# Model help:DredgeSlotBW

## DredgeSlotBW

This model is a calculator for aggradation and degradation of sediment mixtures in gravel-bed streams subject to cyclic hydrographs.

## Model introduction

This program calculates the 1D bed evolution of a sand-bed river after installation of a dredge slot.

## 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
Flow discharge (Q) m3 / s
Flood Intermittency (I) flood intermittency -
Channel width (B) m
Median grain size (sand) (d) median grain diameter of sand mm
Grain size such that 90% is finer (sand) (D) mm
Submerged specific gravity of sediment (R) -
Bed slope (S) -
Reach slope
Reach length (L) m
Depth of dredge slot (H) m
Fraction of reach length defining upstream end of dredge slot (u) -
Fraction of reach length defining downstream end of dredge slot (r) -
Bed porosity (l) -
Upwinding coefficient (1 = full upwinding, 0.5 for central difference) -
Number of spatial steps desired (no more than 2000) (M) -
Time step (t) days
Number of iterations per print statement (i) -
Iterations of prints desired (p) -
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

• bedload calculation using Ashida-Michiue formula
 $\displaystyle{ q_{Bj} = 17 \tau _{*j} ^ \left ( {\frac{3}{2}} \right ) \left ( {\frac{1 - \tau _{*cj}}{\tau _{*j}}} \right ) \left ( 1 - \sqrt{ {\frac{\tau _{*cj}}{\tau _{*j}}}} \right ) \ast p_{j} }$ (1)
• Entrainment of suspended sediment
 $\displaystyle{ E_{si} = {\frac{B \left ( \lambda X_{i} \right ) ^5 }{1 + {\frac{B}{0.3}} \left ( \lambda X_{i} \right ) ^ 5}} }$ (2)
 $\displaystyle{ X_{i} = \left ( {\frac{u_{*sk}}{v_{si}}} R_{pi} ^ \left (0.6\right ) \right ) S_{0} ^ \left (0.08\right ) \left ( {\frac{D_{i}}{D_{50}}}\right ) ^ \left ( 0.2 \right ) }$ (3)
• Overall suppression of entrainment due to mixture effects
 $\displaystyle{ \lambda = 1 - 0.28 \delta _{\Phi} }$ (4)
• Particle Reynolds number
 $\displaystyle{ R_{pi} = {\frac{\sqrt{ R g D_{i} } D_{i}}{\nu}} }$ (5)

## Notes

In the calculation of River Bed Elevation Variation with a Dredge Slot: the river is assumed to be sand-bed. The calculation proceeds using a backwater formulation. Flow resistance is computed using the Wright-Parker (2004) formulation. The bedload transport rate is computed using the Ashida-Michiue (1972) formulation. The rate of entrainment into suspension is computed using the Wright-Parker formulation without the stratification correction.

The calculation begins with the assumption of a prevailing mobile-bed normal flow equilibrium before installation of the dredge slot. The flow depth H, volume bedload transport rate per unit width qb and volume suspended transport rate per unit width qs at normal flow are computed based on input values of discharge Qww, channel width B, bed material sizes D50 and D90, sediment submerged specific gravity Rr and bed slope S.

The sediment is assumed to be sufficiently uniform so that D50 and D90 are unchanging in space and time. The input parameter Inter specifies the fraction of any year for which flood flow prevails. At other times of the year the river is assumed to be morphologically dormant.

The reach is assumed to have length L. The dredge slot is excavated at time t = 0, and then allowed to fill in time with no subsequent excavation. The depth of initial excavation below the bottom of the bed prevailing at normal equilibrium is an input variable with the name Hslot. The dredge slot extends from an upstream point equal to ru*L to a downstream point rd*Hslot, where ru and rd are user-input values.

The porosity lamp of the sediment deposit is a user-input parameter.

The bedload transport relation used in the calculation is that of Ashida and Michiue (1972). The formulation for entrainment of sediment into suspension is that of Wright and Parker (2004). The formulation for flow resistance is that of Wright and Parker (2004). The flow stratification correction of Wright-Parker is not implemented here for simplicity. A quasi-equilibrium formulation is used to computed the transport rate of suspended sediment from the entrainment rate.

A backwater calculation is used to compute the flow. The water surface elevation at the downstream end of the reach is held constant at the value associated with normal flow equilibrium.

Iteration is required to compute: a) the flow depth prevailing at normal flow; b) the friction slope and depth prevailing at normal flow, b) the friction slope and depth associated with skin friction associated with skin friction from any given value of depth, and b) the minimum Shields number below which form drag is taken to vanish.

• Note on model running

The model is allowed up to 2000 spatial steps, any more than that will cause a memory overwrite and the data cannot be trusted

The Normal flow data is included in the initial output, at the bottom of the file.

The sediment is assumed to be sufficiently uniform such that D50 and D90 do not change in space or time.

The bedload transport calculations use an Ashida-Michiue formulation (1972), the entrainment of suspended sediment uses that of Wright and Parker (2004), as does the formulation for flow resistance.

## 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: