Aqueous and Aeolian Bedforms

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1 Aqueous and Aeolian Bedforms 1 Further reading & review articles R.A. Bagnold, 1941, The physics of blown sand and desert dunes Charru et al., 2013, Sand ripples and dunes, Ann. Review of Fluid Mech. 2 1

2 Transport mechanisms: sediment in air Correlation between air & water: Creep: in motion along the bed Rolling, sliding, quivering Movement is not continuous or uniform, brief gusts and pulses Saltation: grains hop in parabolic trajectories Launced from bed, arching trajectories, splash into bed Suspension: particles suspended in the air Fine windblown silt & dust: vertical velocity << settling velocity Sand: vertical velocity ~ settling velocity effect of turbulence 3 More on saltation Saltation trajectories & speed: Ballistic paths for grains mm Chain reaction: multiple particles First grains dislodge further grains Little viscous damping Fluid threshold Wind speed influences movement: Fluid threshold: get grains going starts lifting & splashing process Impact threshold: keeps grains going stops saltation process Threshold wind speed: V ~ 1.5 m/s for 0.1 mm particles From: R.A. Bagnold, The Geographical Journal, 1937 Impact threshold 4 2

, 1976, figure 1b 5 More on suspension Suspension trajectories & speed: Carried high by turbulence Suspended in air for grains <

3 Threshold speed: windtunnel experiments Shields diagram: Re* versus Shield s parameter: Empirical data: separates movement from non-movement From: Iversen et al., 1976, figure 1b 5 More on suspension Suspension trajectories & speed: Carried high by turbulence Suspended in air for grains < 0.06 mm Dust storms: soil erosion, moves great distances Dust storms: downdraft, moves laterally as a density current Elevations of 2500 m, speeds of 200 m/s From: NASA SeaWIFS Project ( 6 3

Bedform formation Aqueous and aeolian bedform formation: Connection: migration velocity and height Bedforms on aeolian barchan dunes Aqueous barchan dunes Aeolian barchan dunes From: Charru et al.

4 Bedform formation Aqueous and aeolian bedform formation: Connection: migration velocity and height Bedforms on aeolian barchan dunes Aqueous barchan dunes Aeolian barchan dunes From: Charru et al., Ann. Review of Fluid Mech., Comparing aeolian & aqueous systems Typical density differences influence mechanics Sand: 2.5x denser than water, over 2000x denser than air Saltation in air: grains bounce 100D 1000D above surface Grain impact & collisions assure saltation, maintains process Velocity of air is decreased due to loss momentum of particles Sand flux is affected by wind speed and size of grains Bedload in water: grains rise a few D above surface Shear stress effects of flow maintain bedload Velocity of water not affected, particles maintain momentum Sand flux depends on shape of the bed Following thesis of D. Cocks 8 4

Aeolian vs aqueous bedforms Comparison migration & Re-number: UDp Re p Aqueous dunes: Aeolian dunes:

4 m/s, = 1.004.10-6, U char = 8 m/s, = 15.68.10-6, D=0.002 D=0.

later on aeolian (air-driven) bedforms 9 Applications aqueous dunes 2D aqueous dune migration in a slit

5 Aeolian vs aqueous bedforms Comparison migration & Re-number: UDp Re p Aqueous dunes: Aeolian dunes: Migration speed: Migration speed: c d ~ 20cm/10min = m/s c d ~ 25m/year = m/s U char = 0.4 m/s, = , U char = 8 m/s, = , D=0.002 D=0.002 Particle Re p = ~ 800 Particle Re p ~ 1000 Let s first focus on aqueous (= water-driven) bedforms, later on aeolian (air-driven) bedforms 9 Applications aqueous dunes 2D aqueous dune migration in a slit Initial conditions: Observed: Ripple formation Slipface creation & migration Bifurcation: splitting and merging dunes Small dune catches up, or runs away 10 5

6 Bedforms: shifting bodies Deformable boundary under action of shear Stable: planar bed Unstable: undular bed Kelvin-Helmholtz instabilities due to density difference Drag: Form drag: exerted on bedforms, normal to bed surface no sediment transport, (no influence on grains) Skin drag: exerted on particle sediment transport Skin friction: t 0 ~ U 2 Adapted from Raudkivi, Bedforms: shifting bodies under shear Bedforms shear stress determines type: Skin friction: flat bed (boundary roughness) Form drag: developing bedforms Skin friction: t 0 ~ U 2 Adapted from Raudkivi,

7 Bedforms in aqueous environments Shifting bodies: type depends on flow regime Ripples: small, steep, wavelengths scales with D sediment size is smaller than viscous sublayer Dunes: larger, less steep, height limited by water depth Plane (flat) bed: dunes wash out, flat surface Antidunes: low water depth, near supercritical flow Oscillatory motion above sand bed: ripple formation Positive phase advance stress drag particles to crests Adapted from D.B. Simons, Bedforms: flow regimes Type of flow Froude number: Ratio of inertial to gravitational forces Fr < 1: subcritical, lower flow regime Water surface: out-of-phase with bedform or no disturbance Waves travel upstream, bedforms (ripples, dunes, sand waves): travel downstream with stoss-side erosion Fr > 1: supercritical, upper flow regime Water surface: in-phase with bedforms Waves can t travel upstream, bedforms (anti-dunes, chutes & pools): travel upstream with lee-side erosion Usually at higher flow velocity and lower depths 14 7

8 Bedforms: flow regimes (2) Upper flow regime: Fr > Fr c & supercritical Lower flow regime: Fr < Fr c & subcritical Flow depth: m Boguchwal & Southard, 1990, adapted by Ashley, Origin and dimensions of ripples High stress sweeps: pile of grains disturbance Separation zone of fully developed ripples: L/3 = 300 D Bedform wavelength: 0.05 m < L < 0.6 m ~ 1000D, Bedform height: m < h < 0.05 m Form index: L/h = 8-15 k s = 3 D Ripples scale with grain size! 100 k s Note: no ripples for D > 0.7 mm outside viscous sublayer 16 8

9 Origin and dimensions of dunes Growth and equilibrium height of a dune: Bedform wavelength: 0.6 m < L < 100 m ~ 2 p h Flow depth h Bedform height h Bedform height: m < h < 5 m ~ h/3 h/6 Form index: L/h = No dunes for sand with D < 0.15 mm Dunes scale with flow depth, not grain size! Ripples can coexist on the back of dunes: Equilibrium as large bedforms generate boundary layers Small bedforms are therefore locally stable 17 Correlation between wavelength & height G.M. Ashley, 1990, after data by Flemming,

Interplay between dunes and ripples Comparison between dunes and ripples: Geometry (ratios) and movement similar Free surface is not

instability Dunes: bedload + suspended load, long-wavelength instability Instability analysis [f(fr)] on governing equations: In

19 Bedform formation in aeolian systems Dune morphology depends on: Amount of available sand Wind variability Unidirectional winds,

10 Interplay between dunes and ripples Comparison between dunes and ripples: Geometry (ratios) and movement similar Free surface is not essential for existence (antidunes do) Dunes are much larger than ripples Other differences: Ripples: bedload, short-wavelength instability Dunes: bedload + suspended load, long-wavelength instability Instability analysis [f(fr)] on governing equations: In ripple-mode or dune-mode? In dune or antidune (forward/backward marching) region? 19 Bedform formation in aeolian systems Dune morphology depends on: Amount of available sand Wind variability Unidirectional winds, increasing sand supply: Barchan dunes Barchanoid ridge Transverse dunes Complex wind regime, variable sand supply: Linear dunes Star dunes Reversing dunes From: McKee, A study of global sand seas,

Large-scale features: sand dunes Dune morphology depends on: Amount of available sand Wind variability Dimensions scale with particle size and wind speeds Minimum size dune: ~ 1.

self-organization due to unstable flat surface Scale with particle size and wind speeds: Ripples in aeolian systems: Ripple index: 15 20 L = 13-300 mm, H = 0.

11 Large-scale features: sand dunes Dune morphology depends on: Amount of available sand Wind variability Dimensions scale with particle size and wind speeds Minimum size dune: ~ 1.5 m: Competition between saturation length and separation bubble Particle segregation: Coarser at troughs than crests natural selection by wind 21 Small-scale features: sand ripples Aeolian self-organization due to unstable flat surface Scale with particle size and wind speeds: Ripples in aeolian systems: Ripple index: L = mm, H = mm Fast propagation: ~ 1 cm/minute Granule ripples in aeolian systems: Ripple index: L = m, H = m Slow propagation: over decades Particle segregation: Coarser at crest than in troughs Sheltering & saltation shadow From: R.P. Sharp, Journal of Geology, 1963 & A.J. Parsons,

12 Correlation between wavelength & height G.M. Ashley, 1990, after data by Lancaster,

Sand transport over a barchan dune

Sand transport over a barchan dune F. Charru (1), V. Laval (1) 1. IMFT, Toulouse, France - corresponding author: francois.charru@imft.fr Abstract The present work investigates an important and yet unsolved