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

First tab header

Second tab header

Etc. tab header

Parameter	Description	Unit
First parameter	Description parameter	[Units]

Parameter	Description	Unit
First parameter	Description parameter	[Units]

Uses ports

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Provides ports

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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 x^* \right ) }[/math]

(2)

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

(3)

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

(4)

[math]\displaystyle{ \beta = {\frac{ \left (1 - \lambda _{p} \right ) B_{f} \xi _{d} L}{I_{f} \Omega \left ( 1 + \Lambda \right ) Q_{tbf,feed}}} }[/math]

(5)

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

(6)

[math]\displaystyle{ \eta = \xi _{do} + \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 \left ( R g D \right ) 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 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

Notes

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Numerical scheme

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

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