Model help:SteadyStateAg
From CSDMS
SteadyStateAg
This model is a calculator for approach to equilibrium in recirculating and feed flumes
Model introduction
This program implements the calculation for steady-state aggradation of a sand-bed river in response to sea level rise at a constant rate.
Model parameters
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
<math>S_{u}= {\frac{R C_{f} ^ \left ( {\frac{1}{2}}\right )} {\alpha _{EH} \tau _{form} ^*}} {\frac{Q_{tbf,feed}}{Q_{bf}}} </math> (1)
<math>{\frac{S}{S_{u}}} = \left ( 1 - \beta \hat{x}\right ) </math> (2)
<math>\hat{\eta} = {\frac{\eta_{dev}}{L}} </math> (3)
<math>\hat{x} = {\frac{x}{L}} </math> (4)
<math>\beta = {\frac{ \left (1 - \lambda _{p} \right ) B_{f} \dot{\xi} _{d} L}{I_{f} \Omega \left ( 1 + \Lambda \right ) Q_{tbf,feed}}} </math> (5)
<math>\hat{\eta} = S_{u} [ \left ( 1 - {\frac{1}{2}} \beta \right ) - \hat{x} + {\frac{1}{2}} \beta \hat{x} ^2 ] </math> (6)
<math>\eta = \xi _{do} + \dot{\xi} _{d} t + \eta _{dev} \left ( x \right ) </math> (7)
<math>{\frac{B_{bf}}{D}} = {\frac{C_{f}}{\alpha _{EH} \left ( \tau _{form} ^* \right ) ^ \left ( 2.5 \right ) }} {\frac{Q_{tbf}}{\sqrt { R g D } D^2}} </math> (8)
<math>{\frac{H}{D}} = {\frac{\alpha _{EH} \left ( \tau _{form} ^* \right ) ^2}{C_{f} ^ \left ({\frac{1}{2}} \right )}} {\frac{Q_{bf}}{Q_{tbf}}} </math> (9)
<math>{\frac{Q_{tbf}}{Q_{tbf,feed}}} = 1 - \beta \hat{x} </math> (10)
Nomenclature
| Symbol | Description | Unit |
|---|---|---|
| Gt,feed | mean annual bed material sediment feed rate | M / T |
| L | reach length (downchannel distance) | L |
| Lv | reach length (downvalley distance) | L |
| dξd / dt | rate of sea level rise | L / T |
| Qbf | bankfull water discharge | L3 / T |
| Bf | floodplain width | L |
| D | grain size | L |
| Λ | fraction wash load deposited per unit material load deposited | kg/m3 |
| Qtbf,feed | volume bed material sediment transport rate during flood time | L3 / T |
| C | volume concentration of bed material load | M / L3 |
| BMSS | flood concentration of bed material load | M / L3 |
| Su | upstream slope | - |
| β | an coefficient to adjust L to make sure that this parameter < 1. If β> 1 then the sediment transport drops to 0 before reaching the delta | - |
| τform * | channel-forming Shields number | - |
| αEH | coefficient in Engelund-Hansen bed material load relation | - |
| λp | bed porosity | - |
| If | flood intermittency | - |
| Cz | Chezy resistance coefficient | - |
| Ω | channel sinuosity | - |
| R | submerged specific gravity of sediment | - |
| ξdo | water surface elevation at t = 0 | L |
| Δt | time interval for plotting | T |
| xhat | dimensionless downstream coordinate | - |
| x | downstream coordinate | L |
| Qtbf | volume bed material transport during flood stage | L3 / T |
| Sl | bed slope | - |
| ξhat | dimensionless deviatoric bed elevation | - |
| ξdev | deviatoric bed elevation | L |
| Bbf | bankfull channel width | L |
| Hbf | bankfull channel depth | L |
| η | bed elevation | L |
| T | channel-forming Shields number | - |
| X | initial water surface elevation | L |
| t | time interval for plotting | T |
| p | number of prints | - |
Notes
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:
- Upload file: http://csdms.colorado.edu/wiki/Special:Upload
- Create link to the file on your page: [[Image:<file name>]].
See also: Help:Images or Help:Movies
Developer(s)
References
Key papers
Links
Any link, eg. to the model questionnaire, etc.
