Model help:DepDistTotLoadCalc

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The CSDMS Help System

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

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)

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:

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