Model help:WPHydResAMBL
WPHydResAMBL
This model is an implementation of the Wright-Parker (2004) formulation for hydraulic resistance combined with the Ashida-Michiue (1972) bedload formulation.
Model introduction
This model is a Depth-Discharge and Bedload Calculator, uses: 1. Wright-Parker formulation for flow resistance (without stratification correction) 2. Ashida-Michiue formulation for bedload transport.
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
[math]\displaystyle{ \tau_{s} ^* = {\frac{H_{s} S}{R D_{50}}} }[/math] (1)
[math]\displaystyle{ U = 8.32 \sqrt { g H_{s} S } \left ( {\frac{H_{s}}{k_{s}}} \right ) ^ \left ( {\frac{1}{6}} \right ) }[/math] (2)
[math]\displaystyle{ \Gamma = \left ( {\frac{\tau _{s} ^* - 0.05 }{0.7}} \right ) ^ \left ( {\frac{5}{4}} \right ) }[/math] (3)
[math]\displaystyle{ H = [ \Gamma {\frac{R D_{s50}}{S}} \left ( {\frac{\sqrt { g }}{U}} \right ) ^ \left ( 0.7 \right ) ] ^ \left ( {\frac{20}{13}} \right ) }[/math] (4)
[math]\displaystyle{ q_{w} = U H }[/math] (5)
[math]\displaystyle{ \tau ^* = {\frac{H S}{R D_{50}}} }[/math] (6)
[math]\displaystyle{ Fr = {\frac{U}{\sqrt { g H }}} }[/math] (7)
[math]\displaystyle{ u_{*} = \sqrt { g H S } }[/math] (8)
[math]\displaystyle{ u_{*s} = \sqrt { g H_{s} S } }[/math] (9)
[math]\displaystyle{ q_{b} = \sqrt { R g D_{50} } D_{50} \left ( \tau _{s} ^* - 0.05 \right ) \left ( \sqrt { \tau _{s} ^* } - \sqrt { 0.05 } \right ) }[/math] (10)
Symbol | Description | Unit |
---|---|---|
τ^{*} | actual shields stress | - |
τ_{s}^{*} | Shields stress due to skin friction | - |
S | bed slope | - |
D_{50} | median sediment size | L |
D_{90} | size such that 90% of the sediment is finer | L |
D_{s90} | size such that 90% of the sediment is finer in surface layer | L |
n_{k} | factor such that k_{s} = n_{k} D_{s90} | L |
R | submerged specific gravity of sediment | - |
H | low end value of water depth due to skin friction | L |
s | step size for water depth due to skin friction | - |
N | number of steps to make | - |
α_{strat} | factor for stratification (if not included it will be assumed 1) | - |
H_{s} | water depth due to the skin friction | L |
τ_{sg} | shields stress due to skin friction | - |
U | flow velocity | L / T |
q_{w} | flow rate | L^{2} / T |
Fr | Froude number | - |
u_{*} | shear velocity | L / T |
u_{*s} | shear velocity due to skin friction | L / T |
q_{b} | bedload transport rate | L^{2} / T |
g | acceleration due to gravity | L / T^{2} |
k_{s} | grain roughness height associated with skin friction | |
Γ | parameter with no physical meaning (used to calculate H) | |
D_{s50} | median size of surface layer sediment | L |
Notes
This program uses the Wright-Parker formulation to calculate flow resistance, and the Ashida-Michiue formulation to calculate the water depth against water discharge and bedload transport, as well as calculating the flow velocity, shear velocities, shear stress, and several other parameters.
The program takes the inputs given above; the α_{strat} is an optional parameter that may be entered; if the user chooses not to include it, it will automatically be set to 1, and stratification will not be taken into account.
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
- Wright, S. and Parker, G., 2004, Flow resistance and suspended load in sand-bed rivers: simplified stratification model, Journal of Hydraulic Engineering.
- Ashida, K. and M. Michiue, 1972, Study on hydraulic resistance and bedload transport rate in alluvial streams, Transactions, Japan Society of Civil