Model help:RouseVanoniEquilibrium
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]\displaystyle{ {\frac{c}{c_{b}}} = \left ( {\frac{\left ( 1 - \zeta \right ) / \zeta}{\left ( 1 - \zeta \right ) / \zeta _{b} }}\right ) ^ {\frac{V_{s}}{\kappa u_{*}}} }[/math] (1)
- Vertical coordinate in the cross section
[math]\displaystyle{ \zeta = {\frac{z}{H}} }[/math] (2)
- Position near the bed surface where the volume concentration of suspended sediment is equals to c_{b}
[math]\displaystyle{ \zeta _{b} = {\frac{b}{H}} }[/math] (3)
- Concentration of suspended sediment in the water column at ζ=ζ_{b} averaged over turbulence
[math]\displaystyle{ c_{b} = E }[/math] (4)
Symbol | Description | Unit |
---|---|---|
H | water depth | L |
ζ | vertical coordinate in the cross section, ζ = 0 on the bed surface and ζ = H on the water surface | L |
ζ_{b} | position near the bed surface where the volumetric concentration of suspended sediment is equal to C_{b} | L |
u^{*} | shear velocity | L / T |
v_{s} | particle settling velocity computed with the formulation presented by Dietrich (1982) | L / T |
c | concentration of suspended sediment in the water column at elevation ζ averaged over turbulence. | M / L^{3} |
κ | the constant of Von Karman, set equal to 0.4 | - |
b | non-dimensional near-bed distance, defined as ζ_{b} / H | - |
c_{b} | 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 E_{s} / v_{s} | - |
E_{s} | 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/c_{b} | 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: 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
Dietrich, E. W., 1982, Settling velocity of natural particles, Water Resources Research, 18 (6), 1626-1982.