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
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

Suspension: particles suspended in the air
Launced from bed, arching trajectories, splash into bed

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 0.1- 0.3 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
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 (http://www.earthds.info/pdfs/EDS_16.PDF)
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., Ann. Review of Fluid Mech., 2013
7
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:
Aqueous dunes:



Migration speed:
cd ~ 20cm/10min = 3.10-4 m/s
Uchar = 0.4 m/s,  = 1.004.10-6,
D=0.002
Particle Rep = ~ 800

Re p 
Aeolian dunes:



UD p

Migration speed:
cd ~ 25m/year = 8.10-7 m/s
Uchar = 8 m/s,  = 15.68.10-6,
D=0.002
Particle Rep ~ 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
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: t0 ~ U2
Adapted from Raudkivi, 1990
11
Bedforms: shifting bodies under shear

Bedforms – shear stress determines type:


Skin friction: flat bed
(boundary roughness)
Form drag: developing
bedforms
Skin friction: t0 ~ U2
Adapted from Raudkivi, 1990
12
6
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, 1967
13
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
Bedforms: flow regimes (2)
Upper flow regime:
Fr > Frc &
supercritical
Lower flow
regime:
Fr < Frc &
subcritical
Flow depth: 0.25 – 0.4 m
Boguchwal & Southard, 1990, adapted by Ashley, 1990
15
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: 0.005 m < h < 0.05 m
Form index: L/h = 8 - 15
 Ripples scale with grain size!
k =3D
s
100 ks
Note: no ripples for D
> 0.7 mm  outside
viscous sublayer
16
8
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: 0.075 m < h < 5 m ~ h/3 – h/6
Form index: L/h = 15 – 25
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, 1988
18
9
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
Star dunes
Reversing dunes
Complex wind regime,
variable sand supply:
Linear dunes
From: McKee, A study of global sand seas, 1979
20
10
Large-scale features: sand dunes

Dune morphology depends on:



Dimensions scale with particle size and wind speeds


Amount of available sand
Wind variability
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:




Granule ripples in aeolian systems:



Ripple index: 15 – 20
L = 13-300 mm, H = 0.6-14mm
Fast propagation: ~ 1 cm/minute

Ripple index: 15 – 20
L = 0.5 – 6.0 m, H = 0.1 – 0.6 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, 1994
22
11
Correlation between wavelength & height
G.M. Ashley, 1990, after data by Lancaster, 1988
23
12