Model help:Acronym1R

Acronym1R

"Acronym1_R” combines Acronym1 scheme with a Manning-Strickler relation for flow resistance.

Model introduction

Acronym1_R is used for computing the volume bedload transport rate per unit width and bedload grain size distribution from a specified surface grain size distribution (with sand removed) (D_b,i, F_f,i), i = 1..N+1, a specific gravity of the sediment (here equal to R + 1), a water discharge Q, a channel width B and a streamwise bed slope S.

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
Submerged Specific Gravity		-
Water discharge		m3 / s
Bed Slope		-
Channel Width		m
Roughness Factor		-

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

• Characteristic grain size for the ith grain size range (spans (D_b,i, D_b,i+1)) (for i=1...N)

[math]\displaystyle{ D_{i}= \sqrt{ D_{b, i} D_{b, i+1} } }[/math]

(1)

• Fraction in the surface layer F_i for the ith grain size range (for i=1...N)

[math]\displaystyle{ F_{i}= \left ( F_{f, i} - F_{f, i+1} \right ) / 100 }[/math]

(2)

• Grain Size on the base-2 logarithmic scale:

[math]\displaystyle{ \Psi= LN_{2}\left (D\right) = {\frac{log_{10}\left (D\right)}{log_{10}\left (2\right)}} }[/math]

(3)

• Geometric mean size of the surface material

[math]\displaystyle{ D_{sg}=2^\left (\bar\Psi_{s} \right ) }[/math]

(4)

[math]\displaystyle{ \bar\Psi_{s}= \sum\limits_{i=1}^N \Psi_{i} F{i} }[/math]

(5)

• Geometric standard deviations of the surface material

[math]\displaystyle{ \sigma_{sg}= 2 ^\sigma }[/math]

(6)

• Arithmetic standard deviations of the surface material

[math]\displaystyle{ \sigma ^2= \sum\limits_{i=1}^N \left (\Psi_{i} - \bar\Psi \right )^2 F_{i} }[/math]

(7)

• Bedload transport relation

[math]\displaystyle{ W_{i}^*= {\frac{Rgq_{bi}}{F_{i}u_{*} ^3}}= 0.00218 G \left (\Phi \right ) }[/math]

(8)

[math]\displaystyle{ \phi= \omega \Phi_{sgo} \left ( {\frac{D_{i}} {D_{sg}}} \right )^ \left (-0.0951 \right ) }[/math]

(9)

[math]\displaystyle{ \Phi_{sgo}= {\frac{\tau_{sg} ^*}{\tau_{ssrg} ^*}} }[/math]

(10)

[math]\displaystyle{ \tau_{sg} ^*={\frac{u_{*} ^2}{R g D_{sg}}} }[/math]

(11)

• Φ> 1.59

[math]\displaystyle{ G \left ( \Phi \right )= 5474 \left ( 1 - {\frac{0.853}{\Phi}} \right ) ^ \left (4.5 \right ) }[/math]

(12)

• 1<=Φ<=1.59

[math]\displaystyle{ G\left (\Phi \right )= exp[ 14.2\left ( \Phi - 1\right ) - 9.28 \left ( \Phi - 1 \right )^2 ] }[/math]

(13)

• Φ< 1

[math]\displaystyle{ G\left (\Phi \right )= \Phi ^\left (14.2 \right ) }[/math]

(14)

[math]\displaystyle{ \omega= 1 + {\frac{\sigma}{\sigma_{O} \left ( \Phi_{sgo} \right ) }} [ \omega_{O} \left ( \Phi_{sgo} \right ) - 1 ] }[/math]

(15)

• total volume gravel bedload transport rate per unit width summed over all sizes

[math]\displaystyle{ q_{bT}= \sum\limits_{i=1}^N q_{bi} }[/math]

(16)

• fraction of gravel bedload in the ith grain size range

[math]\displaystyle{ p_{i}= {\frac{q_{bi}}{q_{bT}}} }[/math]

(17)

• Geometric mean of the bedload

[math]\displaystyle{ D_{lg}= 2 ^\left (\bar\psi_{l} \right ) }[/math]

(18)

[math]\displaystyle{ \Psi_{l}= \sum\limits_{i=1}^\left (Np \right ) \Psi_{i} p_{i} }[/math]

(19)

• Geometric standard deviation of the bedload

[math]\displaystyle{ \delta_{lg}= 2 ^\left ( \delta_{l} \right ) }[/math]

(20)

[math]\displaystyle{ \delta_{l} ^2= \sum\limits_{i=1}^\left (Np \right ) \left ( \Psi_{i} - \bar\Psi_{l} \right )^2 p_{i} }[/math]

(21)

• Grain sizes in the bedload material

[math]\displaystyle{ D_{lx}= 2 ^\left (\Psi_{lx} \right ) }[/math]

(22)

[math]\displaystyle{ \Psi_{lx}= \Psi_{b, i+1} + {\frac{\Psi_{b, j} - \Psi_{b, i+1}}{p_{f, i} - p_{f, i+1}}}\left ( x - p_{f, i+1} \right ) }[/math]

(23)

[math]\displaystyle{ \Psi_{b, i}= Ln_{2} \left ( D_{b, j} \right ) }[/math]

(24)

• Roughness height of the channel (including bed and vertical sidewalls)

[math]\displaystyle{ k_{s} = n_{k} D_{s90} }[/math]

(25)

[math]\displaystyle{ \tau_{b} B = \rho u_{*} ^2 B = \rho g S \left ( H B - H ^2 \right ) }[/math]

(26)

[math]\displaystyle{ {\frac{U}{u_{*}}} = \alpha _{r} \left ( {\frac{H}{k_{s}}} \right )^ {\frac{1}{6}} }[/math]

(27)

[math]\displaystyle{ U = {\frac{Q}{BH}} }[/math]

(28)

[math]\displaystyle{ H = \left ({\frac{k_{s} ^ {\frac{1}{3}} Q ^2}{\alpha_{r} ^2 g B^2 S}} \right )^ {\frac{3}{10}} c_{1} }[/math]

(29)

[math]\displaystyle{ c_{1}= \left ( 1 - {\frac{H}{B}} \right ) ^ \left ({\frac{-3}{10}}\right ) }[/math]

(30)

Nomenclature

Symbol	Description	Unit
D	grain size	L
Di	characteristic grain size for the ith grain size range (i=1...N)	L
Fi	fraction in surface layer for the ith grain size range(for i =1...N)	-
τssrg *	equals to 0.0386	-
ψ	grain sizes on the base-2 logarithmic ψ scale
ρ	density of water	M / L3
ρs	density of sediment	M / L3
R	submerged specific density of sediment, equals to (ρs /ρ-1)	-
u	shear velocity of flow	L / T
g	acceleration of gravity	L / T2
τb	boundary shear stress on the bed	M / (L T)
u*	shear velocity on the bed, equals to sqrt(τb / ρ )	L / T
pi	fraction of gravel bedload in the ith grain size range	L
Dlg	geometric mean of the bedload	L
ψs	equals to τbs / τb
Wi *	dimensionless bedload transport rate for ith grain size	-
qbi	volume gravel bedload transport per unit width of grains in the ith size range	L 2
ω	straining relation in Parker (1990a,b) bedload relation for mixtures
G(Φ)	function in Parker (1990a, b) and Wilcock and Crowe (2003) bedload relation for gravel mixture
ω0	function relation in Parker (1990a, b) bedload relation for mixture	-
Φ	parameter in Parker (1990a, b) bedload relation for mixures
Φsgo	equals to τsg * / τssrg *	-
ψl	grain sizes on the base-2 logarithmic ψ scale for bedload	-
ψlx	grain sizes on the base-2 logarithmic ψ scale for bedload such that x percent of the material is finer	-
Dg	geometric mean	L
σg	geometric standard deviation	-
Dx	diameter such that x% of the distribution is finer	L
nx	user-specified dimensionless roughness factor (the author suggests a value of 2)	-
ks	roughness height of the channel	-
B	channel width	L
U	mean velocity	L / T
αr	coefficient in Manning-Strickler resistance relation, equals to 8.1	-
Q	water discharge	L3 / T
S	channel slope	-
c1	user-specified coefficient	-

Output

Symbol	Description	Unit
qbT	total volume gravel bedload transport rate per unit width summed over all sizes	L2 / T
τsg *	Shields number based on surface geometric mean size	-
Dsg	geometric mean size of the surface material	L
σsg	geometric standard deviations of the surface materials	-
σ	arithmetic standard deviations of the surface materials	-
σlg	geometric standard deviation of the bedload	-
Dsx	grain size in the surface material, such that x percentage of the material is finer	L
Dlx	grain size in the bedload material, such that x percentage of the material is finer	L
σl	arithmetic standard deviations of bedload materials
H	water depth	L

Notes

• Note on the program

The channel is assumed to be rectangular, with the vertical sidewalls having the same roughness as the bed.

Depth is computed according to the relation for momentum balance in the bed region using equation 26 applicable to normal (steady, streamwise uniform) flow. Flow resistance on the bed region is computed using a Manning-Strickler resistance relation.

Equation 29, 30 is solved iteratively for H in the code. Once H is known, the shear velocity u_∗ is computed from equation 26, and the calculation proceeds using the same algorithm as “Acronym1”. It is implicitly assumed in the calculation that all of the boundary shear stress consists of skin friction, with form drag neglected.

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)

Gary Parker

References

• Parker, G., 1990a. Surface based bedload transport relation for gravel rivers. Journal of Hydraulic Research, 28(4), 417~436.(DOI:10.1080/00221689009499058)

• Parker, G.,1990b. The "ACRONYM" series of Pascal programs for computing bedload transport in gravel rivers. External Memorandum M 220, St. Anthony Falls Hydraulic Laboratory, University of Minnesota.

Links

• Model:Acronym1R