Model help:DepDistTotLoadCalc

DepDistTotLoadCalc

This is an illustration of calculation of depth-discharge relation, bed load transport, suspended load transport and total bed material load for a large, low-slope sand-bed river.

Model introduction

This program calculates the same parameters as WPHydResAMBL, as well as calculating the Entrainment, Chézy coefficient, bedload ratios, and various other parameters.

This model is a Depth-Discharge and Total Load calculator, uses: 1. Wright-Parker formulation for flow resistance, 2. Ashida-Michiue formulation for bedload transport, 3. Wright-Parker formulation (without stratification) for suspended load.

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 (S)		-
median sediment size (D50)		mm
90% passing sediment size (D90)	diameter such that 90% of the distribution is finer	mm
factor such that ks = n*D90		-
submerged specific gravity of sediment (R)		-
kinematic viscosity of water (v)		m2 / s
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		m

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]\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{ H = \left ( \Gamma {\frac{R D_{s50}}{S}} \left ( {\frac{\sqrt { g }}{U}} \right ) ^ \left ( 0.7 \right ) \right ) ^ \left ( {\frac{20}{13}} \right ) }[/math]

(3)

[math]\displaystyle{ \Gamma = \left ( {\frac{\tau_{s} ^* - 0.05}{0.7}} \right ) ^ \left ( {\frac{5}{4}} \right ) }[/math]

(4)

[math]\displaystyle{ \tau^* = {\frac {H S}{R D_{50}}} }[/math]

(5)

[math]\displaystyle{ F_{r}= {\frac{U}{\sqrt { g H }}} }[/math]

(6)

[math]\displaystyle{ u_{*} = \sqrt { g H S } }[/math]

(7)

[math]\displaystyle{ u_{*s} = \sqrt { g H_{s} S } }[/math]

(8)

[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]

(9)

[math]\displaystyle{ C_{z} = {\frac{U}{u_{*}}} }[/math]

(10)

[math]\displaystyle{ k_{c} = {\frac{11H}{e^ \left ( \kappa C_{z} \right )}} }[/math]

(11)

[math]\displaystyle{ Z_{u} = {\frac{u_{*s}}{v_{s}}} Re_{p} ^ \left ( 0.6 \right ) S ^ \left ( 0.07 \right ) }[/math]

(12)

[math]\displaystyle{ E = {\frac{5.7 * 10^\left ( -7 \right ) Z_{u} ^5}{1 + {\frac{5.7 * 10^\left ( -7 \right )}{0.3}} Z_{u} ^5}} }[/math]

(13)

[math]\displaystyle{ q_{s} = {\frac{u_{*} E H}{\kappa}} I }[/math]

(14)

[math]\displaystyle{ q_{t} = q_{s} + q_{b} }[/math]

(15)

[math]\displaystyle{ I = \int _{\zeta _{b}} ^ 1 [ {\frac{\left ( 1 - \zeta \right ) / \zeta}{\left ( 1 - \zeta _{b} \right ) / \zeta_{b}}} ] ^ {\frac{V_{s}}{\kappa u_{*}}} ln \left ( 30 {\frac{H}{k_{c}}} \zeta \right ) d \zeta }[/math]

(16)

Nomenclature

Symbol	Description	Unit
S	bed slope	-
D50	median sediment size	L
D90	size such that 90% of the the sediment if finer	L
ks	grain roughness height	L
R	submerged specific gravity of sediment	-
ν	kinematic viscosity of water	L2 / T
nk	factor such that ks = nk Ds90	M / L3
vs	fall velocity of size Ds50	L / T
Hs	depth associated with skin friction	L
g	acceleration due to gravity	L / T2
u*s	shear velocity due to skin friction	L / T
Cz	dimensionless Chezy resistance coefficient	-
kc	composite roughness height associated with both skin friction and form drag	-
E	dimensionless rate of entrainment of bed sediment into suspension	-
ζ	dimensionless upward normal coordinate	-
ζb	equals to 0.05	-
zu	parameter has no physical meaning	-
s	step size for water depth due to skin friction	L
d	median sediment diameter	L
D	diameter such that 90% of the distribution is finer	L
κ	Von Karmen coefficient, equals to 0.4	-
n	factor in the roughness height calculation	-
N	number of steps to make	-
a	factor for stratification (if not included it will be assumed 1)	-
Rep	explicit particle Reynolds number	-
Ds50	median sediment size of the surface layer sediment	-
U	depth- or cross sectionally-averaged flow velocity or layer-average velocity (turbidity current)	L / T
Fr	Froude number	-
u*	shear velocity	L / T
H	cross-sectionally averaged flow depth (river) or flow thickness (turbidity current)	L
τ*	actual shields stress	-
τs*	Shields stress due to skin friction	-
Γ	parameter with no physical meaning (used in calculations of H)	-

Output

Symbol	Description	Unit
I	results of the integral	-
qs	volume suspended load transport rate per unit width	L 2 / T
qt	volume total bed material transport rate per unit width	L2 / T
qw	water discharge per unit width	L2 / T
qb	volume bedload transport rate per unit width	L2 / T

Notes

• Note on model running

The program shares the notes that are expressed in WPHydResAMBL.

The integration carried out in this program is performed with the trapezoidal rule.

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:DepDistTotLoadCalc

• Model_help:WPHydResAMBL