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Modélisation de la formation et de l'évolution à long terme des barres sableuses. Mécanismes physiques.

School of Civil Engineering. Modélisation de la formation et de l'évolution à long terme des barres sableuses. Mécanismes physiques. Roland GARNIER et Nick DODD. Séminaire MAMNO, Bordeaux, 11/03/2007. Introduction The Nearshore Zone. Shore. Offshore. Nearshore. Surf. Shoaling. Swash.

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Modélisation de la formation et de l'évolution à long terme des barres sableuses. Mécanismes physiques.

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  1. School of Civil Engineering Modélisation de la formation et de l'évolution à long terme des barres sableuses.Mécanismes physiques. Roland GARNIER et Nick DODD Séminaire MAMNO, Bordeaux, 11/03/2007

  2. IntroductionThe Nearshore Zone Shore Offshore Nearshore Surf Shoaling Swash Shoreline Shoaling Nearshore Surf Swash Offshore Shore

  3. Introduction Open Beaches Longshore Bar Planar Beach Barred Beach • The surf zone of open/large beaches:2 kinds of beach profile • 2D beach configuration: alongshore uniformity • 3D beach configuration: alongshore non-uniformity • Sometimes very chaotic behaviours • But sometimes well organized patterns: Rhythmic Bars

  4. IntroductionTransverse / Oblique Bar Systems l=30 m • Beach Cusps (Biscarosse, France) Bars (Surf Zone) or Cusps (Swash Zone) ?

  5. IntroductionTransverse / Oblique Bar Systems l = 50 m Ambient Current • Up-Current Oblique Bars (Noordwijk, The Netherlands) Ribas and Kroon, J. Geophys. Res., 2007 Argus Images:Surf Zone Patterns

  6. IntroductionCrescentic Bar Systems l=400 m • Crescentic Bars (Duck Beach, USA)

  7. IntroductionLarge Scale Oblique Bar Systems l=400 m • Large Scale (Down-Current) Oblique Bars (SW, France) i.e. `Barres / Baïnes´ www.geoportail.fr Waves

  8. IntroductionHypothesis: Self Organization Mechanism Self-organized behaviour: Morphology result of interaction between hydrodynamics and morphodynamics Complex & Unexpected response of the system External Forcing Waves Forced behaviour: Morphology result of offshore forcing Wave Breaking Currents Sediment Transport Bed Evolution

  9. IntroductionObjectives • Objectives: 1) Modelling / Understanding the emergence of rhythmic features • Transverse / Oblique Bars • Crescentic Bars 2) Modelling / Understanding their long term behaviours • Saturation Mechanisms • Equilibrium • Tool:The MORFO55 Model (2DH processed based model)

  10. The MORFO55 ModelPresentation • 2DH processed based model for the surf zone • Wave- and depth- averaged nonlinear shallow water equations • 6 PDF coupled equations: • water mass • momentum (2) • sediment conservation • wave energy • wave phase • 6 wave-averaged unknowns: • zs(x,y,t): sea level • vi(x,y,t): horizontal velocity (2 components) • zb(x,y,t): bed level • Hrms(x,y,t): wave height • q(x,y,t): wave angle • Background: • MORFO50: Caballeria et al., 2002, J. Fluid Mech. • Formation of transverse and crescentic bars • MORFO55: Garnier et al., 2006, J. Fluid Mech. • Long term behaviour of transverse bars

  11. The MORFO55 ModelGoverning Equations • Hydrodynamics • Mass • Momentum (2) • Wave Energy • Wave Phase

  12. The MORFO55 ModelGoverning Equations Experimentally proved Infragravity waves, Wave bores • Morphodynamics • Sediment conservation sediment transport : stirring factor current bedslope h: bottom perturbation g: parameter u0: orbital velocity

  13. Experiments • Initial topography: Yu & Slinn, 2003, J. Geophys Res. PB: Planar Beach BB: Barred Beach • Sediment transport: SVR or CWS • Incidence of waves: normal (q=0) or oblique (q>0) • 5 illustrative experiments

  14. Basic StatesHydrodynamics PB BB Barred Beach Planar Beach q=20º q=5º

  15. Basic StatesPotential Stirring PB BB Barred Beach Planar Beach Potential Stirring a/D=C Depth Averaged Concentration SVR SVR CWS

  16. Growth Mechanisms The Bottom Evolution Equation (BEE) • The Bottom Evolution Equation (BEE) • Water Conservation • Sediment Conservation Hypothesis BEE Potential StirringDepth Averaged Concentration INSTABILITY DIFFUSION

  17. Growth MechanismsInstability Conditions Potential StirringDepth Averaged Concentration BEE • accretion condition: • erosion condition: • Instability conditions: accretion on shoal erosion in trough

  18. Transverse BarsGrowth Mechanisms C • Normal Waves: BEE x • Planar Beach • Sediment Transport: SVR

  19. Transverse BarsGrowth Mechanisms shoal trough C • Normal Waves: BEE x • Planar Beach • Sediment Transport: SVR

  20. Transverse BarsGrowth Mechanisms shoal trough C • Normal Waves: BEE x • Planar Beach • Sediment Transport: SVR • Instability if

  21. Transverse BarsGrowth Mechanisms C • Normal Waves: BEE x • Planar Beach • Sediment Transport: SVR • Instability if • Hydrodynamical Response • Difference in Setup • Focus of Energy

  22. Transverse BarsGrowth Mechanisms C • Normal Waves: BEE x • Planar Beach • Sediment Transport: SVR • Instability if • Hydrodynamical Response • Difference in Setup • Focus of Energy BEDSURF MECHANISM

  23. Transverse BarsGrowth Mechanisms C • Normal Waves: BEE x • Planar Beach • Sediment Transport: SVR • Instability if • Hydrodynamical Response • Difference in Setup • Focus of Energy • Circulation Cells

  24. Transverse BarsGrowth Mechanisms C • Normal Waves: BEE x • Planar Beach • Sediment Transport: SVR • Instability if • Hydrodynamical Response BEDSURF MECHANISM Positive Feedback Instabilities can grow

  25. Transverse BarsGrowth Mechanisms C • Normal Waves: BEE x • Planar Beach • Sediment Transport: SVR • Instability if • Hydrodynamical Response BEDSURF MECHANISM Positive Feedback Instabilities can grow • Emergence of off-shore patterns

  26. Transverse BarsModelling

  27. Transverse BarsModelling Vmax = 0.4 m/s

  28. Transverse BarsModelling t = 10 hrs

  29. Oblique Down-Current BarsModelling

  30. Oblique Down-Current BarsModelling Vmax = 1 m/s

  31. Crescentic Bars Growth Mechanisms C • Normal Waves: BEE x • Barred Beach • Sediment Transport: SVR

  32. Crescentic Bars Growth Mechanisms C • Normal Waves: BEE x • Barred Beach • Sediment Transport: SVR • Instability if • Hydrodynamical Response BEDSURF MECHANISM Positive Feedback Instabilities can grow • Emergence of off-shore patterns

  33. Crescentic BarsNormal wave incidence

  34. Crescentic BarsNormal wave incidence Vmax = 0.3 m/s

  35. Crescentic BarsOblique wave incidence

  36. Crescentic BarsOblique wave incidence Vmax = 0.4 m/s

  37. Crescentic BarsOblique wave incidence t1 t2 • l1 = 200 m t = 5 day • l2 = 250 - 300 m • cm = 20 m/day

  38. Oblique Up-Current BarsGrowth Mechanisms: Transverse Bars and CWS ? shoal trough C • Normal Waves: BEE x • Planar Beach • Sediment Transport: CWS

  39. Oblique Up-Current BarsGrowth Mechanisms: Transverse Bars and CWS ? C • Normal Waves: BEE x • Planar Beach • Sediment Transport: CWS • Instability if • Hydrodynamical Response BEDSURF MECHANISM Negative Feedback Instabilities can not grow

  40. Oblique Up-Current BarsGrowth Mechanisms • Oblique Waves: BEE Growth Migration

  41. Oblique Up-Current BarsGrowth Mechanisms shoal trough C • Oblique Waves: BEE x • Planar Beach • Sediment Transport: CWS

  42. Oblique Up-Current BarsGrowth Mechanisms shoal trough C • Oblique Waves: BEE x • Planar Beach • Sediment Transport: CWS • Instability if

  43. Oblique Up-Current BarsGrowth Mechanisms C • Oblique Waves: BEE x • Planar Beach • Sediment Transport: CWS • Instability if • Hydrodynamical Response • BEDSURF MECHANISM NEGATIVE FEEDBACK

  44. Oblique Up-Current BarsGrowth Mechanisms C • Oblique Waves: BEE x • Planar Beach • Sediment Transport: CWS • Instability if • Hydrodynamical Response • BEDSURF MECHANISM NEGATIVE FEEDBACK

  45. Oblique Up-Current BarsGrowth Mechanisms C • Oblique Waves: BEE x • Planar Beach • Sediment Transport: CWS • Instability if • Hydrodynamical Response • BEDSURF MECHANISM NEGATIVE FEEDBACK • BEDFLOW MECHANISM:Deflection of the longshore current

  46. Oblique Up-Current BarsGrowth Mechanisms C • Oblique Waves: BEE x • Planar Beach • Sediment Transport: CWS • Instability if • Hydrodynamical Response • BEDSURF MECHANISM NEGATIVE FEEDBACK • BEDFLOW MECHANISM:Deflection of the longshore current POSITIVE FEEDBACK BEDFLOW > BEDSURF

  47. Oblique Up-Current BarsModelling

  48. Oblique Up-Current BarsModelling • l1 = 50 m t1 = 1 day • l2 = 70 m t2 = 2 day

  49. Saturation MechanismsLocal vs Global Analysis Local Analysis (Analysis “point by point”) • Explains the emergence of bars • Can not easily explain the saturation of their growth: • Still predict erosion/accretion (eg. if bars migrate) • Migration and growth/decay are mixed Global Analysis (Analysis on the whole domain) • Need to define integrated variables (eg. a measure of the amplitude of bars)

  50. Saturation MechanismsGlobal Analysis h bottom perturbation • Water Conservation • Sediment Conservation C depth-averaged concentration • Approximations G diffusivity INSTABILITY DIFFUSION

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