Model help:SteadyStateAg

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

Input Files and Directories

Run Parameters

About

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
Mean annual bed material sediment feed rate		Mt / yr
Reach length (downchannel distance)		km
Rate of sea level rise		mm / yr
Bankfull water discharge		m3 / s
Floodplain width		km
Grain size	grain diameter	mm
Fraction wash load deposited per unit bed material deposited		-
Channel-forming Shield number		-
Coefficient in Engelund-Hansen bed material load relation		-
Bed porosity		-
Flood intermittence		-
Chezy resistance coefficient		-
Channel sinuosity		-
Submerged specific gravity of seidment		-
Initial water surface elevation		m
Time interval for plotting		yr
Number of prints desired		-

Parameter	Description	Unit
Model name	name of the model	-
Author name	name of the model author	-

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]\displaystyle{ S_{u}= {\frac{R C_{f} ^ \left ( {\frac{1}{2}}\right )} {\alpha _{EH} \tau _{form} ^*}} {\frac{Q_{tbf,feed}}{Q_{bf}}} }[/math]

(1)

[math]\displaystyle{ {\frac{S}{S_{u}}} = \left ( 1 - \beta \hat{x}\right ) }[/math]

(2)

[math]\displaystyle{ \hat{\eta} = {\frac{\eta_{dev}}{L}} }[/math]

(3)

[math]\displaystyle{ \hat{x} = {\frac{x}{L}} }[/math]

(4)

[math]\displaystyle{ \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]\displaystyle{ \hat{\eta} = S_{u} [ \left ( 1 - {\frac{1}{2}} \beta \right ) - \hat{x} + {\frac{1}{2}} \beta \hat{x} ^2 ] }[/math]

(6)

[math]\displaystyle{ \eta = \xi _{do} + \dot{\xi} _{d} t + \eta _{dev} \left ( x \right ) }[/math]

(7)

[math]\displaystyle{ {\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]\displaystyle{ {\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]\displaystyle{ {\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	Mt / year
L	reach length (downchannel distance)	km
Lv	reach length (downvalley distance)	km
dξd / dt	rate of sea level rise	mm / year
Qbf	bankfull water discharge	m3 / s
Bf	floodplain width	km
D	grain size	mm
Λ	fraction wash load deposited per unit material load deposited	kg/m3
Qtbf,feed	volume bed material sediment transport rate during flood time	-
C	volume concentration of bed material load	-
BMSS	flood concentration of bed material load	mg / L
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	-
Δt	time interval for plotting	year
xhat	dimensionless downstream coordinate	-
x	downstream coordinate	km
Qtbf	volume bed material transport during flood stage	m3 / s
Sl	bed slope	-
ξhat	dimensionless deviatoric bed elevation	-
ξdev	deviatoric bed elevation	m
Bbf	bankfull channel width	m
Hbf	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	-

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)

Name of the module developer(s)

References

Key papers

Links

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