Model help:SteadyStateAg: Difference between revisions

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==Main equations==
==Main equations==
::::{|
::::{|
|width=500px|<math>\S_{u}= {\frac{R C_{f} ^ \left ( {\frac{1}{2}}\right )} {\alpha _{EH} \tau _{form} ^*}} {\frac{Q_{tbf,feed}}{Q_{bf}}} </math>
|width=500px|<math>S_{u}= {\frac{R C_{f} ^ \left ( {\frac{1}{2}}\right )} {\alpha _{EH} \tau _{form} ^*}} {\frac{Q_{tbf,feed}}{Q_{bf}}} </math>
|width=50px align="right"|(1)
|width=50px align="right"|(1)
|}
|}
::::{|
::::{|
|width=500px|<math>{\frac{S}{S_{u}}} = \left ( 1 - \beta x^* \right ) </math>
|width=500px|<math>{\frac{S}{S_{u}}} = \left ( 1 - \beta \hat{x}\right ) </math>
|width=50px align="right"|(2)
|width=50px align="right"|(2)
|}
|}
::::{|
::::{|
|width=500px|<math>\eta ^* = {\frac{\eta_{dev}}{L}} </math>
|width=500px|<math>\hat{\eta} = {\frac{\eta_{dev}}{L}} </math>
|width=50px align="right"|(3)
|width=50px align="right"|(3)
|}
|}
::::{|
::::{|
|width=500px|<math>x^* = {\frac{x}{L}} </math>
|width=500px|<math>\hat{x} = {\frac{x}{L}} </math>
|width=50px align="right"|(4)
|width=50px align="right"|(4)
|}
|}
::::{|
::::{|
|width=500px|<math>\beta = {\frac{ \left (1 - \lambda _{p} \right ) B_{f} \xi _{d} L}{I_{f} \Omega \left ( 1 + \Lambda \right ) Q_{tbf,feed}}} </math>
|width=500px|<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>
|width=50px align="right"|(5)
|width=50px align="right"|(5)
|}
|}
::::{|
::::{|
|width=500px|<math>\eta^* = S_{u} \left ( \left ( 1 - {\frac{1}{2}} \beta \right ) - x^* + {\frac{1}{2}} \beta \left ( x ^* \right ) ^2 \right ) </math>
|width=500px|<math>\hat{\eta} = S_{u} [ \left ( 1 - {\frac{1}{2}} \beta \right ) - \hat{x} + {\frac{1}{2}} \beta \hat{x} ^2 ] </math>
|width=50px align="right"|(6)
|width=50px align="right"|(6)
|}
|}
::::{|
::::{|
|width=500px|<math>\eta = \xi _{do} + \xi _{d} t + \eta _{dev} \left ( x \right ) </math>
|width=500px|<math>\eta = \xi _{do} + \dot{\xi} _{d} t + \eta _{dev} \left ( x \right ) </math>
|width=50px align="right"|(7)
|width=50px align="right"|(7)
|}
|}
::::{|
::::{|
|width=500px|<math>{\frac{B_{bf}}{D}} = {\frac{C_{f}}{\alpha _{EH} \left ( /tau _{form} ^* \right ) ^ \left ( 2.5 \right ) }} {\frac{Q_{tbf}}{sqrt \left ( R g D \right ) D^2}} </math>
|width=500px|<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>
|width=50px align="right"|(8)
|width=50px align="right"|(8)
|}
|}
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|}
|}
::::{|
::::{|
|width=500px|<math>{\frac{Q_{tbf}}{Q_{tbf,feed}}} = 1 - \beta x^* </math>
|width=500px|<math>{\frac{Q_{tbf}}{Q_{tbf,feed}}} = 1 - \beta \hat{x} </math>
|width=50px align="right"|(10)
|width=50px align="right"|(10)
|}
|}
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| time interval for plotting
| time interval for plotting
| year
| year
|-
| xhat
| dimensionless downstream coordinate
| -
|-
| x
| downstream coordinate
| km
|-
| Q<sub>tbf</sub>
| volume bed material transport during flood stage
| m<sup>3</sup> / s
|-
| Sl
| bed slope
| -
|-
| ξ<sub>hat</sub>
| dimensionless deviatoric bed elevation
| -
|-
| ξ<sub>dev</sub>
| deviatoric bed elevation
| m
|-
| B<sub>bf</sub>
| bankfull channel width
| m
|-
| H<sub>bf</sub>
| bankfull channel depth
| m
|-
| η
| bed elevation
| m
|-
| T
| channel-forming Shields number
| -
|-
| X
| initial water surface elevation
| m
|-
| t
| time interval for plotting
| yr
|-
| p
| number of prints
| -
|-
|-
|}
|}
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</div>
</div>
==Notes==
==Notes==
<span class="remove_this_tag">Any notes, comments, you want to share with the user</span>


<span class="remove_this_tag">Numerical scheme</span>




Revision as of 14:07, 2 May 2011

The CSDMS Help System
The CSDMS Help System

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

Parameter Description Unit
First parameter Description parameter [Units]
Parameter Description Unit
First parameter Description parameter [Units]

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)

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:

See also: Help:Images or Help:Movies

Developer(s)

Name of the module developer(s)

References

Key papers

Links

Any link, eg. to the model questionnaire, etc.

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