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Revision as of 15:18, 24 May 2011
DredgeSlotBW
This model is a calculator for aggradation and degradation of sediment mixtures in gravel-bed streams subject to cyclic hydrographs.
Model introduction
This program calculates the 1D bed evolution of a sand-bed river after installation of a dredge slot.
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
- bedload calculation using Ashida-Michiue formula
[math]\displaystyle{ q_{Bj} = 17 \tau _{*j} ^ \left ( {\frac{3}{2}} \right ) \left ( {\frac{1 - \tau _{*cj}}{\tau _{*j}}} \right ) \left ( 1 - \sqrt{ {\frac{\tau _{*cj}}{\tau _{*j}}}} \right ) \ast p_{j} }[/math] (1)
- Entrainment of suspended sediment
[math]\displaystyle{ E_{si} = {\frac{B \left ( \lambda X_{i} \right ) ^5 }{1 + {\frac{B}{0.3}} \left ( \lambda X_{i} \right ) ^ 5}} }[/math] (2)
[math]\displaystyle{ X_{i} = \left ( {\frac{u_{*sk}}{v_{si}}} R_{pi} ^ \left (0.6\right ) \right ) S_{0} ^ \left (0.08\right ) \left ( {\frac{D_{i}}{D_{50}}}\right ) ^ \left ( 0.2 \right ) }[/math] (3)
- Overall suppression of entrainment due to mixture effects
[math]\displaystyle{ \lambda = 1 - 0.28 \delta _{\Phi} }[/math] (4)
- Particle Reynolds number
[math]\displaystyle{ R_{pi} = {\frac{\sqrt{ R g D_{i} } D_{i}}{\nu}} }[/math] (5)
Symbol | Description | Unit |
---|---|---|
E_{si} | dimensionless entrainment rate of sediment in the ith grain-size range (volume entrainment per bed area per unit fractional bed content) | - |
λ | overall suppression of entrainment due to mixture effects | - |
σ_{Φ} | standard deviation of the bed sediment on the sedimentological Φ scale | - |
u_{*sk} | shear velocity due to sin friction | - |
R_{pi} | particle Reynolds number | - |
B | constant in newly proposed entrainment relation, equals to 7.8*10^{-7} | - |
S_{0} | the ratio of h/D_{50} | - |
ν | kinematic viscosity | - |
D_{i} | characteristic diameter of the ith grain-size range | - |
D_{50} | median grain diameter of the bed material | - |
τ_{*j} | dimensionless tractive force for the j diameter | - |
q_{Bj} | the amount of bed load | - |
τ_{*cj} | critical dimensionless tractive force for the j diameter | - |
p_{j} | abundance ratio of the sediment of j diameter | - |
x | downstream coordinate | m |
η | bed elevation | m |
q_{b} | volume bedload transport per unit width | tons/annum |
q_{s} | volume bedload transport per unit width due to skin friction | tons/annum |
H | water depth | m |
H_{s} | water depth due to skin friction | m |
k_{si} | water surface elevation | m |
Q_{w} | flow discharge | m^{3} / s |
I_{f} | flood intermittency | - |
R_{r} | submerged specific gravity | |
S | bed slope | - |
L | reach length | m |
H_{slot} | depth of dredge slot | m |
r_{U} | fraction of reach length for upstream end of dredge slot | - |
r_{d} | fraction of reach length for downstream end of dredge slot | - |
λ_{p} | bed porosity | - |
a_{U} | upwinding coefficient: a_{u} = 1 corresponds to full upwinding, 0.5 for central difference | - |
M | number of spatial steps (<=2000) | - |
t | time step | yr |
Δt | time step | - |
Δx | spatial step length | - |
Mtoprint | number of time steps to printout | - |
Mprint | number of printouts | - |
Notes
In the calculation of River Bed Elevation Variation with a Dredge Slot: the river is assumed to be sand-bed. The calculation proceeds using a backwater formulation. Flow resistance is computed using the Wright-Parker (2004) formulation. The bedload transport rate is computed using the Ashida-Michiue (1972) formulation. The rate of entrainment into suspension is computed using the Wright-Parker formulation without the stratification correction.
The calculation begins with the assumption of a prevailing mobile-bed normal flow equilibrium before installation of the dredge slot. The flow depth H, volume bedload transport rate per unit width q_{b} and volume suspended transport rate per unit width q_{s} at normal flow are computed based on input values of discharge Q_{ww}, channel width B, bed material sizes D_{50} and D_{90}, sediment submerged specific gravity R_{r} and bed slope S.
The sediment is assumed to be sufficiently uniform so that D_{50} and D_{90} are unchanging in space and time. The input parameter Inter specifies the fraction of any year for which flood flow prevails. At other times of the year the river is assumed to be morphologically dormant.
The reach is assumed to have length L. The dredge slot is excavated at time t = 0, and then allowed to fill in time with no subsequent excavation. The depth of initial excavation below the bottom of the bed prevailing at normal equilibrium is an input variable with the name Hslot. The dredge slot extends from an upstream point equal to r_{u*L} to a downstream point rd*Hslot, where ru and rd are user-input values.
The porosity lamp of the sediment deposit is a user-input parameter.
The bedload transport relation used in the calculation is that of Ashida and Michiue (1972). The formulation for entrainment of sediment into suspension is that of Wright and Parker (2004). The formulation for flow resistance is that of Wright and Parker (2004). The flow stratification correction of Wright-Parker is not implemented here for simplicity. A quasi-equilibrium formulation is used to computed the transport rate of suspended sediment from the entrainment rate.
A backwater calculation is used to compute the flow. The water surface elevation at the downstream end of the reach is held constant at the value associated with normal flow equilibrium.
Iteration is required to compute: a) the flow depth prevailing at normal flow; b) the friction slope and depth prevailing at normal flow, b) the friction slope and depth associated with skin friction associated with skin friction from any given value of depth, and b) the minimum Shields number below which form drag is taken to vanish.
- Note on model running
The model is allowed up to 2000 spatial steps, any more than that will cause a memory overwrite and the data cannot be trusted
The Normal flow data is included in the initial output, at the bottom of the file.
The sediment is assumed to be sufficiently uniform such that D_{50} and D_{90} do not change in space or time.
The bedload transport calculations use an Ashida-Michiue formulation (1972), the entrainment of suspended sediment uses that of Wright and Parker (2004), as does the formulation for flow resistance.
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
- Ashida, K. and M. Michiue, 1972, Study on hydraulic resistance and bedload transport rate in alluvial streams, Transactions, Japan Society of Civil Engineering, 206: 59~69 (in Japanese)
- Wright, S. and G. Parker, 2004, Flow resistance and suspended load in sand-bed rivers: simplified stratification model, Journal of Hydraulic Engineering, 130(8): 796~805.