The morphodynamics of super- and transcritical flow Yves Zech Sandra Soares Frazão Benoit Spinewine, Mourad Bellal, Céline Savary Université catholique de Louvain, Belgium

Morphodynamics and floods Sudden changes in discharge and levels Regime discontinuities  Supercritical flow Intense transport Instabilities and bed forms  Transcritical flow Boundary conditions RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Overview The basic model: Saint-Venant - Exner Regime and solid transport Two-layer model Supercritical flow and bed forms Transcritical flow and boundary conditions RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Overview The basic model: Saint-Venant - Exner Regime and solid transport Two-layer model Supercritical flow and bed forms Transcritical flow and boundary conditions RCEM, October 2005 The morphodynamics of super- and transcritical flow

The basic model : St-Venant - Exner RCEM, October 2005 The morphodynamics of super- and transcritical flow

The basic model : St-Venant - Exner Closure Friction slope Sf Solid discharge qs RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Overview The basic model: Saint-Venant - Exner Regime and solid transport Two-layer model Supercritical flow and bed forms Transcritical flow and boundary conditions RCEM, October 2005 The morphodynamics of super- and transcritical flow

Regime and solid transport Grain mobilization : Shields - van Rijn RCEM, October 2005 The morphodynamics of super- and transcritical flow

Regime and solid transport Solid discharge RCEM, October 2005 The morphodynamics of super- and transcritical flow

Regime and solid transport High transport intensity Common formulae (range of applicability) If interaction between grains > interaction grains / liquid flow  debris flow Sudden changes in transport intensity Acceleration and deceleration: lag  exchanges of momentum  two-layer model Two-layer model instead of time and space lag RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Overview The basic model: Saint-Venant - Exner Regime and solid transport Two-layer model The model Uniform flow and calibration Application to dam-break wave Supercritical flow and bed forms Transcritical flow and boundary conditions RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Overview The basic model: Saint-Venant - Exner Regime and solid transport Two-layer model The model Uniform flow and calibration Application to dam-break wave Supercritical flow and bed forms Transcritical flow and boundary conditions RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model Distinct velocities Distinct concentrations pure water mixture u z RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model Closure : Erosion Shear stresses and Shear stress RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Overview The basic model: Saint-Venant - Exner Regime and solid transport Two-layer model The model Uniform flow and calibration Application to dam-break wave Supercritical flow and bed forms Transcritical flow and boundary conditions RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model Uniform flow conditions : RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model Uniform flow conditions : RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model Uniform flow conditions : RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model Uniform flow conditions : 8 equations 12 variables RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model Uniform flow conditions : calibration RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model Uniform flow conditions : RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model Uniform flow conditions : RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model Uniform flow conditions : RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Two-layer model Uniform flow conditions : qs (m3/s/m) hw : Manning qs : Meyer-Peter - Müller hw : 2-layers qs : MPM hw and qs : 2-layer model Fr RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Overview The basic model: Saint-Venant - Exner Regime and solid transport Two-layer model The model Uniform flow and calibration Application to dam-break wave Supercritical flow and bed forms Transcritical flow and boundary conditions RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Dam-break wave t = 0.0 s t = 0.2 s t = 0.4 s RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Dam-break wave Physical description RCEM, October 2005 The morphodynamics of super- and transcritical flow

Dam-break wave : flat bed Flat bed case PVC Gates moving up h0 hs RCEM, October 2005 The morphodynamics of super- and transcritical flow

Dam-break wave : flat bed Sediment layer underestimated: the concentration is the same in the sediment layer although this one has to de-bulk for moving t = 0.2 s RCEM, October 2005 The morphodynamics of super- and transcritical flow

Dam-break wave : flat bed Sediment layer underestimated: the concentration is the same in the sediment layer although this one has to de-bulk for moving t = 0.4 s RCEM, October 2005 The morphodynamics of super- and transcritical flow

Dam-break wave : flat bed Sediment layer underestimated: the concentration is the same in the sediment layer although this one has to de-bulk for moving t = 0.6 s RCEM, October 2005 The morphodynamics of super- and transcritical flow

Dam-break wave : flat bed Sediment layer underestimated: the concentration is the same in the sediment layer although this one has to de-bulk for moving t = 0.8 s RCEM, October 2005 The morphodynamics of super- and transcritical flow

Dam-break wave : flat bed Sediment layer underestimated: the concentration is the same in the sediment layer although this one has to de-bulk for moving t = 1.0 s RCEM, October 2005 The morphodynamics of super- and transcritical flow

Dam-break wave : stepped bed Stepped-bed case Materials PVC Sand Louvain new flume Gates moving down RCEM, October 2005 The morphodynamics of super- and transcritical flow

Dam-break wave : stepped bed RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Experimental set-up RCEM, October 2005 The morphodynamics of super- and transcritical flow

Dam-break wave : stepped bed PVC - t = 3 t0 z/h0 x/h0 RCEM, October 2005 The morphodynamics of super- and transcritical flow

Dam-break wave : stepped bed PVC - t = 4 t0 z/h0 x/h0 RCEM, October 2005 The morphodynamics of super- and transcritical flow

Dam-break wave : stepped bed PVC - t = 6 t0 z/h0 x/h0 RCEM, October 2005 The morphodynamics of super- and transcritical flow

Dam-break wave : stepped bed PVC - t = 8 t0 z/h0 x/h0 RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Overview The basic model: Saint-Venant - Exner Regime and solid transport Two-layer model Supercritical flow and bed forms Antidune modeling Transcritical flow and boundary conditions RCEM, October 2005 The morphodynamics of super- and transcritical flow

Supercritical flow and bed forms Stepped bed z/h0 x/h0 RCEM, October 2005 The morphodynamics of super- and transcritical flow

Supercritical flow and bed forms 2D two-layer model Sediment layer underestimated: the concentration is the same in the sediment layer although this one has to de-bulk for moving RCEM, October 2005 The morphodynamics of super- and transcritical flow

Supercritical flow and antidunes Two-layer shallow-water computation Flow H. Capart D.L. Young 2002 Two-layer shallow water computations of torrential geomorphic flows The paper applies a two-layer shallow water approach to the simulation of torrential geomorphic flows. The description endows water and slurry layers with their own velocity and inertia, and accounts for both mass and momentum exchanges across sharp interfaces. This allows rather general patterns of water and sediment motion to emerge from interactions between torrential currents and loose sand beds. The description is implemented into a 2D computational scheme based on direction and operator splitting. A Godunov algorithm is used for the hyperbolic operator, and an implicit backwards Euler scheme for the frictional and geomorphic source terms. A bank failure operator can further be nested inside the time-stepping loop. To explore its capabilities, we test the approach on three geomorphological features associated with miniature rivers on intertidal beaches: crescent marks, antidune trains, and runnel bank erosion. Encouraging results are obtained, and suggest that the modelling approach could be extended to torrential geomorphic flows at larger scales. Computed Measured Antidunes RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Overview The basic model: Saint-Venant - Exner Regime and solid transport Two-layer model Supercritical flow and bed forms Transcritical flow and boundary conditions Saint-Venant - Exner approach Limitations 2-layer approach : jump over mobile bed RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Overview The basic model: Saint-Venant - Exner Regime and solid transport Two-layer model Supercritical flow and bed forms Transcritical flow and boundary conditions Saint-Venant - Exner approach Limitations 2-layer approach : jump over mobile bed RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Boundary conditions Saint-Venant - Exner in unit width RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Boundary conditions De Vries analysis : characteristics RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Boundary conditions  2 upstream, 1 downstream boundary conditions x t RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Overview The basic model: Saint-Venant - Exner Regime and solid transport Two-layer model Supercritical flow and bed forms Transcritical flow and boundary conditions Saint-Venant - Exner approach Limitations 2-layer approach : jump over mobile bed RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : aggradation Steep-sloped aggradation q (qs) zb h = hc RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump over mobile bed Initial conditions : steep slope RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump over mobile bed Raise of a gate downstream RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump over mobile bed Stabilisation of the surge RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Water and bed level RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Initial condition : supercritical flow x t zw q (qs) zb RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump on fixed bed zw zw q RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump on fixed bed : upstream zw q Upstream RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump on fixed bed : downstream zw q Downstream RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump on mobile bed zw zw q (qs) RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump on mobile bed zw zw q RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump on mobile bed : upstream zw q x t Upstream RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump on mobile bed : downstream zw q x t Downstream RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump on mobile bed zw zw q x t RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump on mobile bed zw zw q RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump on mobile bed zw zw q RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump on mobile bed zw zw q RCEM, October 2005 The morphodynamics of super- and transcritical flow

Boundary conditions : hydraulic jump Hydraulic jump on mobile bed zw zw q ? RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Overview The basic model: Saint-Venant - Exner Regime and solid transport Two-layer model Supercritical flow and bed forms Transcritical flow and boundary conditions Saint-Venant - Exner approach Limitations : jump over mobile bed 2-layer approach : jump over mobile bed RCEM, October 2005 The morphodynamics of super- and transcritical flow

Two-layer boundary conditions RCEM, October 2005 The morphodynamics of super- and transcritical flow

Two-layer boundary conditions Re (l) (m/s) Im (l) Frw Frw uw = 1 m/s, us = 0.6 m/s, hs = 0.01 m and hw varies from 0.01 to 2.55 m RCEM, October 2005 The morphodynamics of super- and transcritical flow

Two-layer boundary conditions l m/s Frw uw = 1 m/s, us = 0.6 m/s, hs = 0.1 m and hw varies from 0.01 to 2.55 m RCEM, October 2005 The morphodynamics of super- and transcritical flow

Two-layer boundary conditions Supercritical flow 1 = 0 2, 3, 4, 5 > 0 1 < 0 2 = 0 3, 4, 5 > 0 RCEM, October 2005 The morphodynamics of super- and transcritical flow

Two-layer boundary conditions Subcritical flow 1 < 0 2 = 0 3, 4, 5 > 0 1, 2 < 0 3 = 0 4, 5 > 0 RCEM, October 2005 The morphodynamics of super- and transcritical flow

Jump boundary conditions 1 = 0 2, 3, 4, 5 > 0 4 boundary conditions 1 < 0 2, 3, 4 = 0 5 > 0 1 boundary condition RCEM, October 2005 The morphodynamics of super- and transcritical flow

Hydraulic jump on mobile bed RCEM, October 2005 The morphodynamics of super- and transcritical flow

Hydraulic jump on mobile bed zw zw q (qs) RCEM, October 2005 The morphodynamics of super- and transcritical flow

Hydraulic jump on mobile bed t = 9.2 s RCEM, October 2005 The morphodynamics of super- and transcritical flow

Hydraulic jump on mobile bed t = 18.4 s Léger hs à gauche; pas à droite RCEM, October 2005 The morphodynamics of super- and transcritical flow

Hydraulic jump on mobile bed t = 27.6 s RCEM, October 2005 The morphodynamics of super- and transcritical flow

Hydraulic jump on mobile bed t = 36.8 s RCEM, October 2005 The morphodynamics of super- and transcritical flow

Hydraulic jump on mobile bed t = 36.8 s Numerical sediment front a little delayed but also spread. Depending on the initial bottom. The imposed one was a straight line, which was not completely the realty where there were some discontinuities (see the last experimental point below the theoretical one) No measurement before since too fast for digital imaging with a little frame (< 1 m) RCEM, October 2005 The morphodynamics of super- and transcritical flow

Hydraulic jump on mobile bed zw zw q (qs) RCEM, October 2005 The morphodynamics of super- and transcritical flow

Hydraulic jump on mobile bed t = 140 s Water level too high. In the realty a part of kinetic energy due to recirculation is not modelled. Front a little delayed, but also little transport downstream the front contrarily to the realty. Probably linked to the water level and the critical bottom shear stress (disappears after). RCEM, October 2005 The morphodynamics of super- and transcritical flow

Hydraulic jump on mobile bed t = 290 s Now the threshold is clearly exceeded, thus no more problem downstream. Too low: no measurement of the upstream point, thus maybe too high upstream. In the realty deposition of solid discharge is not so clearly defined. RCEM, October 2005 The morphodynamics of super- and transcritical flow

Hydraulic jump on mobile bed t = 545 s RCEM, October 2005 The morphodynamics of super- and transcritical flow

Hydraulic jump on mobile bed t = 630 s RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Conclusions Floods Regime discontinuities  Supercritical flow Intense transport Instabilities and bed forms  Transcritical flow Acceleration / deceleration : lag Boundary conditions RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Conclusions Floods Regime discontinuities  Supercritical flow Intense transport Instabilities and bed forms  Transcritical flow Acceleration / deceleration : lag Boundary conditions  Two layer model… to be improved RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Conclusions Floods Regime discontinuities  Supercritical flow Intense transport Instabilities and bed forms  Transcritical flow Acceleration / deceleration : lag Boundary conditions  Two-layer model… to be improved RCEM, October 2005 The morphodynamics of super- and transcritical flow

The morphodynamics of super- and transcritical flow Yves Zech Sandra Soares Frazão Benoit Spinewine, Mourad Bellal, Céline Savary Université catholique de Louvain, Belgium Thank you for your attention