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
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)
| 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)
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
