{2}{3}} {\frac{\partial}{\partial t}} \left (U_{p}U_{s} \right ) - U_{p} {\frac{\partial D_{s}}{\partial t}} + {\frac{8}{15}}{\frac{\partial}{\partial x}} \left ( U_{p}^2 D_{s} \right ) {\frac{2}{3}} U_{p} {\frac{\partial}{\partial x}} \left (U_{p} D_{s} \right ) = D_{s} g \left ( 1 - {\frac{\rho_{w}}{\rho_{\rho_{m}}}}\right ) S - D_{s} g {\frac{\partial D}{\partial x}} - 2 {\frac{\mu U_{p}}{\rho_{m} D_{s}}} }[/math] (36)

3) Depth-averaged debris flow equations (Momentum (plug flow layer))

[math]\displaystyle{ {\frac{\partial}{\partial t}} \left ( U_{p} D_{p}\right ) + {\frac{\partial}{\partial x}} \left (U_{p}^2 D_{p} \right ) + U_{p}{\frac{\partial D_{s}}{\partial t}} + {\frac{2}{3}}U_{p}{\frac{\partial}{\partial x}} \left (U_{p} D_{s} \right ) = D_{p} g \left ( 1 - {\frac{\rho_{w}}{\rho_{m}}} \right ) S - D_{p} g {\frac{\partial D}{\partial x}} - {\frac{\tau_{y}}{\rho_{m}}} }[/math] (37)
  • Subsidence

1) Isostatic subsidence

[math]\displaystyle{ w \left (x\right ) = {\frac{p\left (x\right ) \alpha ^3}{8D}}exp \left( -{\frac{|x|}{\alpha}}\right ) + sin \left ({\frac{|x|}{\alpha}}\right ) }[/math] (38)
[math]\displaystyle{ \alpha \equiv ^4 \sqrt{{\frac{4D}{\rho_{m}g}}} }[/math] (39)
[math]\displaystyle{ W \left (x\right ) = \sum\limits_{i=-\propto}^\left (\propto\right ) w \left ( x - x_{i} \right ) }[/math] (40)
  • Compaction
[math]\displaystyle{ {\frac{\partial \phi}{\partial \delta}} = - c \left ( \phi - \phi_{0}\right ) }[/math] (41)
  • Subaerial erosion and deposition by river
[math]\displaystyle{ {\frac{\partial \eta}{\partial t}} = \nu {\frac{\partial ^2 \eta}{\partial x^2}} }[/math] (42)

Diffusion coefficient

[math]\displaystyle{ \nu \equiv {\frac{-8 \lt q\gt A \sqrt{c_{f}}}{C_{0}\left ( s - 1 \right )}} }[/math] (43)
  • Cross-shore transport due to ocean storms

1) Closure depth

[math]\displaystyle{ h_{c} = 2.28 H_{ss} - 6.85 \left ({\frac{H_{ss}^2}{g T^2}}\right ) }[/math] (44)

2) Sediment flux for the outer shelf (depth greater than hc)

[math]\displaystyle{ q_{s} = {\frac{16}{3\pi}}{\frac{\rho}{\rho_{s} - \rho}}{\frac{C_{fs}\varepsilon _{ss}}{g}}I_{s}{\frac{U_{om}^3}{w_{s}}}\left ( v_{0} + {\frac{U_{om}^2}{5 w_{s}}}{\frac{\partial h}{\partial x}}\right ) }[/math] (45)

3) Equation for shoaling waves

[math]\displaystyle{ U_{om} \left (h\right ) = {\frac{\gamma b}{2}} \sqrt{g b_{b}} \left ({\frac{h}{h_{b}}}\right )^\left ({\frac{-3}{4}}\right ) }[/math] (46)

4) Komar's (1998) equation for the threshold of sediment motion

[math]\displaystyle{ {\frac{\rho u_{t}^2}{\left ( \rho_{s} - \rho \right ) g d}} = \left\{\begin{matrix} 0.21 \left ({\frac{d_{0}}{d}}\right )^ \left ({\frac{1}{2}}\right ) & for D \lt = 0.5 mm \\ 0.46 \pi \left ({\frac{d_{0}}{d}}\right )^\left ({\frac{1}{4}}\right ) & for D \gt 0.5 mm \end{matrix}\right. }[/math] (47)

5) Near-bottom threshold velocity

[math]\displaystyle{ u_{t} = {\frac{\pi d_{0}}{T}} = {\frac{\pi H}{T sinh \left (2 \pi h / L \right )}} }[/math] (48)

6) Sediment flux within the near-shore zone (depth less than hc)

[math]\displaystyle{ q_{s} = k_{c} \underline{x}^ \left ( 1 - m \right ) {\frac{dh}{dx}} }[/math] (49)
  • Flexure of the lithosphere

1) Deflection of Earth's crust

[math]\displaystyle{ w \left (\lambda r \right ) = {\frac{q \lambda}{2 \pi \rho_{d}g}} Kei \left (\lambda r \right ) }[/math] (50)

2) Flexural parameter

[math]\displaystyle{ \lambda = \left ({\frac{D}{\rho_{d}g}}\right )^ \left ({\frac{-1}{4}}\right ) }[/math] (51)

3) Time delay between the addition of load and the lithosphere's response

[math]\displaystyle{ w \left (t \right ) = w_{0} \left ( 1 - exp \left (- t / t_{0} \right ) \right ) }[/math] (52)

Notes

See the reference Syvitski and Hutton (2001) and Hutton and Syvitski (2008).

Examples

An example run with input parameters, BLD files, as well as a figure / movie of the output

Follow the next steps to include images / movies of simulations:

See also: Help:Images or Help:Movies

Developer(s)

Eric Hutton

References

  • Hutton, E. W. H. and Syvitski, J. P. M., 2008. Sedflux 2.0: An advanced process-response model that generates three-dimensional stratigraphy. Computer & Geosciences, 34, 1319~1337, Doi: [10.1016/j.cageo.2008.02.013].
  • Syvitski, J. P. M. and Hutton, E. W. H., 2001. 2D SEDFLUX 1.0C: an advanced process-response numerical model for the fill of marine sedimentary basins. Computer & Geosciences, 27, 731~753, Doi: [10.1016/S0098-3004(00)00139-4].

Links