Model help:RouseVanoniEquilibrium: Difference between revisions
No edit summary |
No edit summary |
||
| Line 80: | Line 80: | ||
==Main equations== | ==Main equations== | ||
* Non-dimensional expression of the Rouse-Vanoni profile | |||
::::{| | ::::{| | ||
|width=500px|<math>{\frac{c}{c_{b}}} = \left ( {\frac{\left ( 1 - \sigma \right ) / \sigma}{\left ( 1 - \sigma \right ) / \sigma _{b} }}\right ) ^ {\frac{V_{s}}{\kappa u_{*}}} </math> | |width=500px|<math>{\frac{c}{c_{b}}} = \left ( {\frac{\left ( 1 - \sigma \right ) / \sigma}{\left ( 1 - \sigma \right ) / \sigma _{b} }}\right ) ^ {\frac{V_{s}}{\kappa u_{*}}} </math> | ||
|width=50px align="right"|(1) | |width=50px align="right"|(1) | ||
|} | |} | ||
* Vertical coordinate in the cross section | |||
::::{| | ::::{| | ||
|width=500px|<math>\sigma = {\frac{z}{H}} </math> | |width=500px|<math>\sigma = {\frac{z}{H}} </math> | ||
|width=50px align="right"|(2) | |width=50px align="right"|(2) | ||
|} | |} | ||
* Position near the bed surface where the volume concentration of suspended sediment is equals to c<sub>b</sub> | |||
::::{| | ::::{| | ||
|width=500px|<math>\sigma _{b} = {\frac{b}{H}} </math> | |width=500px|<math>\sigma _{b} = {\frac{b}{H}} </math> | ||
|width=50px align="right"|(3) | |width=50px align="right"|(3) | ||
|} | |} | ||
* Concentration of suspended sediment in the water column at ζ=ζ<sub>b</sub> averaged over turbulence | |||
::::{| | ::::{| | ||
|width=500px|<math> | |width=500px|<math>c_{b} = E </math> | ||
|width=50px align="right"|(4) | |width=50px align="right"|(4) | ||
|} | |} | ||
| Line 127: | Line 131: | ||
| - | | - | ||
|- | |- | ||
| | | κ | ||
| the constant of | | the constant of Von Karman, set equal to 0.4 | ||
| - | | - | ||
|- | |- | ||
| Line 139: | Line 143: | ||
| - | | - | ||
|- | |- | ||
| E | |||
| dimensionless rate of entrainment of bed sediment into suspension, equals to E<sub>s</sub> / v<sub>s</sub> | |||
| - | |||
|- | |||
| E<sub>s</sub> | |||
| volume rate of entrainment of bed sediment into suspension per unit bed area per unit time | |||
| - | |||
|- | |||
|} | |} | ||
| Line 147: | Line 159: | ||
| z | | z | ||
| non-dimensional vertical coordinate, defined as ζ / H | | non-dimensional vertical coordinate, defined as ζ / H | ||
| - | |||
|- | |||
| c/c<sub>b</sub> | |||
| volumetric concentration averaged over the turbulence | |||
| - | | - | ||
|- | |- | ||
Revision as of 15:18, 11 May 2011
RouseVanoniEquilibrium
This Program is used to calculate the Rouse-Vanoni profile of suspended sediment.
Model introduction
This model is working as a profile calculator for Rouse-Vanoni Equilibrium Suspended Sediment.
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
- Non-dimensional expression of the Rouse-Vanoni profile
<math>{\frac{c}{c_{b}}} = \left ( {\frac{\left ( 1 - \sigma \right ) / \sigma}{\left ( 1 - \sigma \right ) / \sigma _{b} }}\right ) ^ {\frac{V_{s}}{\kappa u_{*}}} </math> (1)
- Vertical coordinate in the cross section
<math>\sigma = {\frac{z}{H}} </math> (2)
- Position near the bed surface where the volume concentration of suspended sediment is equals to cb
<math>\sigma _{b} = {\frac{b}{H}} </math> (3)
- Concentration of suspended sediment in the water column at ζ=ζb averaged over turbulence
<math>c_{b} = E </math> (4)
| Symbol | Description | Unit |
|---|---|---|
| H | water depth | - |
| ζ | vertical coordinate in the cross section, ζ = 0 on the bed surface and ζ = H on the water surface | - |
| ζb | position near the bed surface where the volumetric concentration of suspended sediment is equal to Cb | - |
| u* | shear velocity | - |
| vs | particle settling velocity computed with the formulation presented by Dietrich (1982) | - |
| c | concentration of suspended sediment in the water column at elevation ζ averaged over turbulence. | - |
| κ | the constant of Von Karman, set equal to 0.4 | - |
| b | non-dimensional near-bed distance, defined as ζb / H | - |
| cb | concentration of suspended sediment in the water column at ζ = ζb averaged over turbulence. | - |
| E | dimensionless rate of entrainment of bed sediment into suspension, equals to Es / vs | - |
| Es | volume rate of entrainment of bed sediment into suspension per unit bed area per unit time | - |
Output
| Symbol | Description | Unit |
|---|---|---|
| z | non-dimensional vertical coordinate, defined as ζ / H | - |
| c/cb | volumetric concentration averaged over the turbulence | - |
Notes
To compute the equilibrium profile the user can choose between:
a) the grid of the excel workbook RTe-bookRouseSpreadsheetFun.xls. This grid has 22 points in the vertical direction. The lowest 19 are equally spaced between z = b and z = b + 18(1-b)/19. The upper three points are located at z = 0.98, z = 0.995 and z = 1, where the concentration of suspended sediment goes to zero.
b) an equally spaced grid with a user specified number of points in the vertical.
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)
References
Dietrich, E. W., 1982, Settling velocity of natural particles, Water Resources Research, 18 (6), 1626-1982.
