Model help:Acronym1

Acronym1

The Acronym1 programs implement the Parker (1990a) surface-based bedload transport relation in order to compute gravel bedload transport rates.

Model introduction

This program calculates the volume bedload transport per unit width and the Shields number, based on the surface geometric mean diameter and the bedload GSD with its various derivatives (mean, stand. dev., interpolations), given the surface GSD.

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
Sediment Specific Gravity		-
Shear velocity of flow		m / s

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)

Nomenclature

Symbol	Description	Unit
D	grain size	mm
Di	characteristic grain size for the ith grain size range (i=1...N)	mm
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	kg/m3
ρs	density of sediment	kg/m3
R	submerged specific density of sediment, equals to (ρs /ρ-1)	-
u	shear velocity of flow	m / s
g	acceleration of gravity	m / s2
τb	boundary shear stress on the bed	kg / (m s)
u*	shear velocity on the bed, equals to sqrt(τb / ρ )	m / s
pi	fraction of gravel bedload in the ith grain size range	mm
Dlg	geometric mean of the bedload	mm
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	m 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	mm
σg	geometric standard deviation	-
Dx	diameter such that x% of the distribution is finer	mm

Output

Symbol	Description	Unit
qbT	total volume gravel bedload transport rate per unit width summed over all sizes	-
τsg *	Shields number based on surface geometric mean size	-
Dsg	geometric mean size of the surface material	mm
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	mm
Dlx	grain size in the bedload material, such that x percentage of the material is finer	-
σl	arithmetic standard deviations of bedload materials

Notes

• Note on equations

The gravel is divided into N grain size ranges bounded by N+1 sizes D_b,i, i = 1 to N+1. The grain size distribution of the surface (active) layer of the bed is specified in terms of the N+1 pairs (D_b,i, F_f,i), i = 1..N+1, where F_f,i denotes the percent finer in the surface layer. Here D_b,1 must be the coarsest size, such that F_f,1 = 100, and D_b,N+1 must be the finest size, such that F_f,N+1 = 0.

The finest size must equal or exceed 2 mm. That is, the sand must be removed from the surface size distribution, and the fractions appropriately renormalized, in determining the surface grain size distribution to be input into Acronym1.

If the boundary shear stress at the bed includes a component of form drag, the component must be removed before computing u_∗.

Once the parameters q_bi are known the total volume bedload transport rate per unit width q_bT and the fractions pi in the bedload can be calculated as equations 16, 17.

The results are presented in terms of q_bT and the grain size distribution of the bedload, which is computed from the values of pi. These same fractions pi are used to compute the geometric mean and geometric standard deviation of the bedload, from the relations of equations 18, 19, 20, 21.

The percent finer in the bedload p_f,i for the grain size D_f,i is obtained from the fractions p_i as follows: p_f,1 = 100 p_f,i = p_f,i-1 - 100 p_i-1 (i=2~N+1)

Once F_f,i is specified (p_f,i is computed) the value D_sx (D_lx) can be computed by interpolation. The interpolation should be done using a logarithmic scale for grain size. For example, consider the computation of D_lx where p_f,i ≤ x ≤ p_f,i+1. Then we got equation 22, 23, using equation 24.

In order to carry out the above calculation it is necessary to specify specific gravity of the sediment R + 1, the shear velocity of the flow u, and the grain size distribution of the material in excess of 2 mm in the surface layer (D_b,i, F_f,i), i = 1 to N+1. The relation then predicts the total volume bedload transport rate per unit width q_bT of material in excess of 2 mm, as well as the grain size distribution of this load (D_b,i, p_f,i).

• Note on running the program

User may enter GSD on either a 0.00-1.00 scale or a 0%-100% scale, and the program will automatically convert it to a 0% -100% scale.

In the case of a uniform diameter, the user should simply enter the diameter in the diameter column, and 0 in the % passing column.

This formulation does not work for sand, so if sand is present and the border value of 2mm is present the program cuts off all sand (<2mm) and renormalizes the remaining distribution; if sand is present and the border value of 2mm is not present the program alerts the user and exits.

This formulation requires endpoints at 0% and 100%, so if these boundary values are not present the program will automatically interpolate them.

The program automatically organizes the data, so the user may enter the distribution in whatever order they desire.

Note, the Acronym family of functions do not have a GetData function, because there is no time loop, and all the data is being outputted already.

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:Acronym1]