Model help:AgDegNormalGravMixHyd
AgDegNormalGravMixHyd
This is a module that calculates the evolution of a gravel bed river under an imposed cycled hydrograph.
Model introduction
This program is a close relative of AgDegNormGravMixPW. It computes aggradation and degradation in gravel-bed river subject to a repeated hydrograph. The sediment is modeled as mixture of different grain sizes and the bedload formulation is that of Parker (1990) that was derived to compute the transport of gravel only.
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
- time duration of a short flood
[math]\displaystyle{ \Delta t_{w} = n_{step,w} \Delta t_{f} }[/math] (1)
- Total time for flood
[math]\displaystyle{ P = \sum\limits_{w=1}^W n_{step,w} }[/math] (2)
Symbol | Description | Unit |
---|---|---|
Q_{w} | constant water discharge for the Wth flood | L ^{3} / T |
Q_{p} | discharge for each time step p (p =1...P) | L ^{3} / T |
p | time step in the hydrograph | |
P | Total time for flood | |
Δt_{w} | time duration of a short flood | T |
Δt_{f} | a short flood time step | T |
n_{step,w} | an integer number of the flood time step | T |
η | river bed elevation | L |
t | time step | T |
B | river width | L |
D | grain size of the bed sediment | L |
D_{bi} | bound diameter | L |
λ_{p} | bed porosity | - |
α | the parameter that governs the grain size distribution of the sediment at the active layer-substrate interface during bed aggredation | - |
F_{fi} | grain size distribution of the active layer for initial condition | - |
F_{i} | fraction of sediment in the ith grain size range in the active layer | - |
f_{subfi} | fraction of sediment in the ith grain size range in the substrate layer for initial condition | - |
n_{pp} | number of grain sizes for which a percent finer is specified, it must have the value between 2 and 9 | - |
D_{bnew} | bound of the distribution such that the fraction of sediment finer than D_{bnew} is equal to 0 | L |
F_{subfli} | percent finer than ith grain size range for the substrate layer for initial condition | - |
f_{li} | fraction of sediment in the ith grain size range in the active-layer substrate interface | - |
p_{i} | fraction of sediment in the ith grain size range in the bedload | - |
F_{sub,i} | fraction of substrate material in the ith size range | - |
D_{s90} | the diameter of the bed surface such that the 90% of the sediment is finer | L |
n_{a} | user specified order-one non dimensional constant | - |
p_{ffi} | the percent that is finer than the ith size range for upstream boundary conditon | - |
η_{d} | fixed bed elevation at the downstream end of the modeled reach | L |
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 |
q_{w} | water discharge per unit width | L^{2} / T |
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 |
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 | - |
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_{f} | bed friction coefficient, equals to τ_{b} / (ρ U^{2} ) | - |
C_{Z} | dimensionless Chezy resistance coefficient. | - |
S_{l} | initial bed slope of the river | - |
η_{i} | initial bed elevation | L |
D_{sub50} | median size of the substrate layer | L |
D_{subg} | geometric mean size of the substrate layer | L |
L_{a} | thickness of the active layer | L |
x | downstream coordinate | 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 | - |
Output
Symbol | Description | Unit |
---|---|---|
H | water depth | L |
ξ | water surface elevation | L |
τ_{b} | bed shear stress | M / (T^{2} L) |
S | bed slope | - |
q_{t} | total bed material load | L^{2} / T |
Notes
This program computes the time evolution of the long profile of a river of constant width carrying a mixture of gravel sizes, the downstream end of which has a prescribed elevation. In particular, the program computes the time evolution of the spatial profiles of bed elevation, total gravel bedload transport rate and grain size distribution of the surface (active) layer of the bed.
The flow is specified in terms of a hydrograph repeated a specified number of times annually, rather than a constant flood discharge and an intermittency.
The river has constant width. The upstream point, at which sediment is fed, is fixed in the horizontal to be at x = 0. The vertical elevation of the upstream point may change freely as the bed aggrades or degrades.In the program it is assumed that all gravel reaching the topset-foreset break is captured in the delta.
The reach has constant length L, so that the downstream point is fixed in the horizontal at x = L. This downstream point has a user-specified initial elevation η_{dI}.
Gravel bedload transport of mixtures is computed using the Parker (1990) surface-based formulation. Sand and finer material must be excluded from the grain size distributions before implementing this relation.
The grain size distributions of the sediment feed, initial surface material and substrate material must be specified. It is assumed that the grain size distribution of the sediment feed rate does not change in time, the initial grain size distribution of the surface material is the same at every node, the grain size distribution of the substrate is the same at every node and does not vary in the vertical.
The program does not store the vertical and streamwise structure of the new substrate created as the bed aggrades. As a result, is cannot capture the case of aggradation followed by degradation. Again, the constraint is easy to relax, but at the price of increased memory requirements for storing the newly-created substrate.
To perform a numerical calculation with a flow hydrograph, the actual hydrograph must be specified in terms of W constant water discharges Q_{w}, where w = 1 … W, each extending for time duration Δt_{w}. The river is assumed to be morphologically inactive when it is not in flood. The morphodynamic evolution is computed solving the equation of sediment continuity (i.e. Exner equation).
- Note on model running
The program may take a few seconds to calculate, depending on the user’s inputs—this is a calculation intensive program—please give the program some time to make the calculations.
There are no output values at time=0 for the geometric mean diameter of the load and the ration between the total bedload transport rate and the feed rate, because these are calculated in the time loop; they are not initial values.
Due to the many variables that are dependent upon user inputted values in this function the “ReadIn” function is called in the main, instead of in the Initialize portion of the code.
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
- Parker, G., 1990, Surface-based bedload transport relation for gravel rivers, Journal of Hydraulic Research, 28(4): 417-436.
- Wilcock, P. R., and Crowe, J. C., 2003, Surface-based transport model for mixed-size sediment, Journal of Hydraulic Engineering, 129(2), 120-128.