Model help:AgDegNormGravMixSubPW: Difference between revisions
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| Line 179: | Line 179: | ||
| Q | | Q | ||
| flood discharge | | flood discharge | ||
| | | L <sup>3</sup> / T | ||
|- | |- | ||
| x | | x | ||
| streamwise coordinate | | streamwise coordinate | ||
| | | L | ||
|- | |- | ||
| η | | η | ||
| river bed elevation | | river bed elevation | ||
| | | L | ||
|- | |- | ||
| t | | t | ||
| time step | | time step | ||
| | | T | ||
|- | |- | ||
| B | | B | ||
| river width | | river width | ||
| | | L | ||
|- | |- | ||
| D | | D | ||
| grain size of the bed sediment | | grain size of the bed sediment | ||
| | | L | ||
|- | |- | ||
| D<sub>bi</sub> | | D<sub>bi</sub> | ||
| bound diameter | | bound diameter | ||
| | | L | ||
|- | |- | ||
| λ<sub>p</sub> | | λ<sub>p</sub> | ||
| Line 247: | Line 247: | ||
| D<sub>s90</sub> | | D<sub>s90</sub> | ||
| the diameter of the bed surface such that the 90% of the sediment is finer | | the diameter of the bed surface such that the 90% of the sediment is finer | ||
| | | L | ||
|- | |- | ||
| n<sub>a</sub> | | n<sub>a</sub> | ||
| Line 259: | Line 259: | ||
| η<sub>d</sub> | | η<sub>d</sub> | ||
| fixed bed elevation at the downstream end of the modeled reach | | fixed bed elevation at the downstream end of the modeled reach | ||
| | | L | ||
|- | |- | ||
| R | | R | ||
| Line 267: | Line 267: | ||
| ξ<sub>d</sub> | | ξ<sub>d</sub> | ||
| downstream water surface elevation | | downstream water surface elevation | ||
| | | L | ||
|- | |- | ||
| q<sub>w</sub> | | q<sub>w</sub> | ||
| water discharge per unit width | | water discharge per unit width | ||
| | | L<sup>2</sup> / T | ||
|- | |- | ||
| k<sub>c</sub> | | k<sub>c</sub> | ||
| composite roughness height | | composite roughness height | ||
| | | L | ||
|- | |- | ||
| G | | G | ||
| imposed annual sediment transfer rate from upstream | | imposed annual sediment transfer rate from upstream | ||
| | | M / T | ||
|- | |- | ||
| G<sub>tf</sub> | | G<sub>tf</sub> | ||
| Line 287: | Line 287: | ||
| ξ<sub>d</sub> | | ξ<sub>d</sub> | ||
| downstream water surface elevation | | downstream water surface elevation | ||
| | | L | ||
|- | |- | ||
| L | | L | ||
| length of reach under consideration | | length of reach under consideration | ||
| | | L | ||
|- | |- | ||
| q<sub>w</sub> | | q<sub>w</sub> | ||
| water discharge per unit width | | water discharge per unit width | ||
| | | L<sup>2</sup> / T | ||
|- | |- | ||
| i | | i | ||
| Line 323: | Line 323: | ||
| U | | U | ||
| flow velocity | | flow velocity | ||
| | | L / T | ||
|- | |- | ||
| C<sub>f</sub> | | C<sub>f</sub> | ||
| Line 331: | Line 331: | ||
| g | | g | ||
| acceleration of gravity | | acceleration of gravity | ||
| | | L / T<sup>2</sup> | ||
|- | |- | ||
| α<sub>r</sub> | | α<sub>r</sub> | ||
| Line 339: | Line 339: | ||
| k<sub>s</sub> | | k<sub>s</sub> | ||
| grain roughness | | grain roughness | ||
| | | L | ||
|- | |- | ||
| n<sub>k</sub> | | n<sub>k</sub> | ||
| Line 351: | Line 351: | ||
| ρ | | ρ | ||
| fluid density | | fluid density | ||
| | | M / L<sup>3</sup> | ||
|- | |- | ||
| ρ<sub>s</sub> | | ρ<sub>s</sub> | ||
| sediment density | | sediment density | ||
| | | M / L<sup>3</sup> | ||
|- | |- | ||
| τ<sub>c</sub> | | τ<sub>c</sub> | ||
| Line 371: | Line 371: | ||
| q<sub>t</sub> | | q<sub>t</sub> | ||
| volume sediment transport rate per unit width | | volume sediment transport rate per unit width | ||
| | | L<sup>2</sup> / T | ||
|- | |- | ||
| I<sub>f</sub> | | I<sub>f</sub> | ||
| Line 379: | Line 379: | ||
| t<sub>f</sub> | | t<sub>f</sub> | ||
| cumulative time the river has been in flood | | cumulative time the river has been in flood | ||
| | | T | ||
|- | |- | ||
| G<sub>t</sub> | | G<sub>t</sub> | ||
| the annual sediment yield | | the annual sediment yield | ||
| | | M / T | ||
|- | |- | ||
| t<sub>a</sub> | | t<sub>a</sub> | ||
| Line 391: | Line 391: | ||
| Q<sub>f</sub> | | Q<sub>f</sub> | ||
| sediment transport rate during flood discharge | | sediment transport rate during flood discharge | ||
| L<sup>2</sup> / T | |||
|- | |- | ||
| α<sub>t</sub> | | α<sub>t</sub> | ||
| Line 420: | Line 421: | ||
| D<sub>sub50</sub> | | D<sub>sub50</sub> | ||
| median size of the substrate layer | | median size of the substrate layer | ||
| | | L | ||
|- | |- | ||
| D<sub>subg</sub> | | D<sub>subg</sub> | ||
| geometric mean size of the substrate layer | | geometric mean size of the substrate layer | ||
| | | L | ||
|- | |- | ||
| L<sub>a</sub> | | L<sub>a</sub> | ||
| thickness of the active layer | | thickness of the active layer | ||
| | | L | ||
|- | |- | ||
| σ | | σ | ||
| subsidence rate | | subsidence rate | ||
| | | L / T | ||
|- | |- | ||
| r<sub>B</sub> | | r<sub>B</sub> | ||
| Line 448: | Line 449: | ||
| τ | | τ | ||
| shear stress on bed surface | | shear stress on bed surface | ||
| | | - | ||
|- | |- | ||
| q<sub>b</sub> | | q<sub>b</sub> | ||
| bed material load | | bed material load | ||
| | | M / T | ||
|- | |- | ||
| Δx | | Δx | ||
| spatial step length, equals to L / M | | spatial step length, equals to L / M | ||
| | | L | ||
|- | |- | ||
| Q<sub>w</sub> | | Q<sub>w</sub> | ||
| flood discharge | | flood discharge | ||
| | | L<sup>3</sup> / T | ||
|- | |- | ||
| Δt | | Δt | ||
| time step | | time step | ||
| | | T | ||
|- | |- | ||
| Ntoprint | | Ntoprint | ||
| Line 484: | Line 485: | ||
| p<sub>feed</sub> | | p<sub>feed</sub> | ||
| GSD of the feed | | GSD of the feed | ||
| | | M / T | ||
|- | |- | ||
| F<sub>fs</sub> | | F<sub>fs</sub> | ||
| Line 510: | Line 511: | ||
| η | | η | ||
| bed surface elevatioon | | bed surface elevatioon | ||
| | | L | ||
|- | |- | ||
| H | | H | ||
| water depth | | water depth | ||
| | | L | ||
|- | |- | ||
| ξ | | ξ | ||
| water surface elevation | | water surface elevation | ||
| | | L | ||
|- | |- | ||
| τ<sub>b</sub> | | τ<sub>b</sub> | ||
| bed shear stress | | bed shear stress | ||
| | | M / (T<sup>2</sup> L) | ||
|- | |- | ||
| S | | S | ||
| Line 530: | Line 531: | ||
| q<sub>t</sub> | | q<sub>t</sub> | ||
| total bed material load | | total bed material load | ||
| | | L<sup>2</sup> / T | ||
|- | |- | ||
| L<sub>max</sub> | | L<sub>max</sub> | ||
| maximum length of basin that the sediment supply can fill | | maximum length of basin that the sediment supply can fill | ||
| | | L | ||
|- | |- | ||
|} | |} | ||
Revision as of 12:47, 26 May 2011
AgDegNormGravMixSubPW
It is the calculator for evolution of upward-concave bed profiles in rivers carrying sediment mixtures in subsiding basins.
Model introduction
This program calculates the bed surface evolution for a river of constant width with a mixture of gravel sizes with a load computed either by the Parker relation or the Wilcock-Crowe relation, as in the case of AgDegNormGravMixPW, but this program also takes into effect the subsidence.
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
| Symbol | Description | Unit |
|---|---|---|
| Q | flood discharge | L 3 / T |
| x | streamwise coordinate | L |
| η | river bed elevation | L |
| t | time step | T |
| B | river width | L |
| D | grain size of the bed sediment | L |
| Dbi | bound diameter | L |
| λp | bed porosity | - |
| α | the parameter that governs the grain size distribution of the sediment at the active layer-substrate interface during bed aggredation | - |
| Ffi | grain size distribution of the active layer for initial condition | - |
| Fi | fraction of sediment in the ith grain size range in the active layer | - |
| fsubfi | fraction of sediment in the ith grain size range in the substrate layer for initial condition | - |
| Ffli | percent finer than ith grain size range for the bed surface for initial condition | - |
| Fsubfli | percent finer than ith grain size range for the substrate layer for initial condition | - |
| fli | fraction of sediment in the ith grain size range in the active-layer substrate interface | - |
| pi | fraction of sediment in the ith grain size range in the bedload | - |
| Fsub,i | fraction of substrate material in the ith size range | - |
| Ds90 | the diameter of the bed surface such that the 90% of the sediment is finer | L |
| na | user specified order-one non dimensional constant | - |
| pffi | the percent that is finer than the ith size range for upstream boundary conditon | - |
| ηd | fixed bed elevation at the downstream end of the modeled reach | L |
| R | submerged specific gravity | - |
| ξd | downstream water surface elevation | L |
| qw | water discharge per unit width | L2 / T |
| kc | composite roughness height | L |
| G | imposed annual sediment transfer rate from upstream | M / T |
| Gtf | upstream sediment feed rate | - |
| ξd | downstream water surface elevation | L |
| L | length of reach under consideration | L |
| qw | water discharge per unit width | L2 / T |
| i | number of time steps per printout | - |
| p | number of printouts desired | - |
| M | number of spatial intervals | - |
| R | submerged specific gravity of sediment | - |
| Sf | friction slope | - |
| Fr | Froude number | - |
| U | flow velocity | L / T |
| Cf | bed friction coefficient | - |
| g | acceleration of gravity | L / T2 |
| αr | coefficient in Manning-Stricker, dimensionless coefficient between 8 and 9 | - |
| ks | grain roughness | L |
| nk | dimensionless coefficient typically between 2 and 5 | - |
| τ* | Shield number | - |
| ρ | fluid density | M / L3 |
| ρs | sediment density | M / L3 |
| τc | critical Shields number for the onset of sediment motion | - |
| ψs | the fraction of bed shear stress | - |
| qt * | Einstein number | - |
| qt | volume sediment transport rate per unit width | L2 / T |
| If | flood intermittency | - |
| tf | cumulative time the river has been in flood | T |
| Gt | the annual sediment yield | M / T |
| ta | the number of seconds in a year | - |
| Qf | sediment transport rate during flood discharge | L2 / T |
| αt | dimensionless coefficient in the sediment transport equation, equals to 8 | - |
| nt | exponent in sediment transport relation, equals to 1.5 | - |
| τc * | reference Shields number in sediment transport relation, equals to 0.047 | |
| Cf | bed friction coefficient, equals to τb / (ρ U2 ) | - |
| CZ | dimensionless Chezy resistance coefficient. | |
| Sl | initial bed slope of the river | - |
| ηi | initial bed elevation | - |
| Dsub50 | median size of the substrate layer | L |
| Dsubg | geometric mean size of the substrate layer | L |
| La | thickness of the active layer | L |
| σ | subsidence rate | L / T |
| rB | the ratio of depositional width to channel width | - |
| Ω | channel sinuosity | - |
| Λ | units of wash load deposited in the system per unit of bed material load | - |
| τ | shear stress on bed surface | - |
| qb | bed material load | M / T |
| Δx | spatial step length, equals to L / M | L |
| Qw | flood discharge | L3 / T |
| Δt | time step | T |
| Ntoprint | number of time steps to printout | - |
| Nprint | number of printouts | - |
| aU | upwinding coefficient (1=full upwind, 0.5=central difference) | - |
| αs | coefficient in sediment transport relation | - |
| pfeed | GSD of the feed | M / T |
| Ffs | GSD of the substrate | - |
| Ff | GSD of the final surface | - |
| Fup | GSD at the upstream end | - |
| Fdown | GSD at the downstream end | - |
Output
| Symbol | Description | Unit |
|---|---|---|
| η | bed surface elevatioon | L |
| H | water depth | L |
| ξ | water surface elevation | L |
| τb | bed shear stress | M / (T2 L) |
| S | bed slope | - |
| qt | total bed material load | L2 / T |
| Lmax | maximum length of basin that the sediment supply can fill | L |
Notes
The river is assumed to be morphologically active for If fraction of time, during which the flow is approximated as constant. Otherwise, the river is assumed to be morphologically dead.
The river flows into a basin that is subsiding with rate σ. The basin has constant width. For each unit of bedload deposited, L units of washload (typically sand transported in suspension) is deposited across the depositional basin.
If run for a sufficient length of time, the river profile approaches a steady-state balance between subsidence. At this steady state the profile displays both an upward-concave elevation profile and downstream fining of the surface material.
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.
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 ηd.
Gravel bedload transport of mixtures is computed with a user-specified selection of the Parker (1990), or Wilcock-Crowe (2003) surface-based formulations for gravel transport.Sand and finer material must first be excluded from the grain size distributions, which then must be renormalized for gravel content only, in the case of the Parker (1990) relation. In the case of the Wilcock-Crowe (2003) relation, the sand is retained in the computation.
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.
The flow is calculated using the normal flow (local equilibrium) approximation.
- Note on model running
In the case of the load relation due to Parker (1990), the grain size distributions are automatically re-normalized because the relation is for the transport of gravel only in the case of the load relation due to Wilcock-Crowe (2003), the sand and the fine sediment are retained for the computation.
The input grain size distributions may be on a 0-100% or a 0.00-1.00 scale, and the program will automatically scale.
The input grain size distributions must have bounds at 0% and 100% (1.00) to properly perform the calculation. If the user does not input the bounds the program will automatically interpolate upper and lower bounds DbU and DbL such that ffU = 100 (1.00) and ffL = 0
The water depth is calculated using a Chézy formulation, when only the Chézy coefficient is present in the inputted file, and with the Manning-Strickler formulation, when only the roughness height, kc, value is present. When both are present the program will ask the user which formulation they would like to use.
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
- 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.
