Model help:Acronym1: Difference between revisions
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2) Create a new page for each model, by using the following URL: | 2) Create a new page for each model, by using the following URL: | ||
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* Replace <modelname> with the name of a model | * Replace <modelname> with the name of a model | ||
3) Than follow the link "edit this page" | 3) Than follow the link "edit this page" | ||
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==Model introduction== | ==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. | |||
<div id=CMT_MODEL_PARAMETERS> | <div id=CMT_MODEL_PARAMETERS> | ||
==Model parameters== | ==Model parameters== | ||
= | = Input Files and Directories = | ||
{|{{Prettytable}} class = "wikitable unsortable" cellspacing="0" cellpadding="0" style="margin:0em 0em 0em 0;" | {|{{Prettytable}} class = "wikitable unsortable" cellspacing="0" cellpadding="0" style="margin:0em 0em 0em 0;" | ||
|- | |- | ||
!Parameter!!Description!!Unit | !Parameter!!Description!!Unit | ||
|-valign="top" | |-valign="top" | ||
|width="20%"| | |width="20%"|Input directory | ||
|width="60%"| | |width="60%"|Path to input files | ||
|width="20%"| | |width="20%"| | ||
|- | |||
|Site prefix | |||
|Site prefix for Input/Output files | |||
| | |||
|- | |||
|Case prefix | |||
|Case prefix for Input/Output files | |||
| | |||
|- | |||
|} | |} | ||
= | = Run Parameters = | ||
{|{{Prettytable}} class = "wikitable unsortable" cellspacing="0" cellpadding="0" style="margin:0em 0em 0em 0;" | {|{{Prettytable}} class = "wikitable unsortable" cellspacing="0" cellpadding="0" style="margin:0em 0em 0em 0;" | ||
|- | |- | ||
!Parameter!!Description!!Unit | !Parameter!!Description!!Unit | ||
|-valign="top" | |-valign="top" | ||
|width="20%"| | |width="20%"|Sediment Specific Gravity | ||
|width="60%"| | |width="60%"| | ||
|width="20%"| | |width="20%"| - | ||
|- | |||
|Shear velocity of flow | |||
| | |||
| m / s | |||
|- | |||
|} | |} | ||
= | = About = | ||
{|{{Prettytable}} class = "wikitable unsortable" cellspacing="0" cellpadding="0" style="margin:0em 0em 0em 0;" | |||
|- | |||
!Parameter!!Description!!Unit | |||
|-valign="top" | |||
|width="20%"|Model name | |||
|width="60%"|Name of the model | |||
|width="20%"| - | |||
|- | |||
|Author name | |||
| Name of the model author | |||
| - | |||
|- | |||
|} | |||
<headertabs/> | <headertabs/> | ||
==Uses ports== | ==Uses ports== | ||
Line 55: | Line 78: | ||
==Main equations== | ==Main equations== | ||
* | * Characteristic grain size for the ith grain size range (spans (D<sub>b,i</sub>, D<sub>b,i+1</sub>)) (for i=1...N) | ||
::::{| | ::::{| | ||
|width= | |width=530px|<math>D_{i}= \sqrt{ D_{b, i} D_{b, i+1} } </math> | ||
|width= | |width=50p=x align="right"|(1) | ||
|} | |} | ||
* Fraction in the surface layer F<sub>i</sub> for the ith grain size range (for i=1...N) | |||
::::{| | ::::{| | ||
|width= | |width=530px|<math>F_{i}= \left ( F_{f, i} - F_{f, i+1} \right ) / 100 </math> | ||
|width= | |width=50p=x align="right"|(2) | ||
|} | |} | ||
* Grain Size on the base-2 logarithmic scale: | |||
::::{| | ::::{| | ||
|width= | |width=500px|<math>\Psi= LN_{2}\left (D\right) = {\frac{log_{10}\left (D\right)}{log_{10}\left (2\right)}} </math> | ||
|width= | |width=50px align="right"|(3) | ||
|} | |} | ||
* Geometric mean size of the surface material | |||
::::{| | ::::{| | ||
|width= | |width=500px|<math>D_{sg}=2^\left (\bar\Psi_{s} \right ) </math> | ||
|width= | |width=50px align="right"|(4) | ||
|} | |} | ||
::::{| | ::::{| | ||
|width=500px|<math> | |width=500px|<math>\bar\Psi_{s}= \sum\limits_{i=1}^N \Psi_{i} F{i} </math> | ||
|width=50px align="right"|(5) | |width=50px align="right"|(5) | ||
|} | |} | ||
* Geometric standard deviations of the surface material | |||
::::{| | ::::{| | ||
|width=500px|<math>\ | |width=500px|<math>\sigma_{sg}= 2 ^\sigma </math> | ||
|width=50px align="right"|(6) | |width=50px align="right"|(6) | ||
|} | |} | ||
* Arithmetic standard deviations of the surface material | |||
::::{| | ::::{| | ||
|width=500px|<math>\ | |width=500px|<math>\sigma ^2= \sum\limits_{i=1}^N \left (\Psi_{i} - \bar\Psi \right )^2 F_{i} </math> | ||
|width=50px align="right"|(7) | |width=50px align="right"|(7) | ||
|} | |} | ||
* Bedload transport relation | |||
::::{| | ::::{| | ||
|width= | |width=530px|<math>W_{i}^*= {\frac{Rgq_{bi}}{F_{i}u_{*} ^3}}= 0.00218 G \left (\Phi \right ) </math> | ||
|width= | |width=50p=x align="right"|(8) | ||
|} | |} | ||
::::{| | ::::{| | ||
|width=530px|<math> | |width=530px|<math>\phi= \omega \phi_{sgo} \left ( {\frac{D_{i}} {D_{sg}}} \right )^ \left (-0.0951 \right ) </math> | ||
|width=50p=x align="right"|(9) | |width=50p=x align="right"|(9) | ||
|} | |} | ||
::::{| | ::::{| | ||
|width=530px|<math> | |width=530px|<math> \phi_{sgo}= {\frac{\tau_{sg} ^*}{\tau_{ssrg} ^*}} </math> | ||
|width=50p=x align="right"|(10) | |width=50p=x align="right"|(10) | ||
|} | |} | ||
::::{| | ::::{| | ||
|width=530px|<math> \ | |width=530px|<math>\tau_{sg} ^*={\frac{u_{*} ^2}{R g D_{sg}}} </math> | ||
|width=50p=x align="right"|(11) | |width=50p=x align="right"|(11) | ||
|} | |} | ||
::::{| | ::::{| | ||
|width=530px|<math>\ | |width=530px|<math> G \left ( \phi \right )= \left\{\begin{matrix} 5474 \left ( 1 - {\frac{0.853}{\phi}} \right ) ^ \left (4.5 \right ) & \phi > 1.59 \\ exp[ 14.2\left ( \phi - 1\right ) - 9.28 \left ( \phi - 1 \right )^2 ] & 1 <= \phi <= 1.59 \\ \phi ^\left (14.2 \right ) & \phi < 1 \end{matrix}\right. </math> | ||
|width=50p=x align="right"|(12) | |width=50p=x align="right"|(12) | ||
|} | |} | ||
::::{| | ::::{| | ||
|width=530px|<math> | |width=530px|<math>\omega= 1 + {\frac{\sigma}{\sigma_{O} \left ( \phi_{sgo} \right ) }} [ \omega_{O} \left ( \phi_{sgo} \right ) - 1 ] </math> | ||
|width=50p=x align="right"|(13) | |width=50p=x align="right"|(13) | ||
|} | |} | ||
* | * total volume gravel bedload transport rate per unit width summed over all sizes | ||
::::{| | ::::{| | ||
|width=530px|<math> | |width=530px|<math>q_{bT}= \sum\limits_{i=1}^N q_{bi} </math> | ||
|width=50p=x align="right"|(14) | |width=50p=x align="right"|(14) | ||
|} | |} | ||
* | * fraction of gravel bedload in the ith grain size range | ||
::::{| | ::::{| | ||
|width=530px|<math> | |width=530px|<math>p_{i}= {\frac{q_{bi}}{q_{bT}}} </math> | ||
|width=50p=x align="right"|(15) | |width=50p=x align="right"|(15) | ||
|} | |} | ||
* Geometric mean of the bedload | |||
::::{| | ::::{| | ||
|width=530px|<math> | |width=530px|<math>D_{lg}= 2 ^\left (\bar\psi_{l} \right ) </math> | ||
|width=50p=x align="right"|(16) | |width=50p=x align="right"|(16) | ||
|} | |} | ||
::::{| | ::::{| | ||
|width=530px|<math> | |width=530px|<math>\Psi_{l}= \sum\limits_{i=1}^\left (Np \right ) \Psi_{i} p_{i} </math> | ||
|width=50p=x align="right"|(17) | |width=50p=x align="right"|(17) | ||
|} | |} | ||
* Geometric standard deviation of the bedload | |||
::::{| | ::::{| | ||
|width=530px|<math> | |width=530px|<math>\delta_{lg}= 2 ^\left ( \delta_{l} \right ) </math> | ||
|width=50p=x align="right"|(18) | |width=50p=x align="right"|(18) | ||
|} | |} | ||
::::{| | ::::{| | ||
|width=530px|<math> | |width=530px|<math>\delta_{l} ^2= \sum\limits_{i=1}^\left (Np \right ) \left ( \Psi_{i} - \bar\Psi_{l} \right )^2 p_{i} </math> | ||
|width=50p=x align="right"|(19) | |width=50p=x align="right"|(19) | ||
|} | |} | ||
* Grain sizes in the bedload material | |||
::::{| | ::::{| | ||
|width=530px|<math> | |width=530px|<math>D_{lx}= 2 ^\left (\Psi_{lx} \right ) </math> | ||
|width=50p=x align="right"|(20) | |width=50p=x align="right"|(20) | ||
|} | |} | ||
::::{| | ::::{| | ||
|width=530px|<math>\ | |width=530px|<math>\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> | ||
|width=50p=x align="right"|(21) | |width=50p=x align="right"|(21) | ||
|} | |} | ||
::::{| | ::::{| | ||
|width=530px|<math>\ | |width=530px|<math>\Psi_{b, i}= Ln_{2} \left ( D_{b, j} \right ) </math> | ||
|width=50p=x align="right"|(22) | |width=50p=x align="right"|(22) | ||
|} | |} | ||
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{| {{Prettytable}} class="wikitable sortable" | {| {{Prettytable}} class="wikitable sortable" | ||
!Symbol!!Description!!Unit | !Symbol!!Description!!Unit | ||
|- | |||
| D | |||
| grain size | |||
| L | |||
|- | |- | ||
| D<sub>i</sub> | | D<sub>i</sub> | ||
| characteristic grain size ( | | characteristic grain size for the ith grain size range (i=1...N) | ||
| | | L | ||
|- | |- | ||
| F<sub>i</sub> | | F<sub>i</sub> | ||
| surface layer (for i =1 | | fraction in surface layer for the ith grain size range(for i =1...N) | ||
| - | | - | ||
|- | |- | ||
| | | τ<sub>ssrg</sub> <sup>*</sup> | ||
| equals to 0.0386 | |||
| | |||
| - | | - | ||
|- | |- | ||
| | | ψ | ||
| | | grain sizes on the base-2 logarithmic ψ scale | ||
| | | | ||
|- | |- | ||
| ρ | | ρ | ||
| density of water | | density of water | ||
| | | M / L<sup>3</sup> | ||
|- | |- | ||
| ρ<sub>s</sub> | | ρ<sub>s</sub> | ||
| density of sediment | | density of sediment | ||
| | | M / L<sup>3</sup> | ||
|- | |- | ||
| R | | R | ||
| submerged specific density of sediment | | submerged specific density of sediment, equals to (ρ<sub>s</sub> /ρ-1) | ||
| - | | - | ||
|- | |||
| u | |||
| shear velocity of flow | |||
| L / T | |||
|- | |- | ||
| g | | g | ||
| acceleration of gravity | | acceleration of gravity | ||
| | | L / T<sup>2</sup> | ||
|- | |- | ||
| τ<sub>b</sub> | | τ<sub>b</sub> | ||
| boundary shear stress on the bed | | boundary shear stress on the bed | ||
| | | M / (L T) | ||
|- | |||
| u<sub>*</sub> | |||
| shear velocity on the bed, equals to sqrt(τ<sub>b</sub> / ρ ) | |||
| L / T | |||
|- | |||
| p<sub>i</sub> | |||
| fraction of gravel bedload in the ith grain size range | |||
| L | |||
|- | |||
| ψ<sub>s</sub> | |||
| equals to τ<sub>bs</sub> / τ<sub>b</sub> | |||
| | |||
|- | |- | ||
| | | W<sub>i</sub> <sup>*</sup> | ||
| | | dimensionless bedload transport rate for ith grain size | ||
| | | - | ||
|- | |- | ||
| q<sub>bi</sub> | | q<sub>bi</sub> | ||
| volume gravel bedload transport per unit width of grains in the ith size range | | volume gravel bedload transport per unit width of grains in the ith size range | ||
| | | L <sup>2</sup> | ||
|- | |||
| 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 | ||
| | | | ||
|- | |||
| ω<sub>0</sub> | |||
| function relation in Parker (1990a, b) bedload relation for mixture | |||
| - | |||
|- | |- | ||
| | | Φ | ||
| | | parameter in Parker (1990a, b) bedload relation for mixures | ||
| | | | ||
|- | |- | ||
| | | Φ<sub>sgo</sub> | ||
| | | equals to τ<sub>sg</sub> <sup>*</sup> / τ<sub>ssrg</sub> <sup>*</sup> | ||
| - | |||
|- | |||
| ψ<sub>l</sub> | |||
| grain sizes on the base-2 logarithmic ψ scale for bedload | |||
| - | | - | ||
|- | |- | ||
| | | ψ<sub>lx</sub> | ||
| | | grain sizes on the base-2 logarithmic ψ scale for bedload such that x percent of the material is finer | ||
| | | - | ||
|- | |||
| D<sub>g</sub> | |||
| geometric mean | |||
| L | |||
|- | |- | ||
| | | σ<sub>g</sub> | ||
| | | geometric standard deviation | ||
| - | | - | ||
|- | |||
| D<sub>x</sub> | |||
| diameter such that x% of the distribution is finer | |||
| L | |||
|- | |- | ||
|} | |} | ||
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| q<sub>bT</sub> | | q<sub>bT</sub> | ||
| total volume gravel bedload transport rate per unit width summed over all sizes | | total volume gravel bedload transport rate per unit width summed over all sizes | ||
| L<sup>2</sup> / T | |||
|- | |||
| τ<sub>sg</sub> <sup>*</sup> | |||
| Shields number based on surface geometric mean size | |||
| - | | - | ||
|- | |- | ||
| | | D<sub>sg</sub> | ||
| | | geometric mean size of the surface material | ||
| | | L | ||
|- | |||
| σ<sub>sg</sub> | |||
| geometric standard deviations of the surface materials | |||
| - | |||
|- | |||
| D<sub>lg</sub> | |||
| geometric mean size of the bedload | |||
| L | |||
|- | |||
| σ<sub>lg</sub> | |||
| geometric standard deviation of the bedload | |||
| - | |||
|- | |||
| σ<sub>l</sub> | |||
| arithmetic standard deviations of bedload materials | |||
| - | |||
|- | |||
| σ | |||
| arithmetic standard deviations of the surface materials | |||
| - | |||
|- | |- | ||
| | | D<sub>sx</sub> | ||
| | | grain size in the surface material, such that x percentage of the material is finer | ||
| | | L | ||
|- | |- | ||
| D<sub>lx</sub> | |||
| grain size in the bedload material, such that x percentage of the material is finer | |||
| L | |||
|- | |||
| σ<sub>lx</sub> | |||
| arithmetic standard deviations of bedload materials | |||
| L | |||
|- | |||
|} | |} | ||
</div> | </div> | ||
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==Notes== | ==Notes== | ||
* Note on equations | * Note on equations | ||
The gravel is divided into N grain size ranges bounded by N+1 sizes D<sub>b</sub>,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<sub>b</sub>,i, F<sub>f</sub>,i), i = 1..N+1, where F<sub>f,i</sub> denotes the percent finer in the surface layer. Here D<sub>b,1</sub> must be the coarsest size, such that F<sub>f</sub>,1 = 100, and D<sub>b,N+1</sub> must be the finest size, such that F<sub>f,N+1</sub> = 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 re-normalized, 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<sub>∗</sub>. | If the boundary shear stress at the bed includes a component of form drag, the component must be removed before computing u<sub>∗</sub>. | ||
Once the parameters q<sub>bi</sub> are known the total volume | Once the parameters q<sub>bi</sub> are known, the total volume bed load transport rate per unit width q<sub>bT</sub> and the fractions pi in the bedload can be calculated as equations 14. | ||
The results are presented in terms of q<sub>bT</sub> and the grain size distribution of the | The results are presented in terms of q<sub>bT</sub> and the grain size distribution of the bed load, 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 16, 17, 18, 19. | ||
The percent finer in the bedload p<sub>f,i</sub> for the grain size D<sub>f,i</sub> is obtained from the fractions p<sub>i</sub> as follows: | The percent finer in the bedload p<sub>f,i</sub> for the grain size D<sub>f,i</sub> is obtained from the fractions p<sub>i</sub> as follows: | ||
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p<sub>f,i</sub> = p<sub>f,i-1</sub> - 100 p<sub>i-1</sub> (i=2~N+1) | p<sub>f,i</sub> = p<sub>f,i-1</sub> - 100 p<sub>i-1</sub> (i=2~N+1) | ||
Once F<sub>f,i</sub> is specified (p<sub>f</sub>,i is computed) the value D<sub>sx</sub> (D<sub>lx</sub>) can be computed by interpolation. The interpolation should be done using a logarithmic scale for grain size. For example, consider the computation of D<sub>lx</sub> where p<sub>f,i</sub> ≤ x ≤ p<sub>f,i+1</sub>. Then we got equation 20, 21, using equation 22. | |||
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<sub>b,i</sub>, F<sub>f,i</sub>), i = 1 to N+1. The relation then predicts the total volume bed load transport rate per unit width q<sub>bT</sub> of material in excess of 2 mm, as well as the grain size distribution of this load (D<sub>b,i</sub>, p<sub>f,i</sub>). | |||
* 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 re-normalizes 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== | ==Examples== | ||
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<span class="remove_this_tag">Follow the next steps to include images / movies of simulations:</span> | <span class="remove_this_tag">Follow the next steps to include images / movies of simulations:</span> | ||
* <span class="remove_this_tag">Upload file: | * <span class="remove_this_tag">Upload file: https://csdms.colorado.edu/wiki/Special:Upload</span> | ||
* <span class="remove_this_tag">Create link to the file on your page: <nowiki>[[Image:<file name>]]</nowiki>.</span> | * <span class="remove_this_tag">Create link to the file on your page: <nowiki>[[Image:<file name>]]</nowiki>.</span> | ||
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==References== | ==References== | ||
* Parker, G. | * Parker, G., 1990a. Surface based bedload transport relation for gravel rivers. Journal of Hydraulic Research, 28(4), 417~436.(DOI:[http://dx.doi.org/10.1080/00221689009499058 10.1080/00221689009499058]) | ||
* Parker, G. | * 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== | ==Links== | ||
* [[ | * [[Model:Acronym1]] | ||
[[Category:Utility components]] | [[Category:Utility components]] |
Latest revision as of 17:19, 19 February 2018
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
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 (Db,i, Db,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 Fi 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)
[math]\displaystyle{ G \left ( \phi \right )= \left\{\begin{matrix} 5474 \left ( 1 - {\frac{0.853}{\phi}} \right ) ^ \left (4.5 \right ) & \phi \gt 1.59 \\ exp[ 14.2\left ( \phi - 1\right ) - 9.28 \left ( \phi - 1 \right )^2 ] & 1 \lt = \phi \lt = 1.59 \\ \phi ^\left (14.2 \right ) & \phi \lt 1 \end{matrix}\right. }[/math] (12)
[math]\displaystyle{ \omega= 1 + {\frac{\sigma}{\sigma_{O} \left ( \phi_{sgo} \right ) }} [ \omega_{O} \left ( \phi_{sgo} \right ) - 1 ] }[/math] (13)
- 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] (14)
- fraction of gravel bedload in the ith grain size range
[math]\displaystyle{ p_{i}= {\frac{q_{bi}}{q_{bT}}} }[/math] (15)
- Geometric mean of the bedload
[math]\displaystyle{ D_{lg}= 2 ^\left (\bar\psi_{l} \right ) }[/math] (16)
[math]\displaystyle{ \Psi_{l}= \sum\limits_{i=1}^\left (Np \right ) \Psi_{i} p_{i} }[/math] (17)
- Geometric standard deviation of the bedload
[math]\displaystyle{ \delta_{lg}= 2 ^\left ( \delta_{l} \right ) }[/math] (18)
[math]\displaystyle{ \delta_{l} ^2= \sum\limits_{i=1}^\left (Np \right ) \left ( \Psi_{i} - \bar\Psi_{l} \right )^2 p_{i} }[/math] (19)
- Grain sizes in the bedload material
[math]\displaystyle{ D_{lx}= 2 ^\left (\Psi_{lx} \right ) }[/math] (20)
[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] (21)
[math]\displaystyle{ \Psi_{b, i}= Ln_{2} \left ( D_{b, j} \right ) }[/math] (22)
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 |
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 |
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 | - |
Dlg | geometric mean size of the bedload | L |
σlg | geometric standard deviation of the bedload | - |
σl | arithmetic standard deviations of bedload materials | - |
σ | arithmetic standard deviations of the surface materials | - |
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 |
σlx | arithmetic standard deviations of bedload materials | L |
Notes
- Note on equations
The gravel is divided into N grain size ranges bounded by N+1 sizes Db,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 (Db,i, Ff,i), i = 1..N+1, where Ff,i denotes the percent finer in the surface layer. Here Db,1 must be the coarsest size, such that Ff,1 = 100, and Db,N+1 must be the finest size, such that Ff,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 re-normalized, 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 qbi are known, the total volume bed load transport rate per unit width qbT and the fractions pi in the bedload can be calculated as equations 14.
The results are presented in terms of qbT and the grain size distribution of the bed load, 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 16, 17, 18, 19.
The percent finer in the bedload pf,i for the grain size Df,i is obtained from the fractions pi as follows: pf,1 = 100 pf,i = pf,i-1 - 100 pi-1 (i=2~N+1)
Once Ff,i is specified (pf,i is computed) the value Dsx (Dlx) can be computed by interpolation. The interpolation should be done using a logarithmic scale for grain size. For example, consider the computation of Dlx where pf,i ≤ x ≤ pf,i+1. Then we got equation 20, 21, using equation 22.
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 (Db,i, Ff,i), i = 1 to N+1. The relation then predicts the total volume bed load transport rate per unit width qbT of material in excess of 2 mm, as well as the grain size distribution of this load (Db,i, pf,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 re-normalizes 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: https://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)
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.