Model help:DepDistTotLoadCalc

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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

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]

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

(4)

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

(5)

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

(6)

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

(7)

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

(8)

<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>

(9)

<math>C_{z} = {\frac{U}{u_{*}}} </math>

(10)

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

(11)

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

(12)

<math>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>q_{s} = {\frac{u_{*} E H}{\kappa}} I </math>

(14)

<math>q_{t} = q_{s} + q_{b} </math>

(15)

<math>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	mm
D90	size such that 90% of the the sediment if finer	mm
ks	grain roughness height	mm
R	submerged specific gravity of sediment	-
ν	kinematic viscosity of water	m2 / s
nk	factor such that ks = nk Ds90	kg/m3
vs	fall velocity of size Ds50	cm / s
τb	boundary shear stress on the bed	kg / (m s)
u	shear velocity on the bed	m / s
qbi	volume gravel bedload transport per unit width of grains in the ith size range	m 2
u*	shear velocity	m / s
Dlg	geometric mean of the bedload	mm
σlg	geometric standard deviation of the bedload	-
Dsx	size in the surface material, such that x percentage of the material is finer	mm
Dlx	size in the bedload material, such that x percentage of the material is finer	-
Dsx	size in the surface material, such that x percentage of the material is finer	mm
Hs	depth associated with skin friction	m
U	depth- or cross sectionally-averaged flow velocity or layer-average velocity (turbidity current)	m / s
H	cross-sectionally averaged flow depth (river) or flow thickness (turbidity current)	m
qw	water discharge per unit width	m2 / s
τ*	Shields number	-
Fr	Froude number	-
u*	shear velocity	m / s
u*s	shear velocity due to skin friction	m / s
qb	volume bedload transport rate per unit width	m2 / s
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	m2 / s
I	results of the integral	-
qs	volume suspended load transport rate per unit width	m 2 / s
qt	volume total bed material transport rate per unit width	m2 / s
ζ	dimensionless upward normal coordinate	-
Rep		-
Rf		-
Γ	parameter with no physical meaning (used in calculations of H)	-
Ds50		-
τs *		-
k		-
zu	parameter has no physical meaning	-
qt		-
Sb		-
τg		-
τ		-
s	step size for water depth due to skin friction	m
d	median sediment diameter	mm
D	diameter such that 90% of the distribution is finer	mm
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)	-

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: 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

Key papers

Links

• [Model:DepDistTotLoadCalc]