Model help:AgDegNormalFault
AgDegNormalFault
This is used to calculate aggradation and degradation of a river reach using the normal flow approximation; with an extension for calculation of the response to a sudden fault along the reach.
Model introduction
This program computes 1D bed variation in rivers due to differential sediment transport in which it is possible to allow the bed to undergo a sudden vertical fault of a specified amount, at a specified place and time. Faulting is realized by moving all notes downstream of the specified point downward by the amount of the faulting. It uses the same principles of AgDegNormal model but with extension for calculation of the response to a sudden fault along the reach.
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
Use the same equations as AgDegNormal model
Symbol | Description | Unit |
---|---|---|
Q | flood discharge | L ^{3} / T |
t | time step | T |
B | river width | L |
D | grain size of the bed sediment | L |
λ_{p} | bed porosity | - |
q_{w} | water discharge per unit width | L^{2} / T |
k_{c} | composite roughness height | L |
G | imposed annual sediment transfer rate from upstream | M / T |
G_{tf} | upstream sediment feed rate | - |
ξ_{d} | downstream water surface elevation | L |
L | length of reach under consideration | L |
i | number of time steps per printout | - |
p | number of printouts desired | - |
M | number of spatial intervals | - |
R | submerged specific gravity of sediment | - |
S_{f} | friction slope | - |
F_{r} | Froude number | - |
U | flow velocity | L / T |
C_{f} | bed friction coefficient | - |
g | acceleration of gravity | L / T^{2} |
α_{r} | coefficient in Manning-Stricker, dimensionless coefficient between 8 and 9 | - |
k_{s} | grain roughness | L |
n_{k} | dimensionless coefficient typically between 2 and 5 | - |
τ^{*} | Shield number | - |
ρ | fluid density | M / L^{3} |
ρ_{s} | sediment density | M / L^{3} |
τ_{c} | critical Shields number for the onset of sediment motion | - |
ψ_{s} | the fraction of bed shear stress | - |
q_{t} ^{*} | Einstein number | - |
q_{t} | volume sediment transport rate per unit width | L^{2} / T |
I_{f} | flood intermittency | - |
t_{f} | cumulative time the river has been in flood | T |
G_{t} | the annual sediment yield | M / T |
t_{a} | the number of seconds in a year | - |
Q_{f} | sediment transport rate during flood discharge | L^{2} / T |
α_{t} | dimensionless coefficient in the sediment transport equation, equals to 8 | - |
n_{t} | exponent in sediment transport relation, equals to 1.5 | - |
τ_{c} ^{*} | reference Shields number in sediment transport relation, equals to 0.047 | |
C_{Z} | dimensionless Chezy resistance coefficient. | |
S_{l} | initial bed slope of the river | - |
η_{i} | initial bed elevation | L |
τ | shear stress on bed surface | - |
q_{b} | bed material load | M / T |
Δx | spatial step length, equals to L / M | L |
Q_{w} | flood discharge | L^{3} / T |
Δt | time step | T |
Ntoprint | number of time steps to printout | - |
Nprint | number of printouts | - |
a_{U} | upwinding coefficient (1=full upwind, 0.5=central difference) | - |
α_{s} | coefficient in sediment transport relation | - |
u_{*} | shear velocity | L / T |
α_{r} | coefficient in Manning-Strickler resistance relation | - |
τ_{b} ^{*} | non-dimensional total shear stress | - |
r_{f} | the fraction of reach length such that all point downstream of x = r_{f}L undergo downward faulting | - |
Δη | the height of faulting | L |
Output
Symbol | Description | Unit |
---|---|---|
η | bed surface elevatioon | L |
H | water depth | L |
ξ | water surface elevation | L |
τ_{b} | bed shear stress | M / (T^{2} L) |
S | bed slope | - |
Notes
The sediment is assumed to be uniform with size D. All sediment transport is assumed to occur in a specified fraction of time during which the river is in flood, specified by an intermittency. A Manning-Strickler formulation is used for bed resistance. A generic relation of the general form of that due to Meyer-Peter and Muller is used for sediment transport. The flow is computed using the normal flow approximation.
If the channel slope is negative and the water depth is not a number, “nan”, check the time step and the spatial step length. In particular, the time step may be too large or equivalently the spatial step length may be too small. Change these values and run the model again.
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
- Paola, C., Heller, P. L. & Angevine, C. L. 1992 The large-scale dynamics of grain-size variation in alluvial basins. I: Theory. Basin Research, 4, 73-90.
- Meyer-Peter, E., and Müller, R. 1948 Formulas for bed-load transport. Proceedings, 2nd Congress International Association for Hydraulic Research, Rotterdam, the Netherlands, 39-64.