Environmental Fluid Mechanics

, Volume 8, Issue 2, pp 169–198 | Cite as

One-dimensional numerical modelling of dam-break waves over movable beds: application to experimental and field cases

  • Kamal El Kadi Abderrezzak
  • André Paquier
  • Bernard Gay
Original Article

Abstract

This paper reports a numerical study on dam-break waves over movable beds. A one-dimensional (1-D) model is built upon the Saint-Venant equations for shallow water waves, the Exner equation of sediment mass conservation and a spatial lag equation for non-equilibrium sediment transport. The set of governing equations is solved using an explicit finite difference scheme. The model is tested in various idealized experimental cases, with fairly good agreement between the numerical predictions and measurements. Discrepancies are observed at the earlier stage of the dam-break wave and around the dam location due to no vertical velocity component being taken into account. Sensitivity tests confirm that the friction coefficient is an important parameter for the evaluation of sediment transport processes operating during a dam-break wave. The influence of the non-equilibrium adaptation length (or the lag distance) is negligible on the wavefront celerity and weak on the free surface and bed profiles, which indicates that one may ignore the spatial lag effect in dam-break wave studies. Finally, the simulation of the Lake Ha!Ha! dyke-break flood event shows that the model can provide relevant results if a convenient formula for computing the sediment transport capacity and an appropriate median grain diameter of riverbed material are selected.

Keywords

Dam-break wave Ha!Ha! River One-dimensional model Sediment transport 

List of notations

A

Wetted area

Ab

Cross-sectional area

B

Channel width at the free surface

BSS

Brier Skill Score (Eq. 19)

C

Conveyance (Eq. 4)

Cr

Courant number

c

Celerity= \(\sqrt{gA/B}\)

Dchar

Lag distance

D50

Particle size for which 50% of the sediment is finer by weight).

F

Flux vector= \(\left[{\begin{array}{l} Q\\ \frac{Q^{2}}{A}+g I_1 \end{array}}\right]\)

g

Gravitational acceleration

h

Flow depth

h0hw,uhs,u

Water head, flow depth and initial bottom step in the upstream reach

hw,d

Flow depth in the downstream reach

I1

Hydrostatic pressure force (Eq. 3a)

I2

Pressure force due to longitudinal width variation (Eq. 3b)

J

Energy slope

K

Manning–Strickler coefficient for flow resistance calculations (Eq. 4)

p

Porosity of bed deposit

Q

Flow discharge

Qs

Volumetric sediment discharge

\(Q_s^{cap}\)

Volumetric sediment transport capacity discharge

\(Q_s^{dep},\, Q_s^{ero},\, Q_s^{I_n},\, Q_s^{O_u} \cdot Q_s^{tra}\)

Sediment fluxes (Eqs. 8 to 10)

Rh

Hydraulic radius

S

Source term= \(\left[{\begin{array}{l} 0\\ -gA\frac{\partial z_b}{\partial x}-gA \frac{Q\left| Q \right|}{C^{2}} +g I_2 \end{array}}\right]\)

t

Time

t0

Characteristic time for dam-break wave propagation = \(\sqrt{h_0/g}\)

U

Conservative hydraulic variables= \(\left[{\begin{array}{l} A\\Q \end{array}}\right]\)

Vb

Bedload velocity assumed equal to the mean flow velocity

x

Longitudinal distance

zb

Bed elevation

ΔAb

Change in the cross-sectional area due to deposition or scour

Δt

Time step

Δx

Space step

\(\delta_i^n\)

Slope of Q (or A) defined by Eq. 12

\(\delta_{i(1)}^n,\, \delta_{i(2)}^n, \,\delta_{i(3)}^n\)

Parameters in Eq. 12

κ

Parameter in Eq. 12

ρ

Density of water

ρs

Density of the sediment

τ

Bottom shear stress = ρ gRJ

τ0

Shields number= \(\frac{\tau}{g({\rho_s -\rho})D_{50}}.\)

τ0,cr

Critical Shields number

χ

Parameter in Eq. 12

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Kamal El Kadi Abderrezzak
    • 1
  • André Paquier
    • 1
  • Bernard Gay
    • 2
  1. 1.CemagrefHydrology-Hydraulics Research UnitLyonFrance
  2. 2.Université Claude Bernard Lyon 1VilleurbanneFrance

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