mathematical modelling of the morphodynamic aspects of the 1996 flood in the Ha! Ha! river

1. mathematical modelling of the morphodynamic aspects of the 1996 flood in the Ha! Ha! river conceptual model and solution Rui M. L. Ferreira :: João G. B. Leal :: António H. Cardoso Instituto Superior Técnico :: september 2005

2. justification of the work severe rainstorms scourged the Saguenay region, south Québec, Canada, in July of 1996. overtopping and sequent failure of an earth fill dyke in lake Ha! Ha! caused a significative increase in the peak flood discharge in River Ha! Ha!. the dam-break wave, superimposed to the hydrologic flood, provoked massive geomorphic impacts in the downstream valley. sound yet simple simulation tools to predict and analyse the consequences of catastrophic events must be perfected. river Ha! Ha! disaster is well documented, thus suitable to be used in model validation. introduction it constitutes a very demanding boundary value problem because of the magnitude of the impacts and because of the transcritical nature of the flow.

3. justification of the work severe rainstorms scourged the Saguenay region, south Québec, Canada, in July of 1996. overtopping and sequent failure of an earth fill dyke in lake Ha! Ha! caused a significative increase in the peak flood discharge in River Ha! Ha!. the dam-break wave, superimposed to the hydrologic flood, provoked massive geomorphic impacts in the downstream valley. sound yet simple simulation tools to predict and analyse the consequences of catastrophic events must be perfected. river Ha! Ha! disaster is well documented, thus suitable to be used in model validation. introduction it constitutes a very demanding boundary value problem because of the magnitude of the impacts and because of the transcritical nature of the flow.

4. justification of the work severe rainstorms scourged the Saguenay region, south Québec, Canada, in July of 1996. overtopping and sequent failure of an earth fill dyke in lake Ha! Ha! caused a significative increase in the peak flood discharge in River Ha! Ha!. the dam-break wave, superimposed to the hydrologic flood, provoked massive geomorphic impacts in the downstream valley. sound yet simple simulation tools to predict and analyse the consequences of catastrophic events must be perfected. river Ha! Ha! disaster is well documented, thus suitable to be used in model validation. introduction it constitutes a very demanding boundary value problem because of the magnitude of the impacts and because of the transcritical nature of the flow.

5. justification of the work severe rainstorms scourged the Saguenay region, south Québec, Canada, in July of 1996. overtopping and sequent failure of an earth fill dyke in lake Ha! Ha! caused a significative increase in the peak flood discharge in River Ha! Ha!. the dam-break wave, superimposed to the hydrologic flood, provoked massive geomorphic impacts in the downstream valley. sound yet simple simulation tools to predict and analyse the consequences of catastrophic events must be perfected. river Ha! Ha! disaster is well documented, thus suitable to be used in model validation. introduction it constitutes a very demanding boundary value problem because of the magnitude of the impacts and because of the transcritical nature of the flow.

6. justification of the work severe rainstorms scourged the Saguenay region, south Québec, Canada, in July of 1996. overtopping and sequent failure of an earth fill dyke in lake Ha! Ha! caused a significative increase in the peak flood discharge in River Ha! Ha!. the dam-break wave, superimposed to the hydrologic flood, provoked massive geomorphic impacts in the downstream valley. sound yet simple simulation tools to predict and analyse the consequences of catastrophic events must be perfected. river Ha! Ha! disaster is well documented, thus suitable to be used in model validation. introduction it constitutes a very demanding boundary value problem because of the magnitude of the impacts and because of the transcritical nature of the flow.

7. objectives of the work to develop a conceptual model suitable to tackle the difficulties posed by the simulation of catastrophic floods, namely the important geomorphic changes and the existence of shocks and critical points. to develop a robust solution technique based on a finite difference discretization. to validate the model with the data of the 1996 river Ha! Ha! Flood (EU funded IMPACT project benchmark data) introduction

8. objectives of the work to develop a conceptual model suitable to tackle the difficulties posed by the simulation of catastrophic floods, namely the important geomorphic changes and the existence of shocks and critical points. to develop a robust solution technique based on a finite difference discretization. to validate the model with the data of the 1996 river Ha! Ha! Flood (EU funded IMPACT project benchmark data) introduction

9. objectives of the work to develop a conceptual model suitable to tackle the difficulties posed by the simulation of catastrophic floods, namely the important geomorphic changes and the existence of shocks and critical points. to develop a robust solution technique based on a finite difference discretization. to validate the model with the data of the 1996 river Ha! Ha! Flood (EU funded IMPACT project benchmark data) introduction

10. structure of the presentation description of the conceptual model presentation of the simulation results

11. structure of the presentation description of the conceptual model presentation of the simulation results

12. structure of the presentation description of the conceptual model presentation of the simulation solutions

13. conceptual model

14. physical system observations suggeststratification fig 1. dam-break wave generated by instantaneous rupture; Shields parameter at dam location is é  ≈ 2.5. observation window located downstream the reservoir, at about 10 times the water depth on the reservoir (10h0). conceptual model

15. cm 0 1 2 3 physical system conceptual model

16. cm 0 1 2 3 physical system upper plane bed conceptual model clear water/suspended sediment contact load bed (immobile particles)

17. cm 0 1 2 3 physical system debris flow conceptual model contact load bed (immobile particles)

18. idealised system fig 2. flow idealised as a multiple layer structure based on stress predominance. clear water/ suspended sediment transition region conceptual model contact load layer collisional region frictional region bed (immobile grains)

19. granular phase fluid phase shallow water flow cinematic non-material boundary conditions negligible segregation between phase – continuum hypothesis incompressible fluid and granular phases one-dimensional conservation equations model development conservation equations two-dimensional conservation equations (profile) conceptual model

20. model development one-dimensional conservation equationsmass and momentum total mass total momentum conceptual model sediment mass Cc capacity transport:

21. velocity in the contact load layer thickness of the contact load layer capacity (equilibrium) concentration model development one-dimensional conservation equationsmass and momentum conceptual model Cc capacity transport:

22. fluid phase stress tensor flux of grain kinetic energy collisional dissipation model development closure equations two-dimensional conservation equations (profile) granular phase constitutive equations conceptual model

23. fluid phase model development closure equations two-dimensional conservation equations (profile) granular phase constitutive equations collisional region described by dense gas kinetic theory (Chapman-Enskog) conceptual model

24. fluid phase model development closure equations two-dimensional conservation equations (profile) granular phase constitutive equations collisional region described by dense gas kinetic theory (Chapman-Enskog) conceptual model negligible streaming component of the stress tensor (chaos molecular)

25. fluid phase closure equations model development closure equations two-dimensional conservation equations (profile) granular phase constitutive equations collisional region described by dense gas kinetic theory (Chapman-Enskog) conceptual model negligible streaming component of the stress tensor (chaos molecular) quasi-elastic approximation: e≈1

26. simulationresults

27. b) a) ’2 = ’1 YL1 hL1 YL2 hL2 YbL1 hR1 hR2 =hR1 initial value problems the dam break flood wave fig 3. idealised geometry for the dam-break problem understood as a Riemann problem. Riemann problem: Wtyeyy dd xcbdc c chdfxc,njlkjncflks <sddsmnjnmvnmvb cfbnv dvb fgb simulation results Non-dimensional parameters:’ = hR/YL ’ = (YbLYbR)/YL

28. initial value problems the dam-break flood wavebed initially flat :: fixed banks :: prismatic channel simulation results evolution of the longitudinal flow profile.

29. initial value problems the dam-break flood wavebed initially flat :: fixed banks :: prismatic channel simulation results evolution of the longitudinal flow profile. comparison between observations and computed results.

30. initial value problems the dam-break flood wavebed initially flat :: erodible banks evolution of the longitudinal flow profile. simulation results evolution of the bed width at the level of the initial bed.

31. initial value problems the dam-break flood wavebed initially flat :: erodible banks bank erosion model 1 m simulation results m: inverse bank slope

32. initial value problems the dam-break flood wavebed initially flat :: erodible banks evolution of the bed width at the level of the initial bed. simulation results evolution of the inverse bank slope.

33. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! rivergeometry and flood hydrograph simulation results fig 5. flood hydrograph: superposition of the natural flood and the discharge released by the breached dyke. fig 4. plan view of river and lake Ha! Ha!.

34. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! riverobserved geomorphic impacts foto A simulation results fig 6. longitudinal profile of river Ha! Ha!. fig 7. photo A: dyke location after the collapse. note the pronounced erosion (about 12 metres).

35. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! riverobserved geomorphic impacts foto B simulation results fig 6. longitudinal profile of river Ha! Ha!. fig 8. photo B: generalized deposition at Eaux-mortes (about 2meters deposits).

36. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! riverobserved geomorphic impacts foto C simulation results fig 6. longitudinal profile of river Ha! Ha!. fig 9. photo C: bank erosion and channel widening at a convex reach.

37. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! riverobserved geomorphic impacts chute á Perron simulation results fig 6. longitudinal profile of river Ha! Ha!. fig 10. chute á Perron: massive erosion as the flow evaded its normal fixed bed course (from Brooks & Lawrence 1999)

38. Ha! Ha! Bay Chute á Baptiste cross-sections detailed in figure Eaux-mortes Chute á Perron Boilleau “Cut-away” dyke Lake Ha! Ha! a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! rivercomputational domain fig 11. computational domain: discretization of river Ha! Ha! between the lake and Ha! Ha! bay.original data converted to a DTM by Benoit Spinewine ( UCL) and Hervé Capart (Taiwan University). simulation results

39. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! rivercomputational domain fig 12. idealized trapezoidal sections used for computational purposes (computed from an algorithm operating over the DTM data). simulation results

40. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! rivercomputational domain simulation results fig 13. bed width (top) and inverse bank slope (bottom) for computational purposes.

41. S = 0 S < Scrit Lups Ldwn L 1 2 3 ... ... N1 N NS1 NS NF1 NF 1 2 a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! rivercomputational domain simulation results fig 14. extended computational domain featuring two virtual reaches at the upstream and downstream ends for computational purposes.

42. b) a) t t x x t1 t1 (+) (Q,t) = 0 t (Q,A;S,…) = 0 t () t0 t0 xN x xN-1 0 x x1 dx dx a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! rivercomputational domain simulation results fig 15. stencil of the characteristics at the upstream and downstream reaches. boundary conditions at the virtual reaches function in the subcritical regime. the actual dam location is a critical flow point.

43. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! rivernumerical solution simulation results fig 16. step discontinuity at critical flow points in steady flow. TVD algorithm is unable to fix the problem. artificial viscosity of the Von Neuman type is used to correct the problem.

44. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! riverresults of the numerical simulation evolution of the bed elevation variation. simulation results evolution of the Froude number.

45. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! riverresults of the numerical simulation critical flow t = t0 subcritical flow geomorphic hydraulic jump subcritical flow supercritical flow t = t1 > t2 critical flow subcritical flow geomorphic hydraulic jump supercritical flow simulation results t = t2 > t1 fig 17. model for the evolution and disappearing of supercritical reaches, associated to pronounced convex bed profiles, as the bed morphology evolves. geomorphic discontinuity subcritical flow

46. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! riverresults of the numerical simulation evolution of the water depth. simulation results evolution of the bed width.

47. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! riverresults of the numerical simulation longitudinal profile: reaches downstream the eroded dyke. longitudinal profile: “Chute á Baptiste” (fixed bed). simulation results

48. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! riverresults of the numerical simulation simulation results longitudinal profile: “Chute á Perron”.

49. a boundary/initial value problem simulation of the 1996 flood in the Ha! Ha! riverresults of the numerical simulation simulation results fig 18. final bed profiles at “Chute á Perron”. initial bed; field data expressing the final bed profile. Results of scenario HaHaF03 (Ks = 24 m1/3s-1 and ac = 0.0019 s2m-1) are: t = 26 h ( ), t = 32 h ( ), t = 40 h ( ), t = 67.5 h ( ). stands for the results of NTU (Taiwan). stands for the results of the model of Cemagref. Results from Cemagref and NTU taken form Zech et al. (2004).

50. contributions of the present work: a mathematical model for the simulation and analysis of floods featuring intense sediment transport and important morphologic impacts was developed; the model was validated with the data of the 1996 flood in the river Ha! Ha!; although the modelling exercise is of great difficulty, the scales of the phenomena were well reproduced. quantitatively, erosion was not as well reproduced as aggradation; conclusions numerical problems arise in the steady state computations for the initial condition. artificial viscosity proved a better solution than a TVD correction.