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

First tab header

Second tab header

Etc. tab header

Parameter	Description	Unit
First parameter	Description parameter	[Units]

Parameter	Description	Unit
First parameter	Description parameter	[Units]

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
S	bed slope	-
D50	median sediment size	mm
D90	size such that 90% of the sediment is finer	mm
nk	factor such that ks = nk Ds90	mm
R	submerged specific gravity of sediment	-
n	factor in the roughness height calculation	-
H	low end value of water depth due to skin friction	m
s	step size for water depth due to skin friction	m
N	number of steps to make	-
a	factor for stratification (if not included it will be assumed 1)	-
Hs	water depth due to the skin friction	m
τsg	shields stress due to skin friction	N / m2
U	flow velocity	m / s
γ	parameter with no physical meaning (used in calculations of H)	-
qw	flow rate	m2 / s
τ	actual shields stress	N / m2
Fr	Froude number	-
u*	shear velocity	m / s
u*s	shear velocity due to skin friction	m / s
qb	bedload transport rate	m2 / s

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: 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)

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]