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
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 renormalized, in determining the surface grain size distribution to be input into Acronym1.
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
- Grain Size:
[math]\displaystyle{ /tao= LN_{2}left (D\right) = {/frac{log_{10}\left (D\right)}{log_{10}\left (2\right)}} }[/math] (1)
[math]\displaystyle{ /tao_{2}= LN_{2}\left (D_{i}\right) = {/frac{log_{10}\left (D_{2}\right)}{log_{10}\left (2\right)}} }[/math] (2)
[math]\displaystyle{ D_{i}= /sqrt /left ( D_{b, i} D_{b, i+1} /right ) }[/math] (3)
[math]\displaystyle{ F_{i}= \left ( F_{f, i} - F_{f, i=1} \right ) / 100 }[/math] (4)
[math]\displaystyle{ D_{sg}=2^/tao_{s} }[/math] (3)
[math]\displaystyle{ /tao_{s}=/Sigma/tao_{i} F{i} }[/math] (4)
[math]\displaystyle{ /sigma_{sg}= 2 ^/sigma }[/math] (5)
[math]\displaystyle{ /sigma^2= /Sigma \left (/tao_{i} - /tao \right )^2 F_{i} }[/math] (6)
[math]\displaystyle{ W_{i}^*= {/frac{Rgq_{bi}}{F_{i}u_{*}^3}}= 0.00218 G \left (/tao \right ) }[/math] (7)
[math]\displaystyle{ /tao= /omega /tao_{sgo} /left ( {/frac{D_{i}}{D_{sg}}}^-0.0951 }[/math] (8)
[math]\displaystyle{ /pho_{sgo}= {/frac{/tao_{sg}^*}{/tao_{ssrg}^*}} }[/math] (9)
[math]\displaystyle{ /tao_{sg}^*={/frac{u_{*}^2}{RgD_{sg}}} }[/math] (10)
- φ> 1.59
[math]\displaystyle{ G\left (/phi \right )= 5474 \left ( 1 - {/frac{0.853}{/phi}}^4.5 }[/math] (11)
- 1<=φ<=1.59
[math]\displaystyle{ G\left (/phi \right )= exp\left ( 14.2\left ( \phi - 1\right ) - 9.28 \left ( /phi - 1 \right )^2 \right ) }[/math] (12)
- φ< 1
[math]\displaystyle{ G\left (/phi \right )= /phi^14.2 }[/math] (13)
[math]\displaystyle{ /omega= 1 + {/frac{/sigma}{sigma_{o}\left ( /phi_{sgo} /right)}} /left (/omega_{O} /left ( /phi_{sgo} /right ) - 1 /right) }[/math] (14)
[math]\displaystyle{ q_{bT}= /Sigma q_{bi} }[/math] (15)
[math]\displaystyle{ p_{i}= {/frac{q_{bi}}{q_{bT}}} }[/math] (16)
[math]\displaystyle{ D_{lg}= 2^psi_{l} }[/math] (17)
[math]\displaystyle{ /Psi_{l}= /Sigma /Psi_{i} p_{i} }[/math] (18)
[math]\displaystyle{ /delta_{lg}= 2^/delat_{l} }[/math] (19)
[math]\displaystyle{ /delta_{l}^2= /Delta \left ( /Psi_{i} - /Psi_{l} \right )^2 p_{i} }[/math] (20)
[math]\displaystyle{ D_{lx}= 2^/Phi_{lx} }[/math] (21)
[math]\displaystyle{ /Phi_{lx}= /Phi_{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] (22)
[math]\displaystyle{ /Phi_{b, i}= Ln_{2} /left ( D_{b, j} /right ) }[/math] (23)
Notes
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Numerical scheme
Examples
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References
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