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

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
non-dimensional distance from the bed	non-dimensional height in the water column	-
vs settling velocity	settling velocity of the particles	cm / s
u^* shear velocity		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

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)

Nomenclature

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 / L³
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>]].

Developer(s)

Gary Parker

References

Dietrich, E. W., 1982, Settling velocity of natural particles, Water Resources Research, 18 (6), 1626-1982.

Links

Model:RouseVanoniEquilibrium