Model help:WPHydResAMBL

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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

Input Files and Directories

Run Parameters

About

Parameter	Description	Unit
Input directory	path to input files
Site prefix	Site prefix for Input/Output files
Case prefix	Case prefix for Input/Output files

Parameter	Description	Unit
Bed slope		-
Submerged specific gravity of sediment		-
Median sediment size (D50)		mm
90% passing sediment size (D90)	grain diameter such that 90% of the distribution is finer	mm
factor such that ks = n * D90		-
low end value of Hs	low end value of water depth due to skin friction	m
step size for Hs	step size for water depth due to skin friction	m
number of steps to make for Hs		-

Parameter	Description	Unit
Model name	name of the model	-
Author name	name of the model author	-

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>\tau_{s} ^* = {\frac{H_{s} S}{R D_{50}}} </math>

(1)

<math>U = 8.32 \sqrt { g H_{s} S } \left ( {\frac{H_{s}}{k_{s}}} \right ) ^ \left ( {\frac{1}{6}} \right ) </math>

(2)

<math>\Gamma = \left ( {\frac{\tau _{s} ^* - 0.05 }{0.7}} \right ) ^ \left ( {\frac{5}{4}} \right ) </math>

(3)

<math>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>q_{w} = U H </math>

(5)

<math>\tau ^* = {\frac{H S}{R D_{50}}} </math>

(6)

<math>Fr = {\frac{U}{\sqrt { g H }}} </math>

(7)

<math>u_{*} = \sqrt { g H S } </math>

(8)

<math>u_{*s} = \sqrt { g H_{s} S } </math>

(9)

<math>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)

Nomenclature

Symbol	Description	Unit
τ*	actual shields stress	-
τs*	Shields stress due to skin friction	-
S	bed slope	-
D50	median sediment size	L
D90	size such that 90% of the sediment is finer	L
Ds90	size such that 90% of the sediment is finer in surface layer	L
nk	factor such that ks = nk Ds90	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	-
αstrat	factor for stratification (if not included it will be assumed 1)	-
Hs	water depth due to the skin friction	L
τsg	shields stress due to skin friction	-
U	flow velocity	L / T
qw	flow rate	L2 / T
Fr	Froude number	-
u*	shear velocity	L / T
u*s	shear velocity due to skin friction	L / T
qb	bedload transport rate	L2 / T
g	acceleration due to gravity	L / T2
ks	grain roughness height associated with skin friction
Γ	parameter with no physical meaning (used to calculate H)
Ds50	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)

Gary Parker

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

Links

• Model:WPHydResAMBL