Granular Flows
1
Lecture 8: Geomorphology

Comparing a sand dune to a sand pile
-- what are the effects of scale?

Geomorpology: study of landforms

Aeolian processes: sand dunes




Hillslope processes: avalanches & rock slides


Micro, meso & macroscale: from grain to dune
Singing & booming sand dunes
Quicksand & sandcastles
Erosion and deposition
Not in this lecture: fluvial, glacial, tectonic & volcanic processes
2
Aeolian processes – booming sand dunes
From: National Geographic, Death Valley DVD, 2009
3
Micro- versus macroscale?

Processes:



Micro: creep, saltation, suspension
Meso: avalanches, ripples, separation
Macro: dune building, migration
4
Aeolian sand transport

Forces due to the wind:

Aerodynamic forces:






drag force (due to Newton’s turbulent drag):
lift force (due to pressure difference):
ratio on Earth: c = 0.85
Gravitational forces (grain’s weight):
Momentum balance:
Shield’s number: tangential force - resisting grain movement




fluid shear stress ta
reduced density in air ’
packing of grains  internal angle of friction: 
shape and sorting of grains 
From: Wind-blown sand, by H.J. Herrmann
5
Micro processes (1)

Saltation trajectories & speed:



Ballistic paths for grains 0.1- 0.3 mm
Chain reaction: multiple particles
Wind speed:

fluid threshold: initiate saltation
 lifting & splashing

impact threshold: halt saltation
 stops saltation
Threshold wind speed:
 V ~ 1.5 m/s for 0.1 mm particles

From: R.A. Bagnold, The Geographical Journal, 1937
6
Micro processes (2)

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)
7
Meso processes (1) – sand flux

Sand flux q depends on:



Shear velocity u & threshold ut
Grain diameter d, density, etc
Scaling of sand flux q:

Behavior in steady-state (saturated):



far away from fluid threshold: cubic (Bagnold):
close to threshold: not well understood
Unsteady behavior: numerical simulations

saturation flux qs, saturation length scale ls
From: Wind-blown sand, by H.J. Herrmann
8
Meso processes (2) – small-scale features

Sand ripple formation: bedform by surface roughness


Unevenness (random or saltation-induced) perpetuates
Creation of saltation shadow  creation of ripple




fast propagation (~ 1 cm/minute),
wavelength: ~ 10 – 20 cm
height: ~ 1 cm
Granule ripple formation: miniature barchanoid ridges

Creation of jams of coarser grains via surface creep



slow growth and propagation speed,
 exist for decades
wavelength: ~ 2 – 6 m
height: ~ 12.5 – 60 cm
From: R.P. Sharp, Journal of Geology, 1963 & A.J. Parsons, 1994
9
Macro processes (1)

Formation, evolution & migration of dunes:

Coupled (iterative) set of equations between:




shear stress: from perturbations across a hill h(x,y)
sand flux: from the shear velocity & shear stress
height of the dune: from the sand flux

If a dune moves shape-invariantly (h(x,y) = c):




migration velocity vd is inversely related to height h
large dunes move slowly
small dunes move fast
minimum size dune: ~ 1.5 m
 due to competition between saturation length and separation bubble
From: Wind-blown sand, by H.J. Herrmann
10
Macro processes (2)

Migration velocity and height:

Connection between aeolian and aquaous dune formation?
Bedforms
on aeolian
barchan
dunes
Aeolian barchan dunes
Aqueous
barchan
dunes
From: Charru et al., Ann. Review of Fluid Mech., 2013
11
Macro processes (3)

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
12
Macro processes (4)

Entire systems of barchan dunes:

Small barchan dune catches up with a large one:
Swallowing
Breeding
Increasing
height
small dune
Budding
Solitary
behavior
From: O. Duran et al., Phys. Rev E Stat Nonlin Soft Matter Phys, 2005
13
Macro processes (5) – aeolian vs aqueous

Comparison migration & Re-number: Re p 
Aeolian dunes:



Migration speed:
cd ~ 25m/year = 8.10-7 m/s
Uchar = 8 m/s,  = 15.68.10-6,
D=0.002
Particle Rep ~ 1000

UDp

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
2D aqueous dune
migration in a slit
14
Applications – aqueous dunes

Initial conditions:

Observed:



Ripple formation
Slipface creation & migration
Bifurcation: splitting and merging dunes

Small dune catches up, or runs away
15
Applications – dune migration (1)

Ground penetrating radar:

Antenna: electromagnetic waves



traverse entire dune in small steps
Change in electrical conductivity
Analysis of reflected waves
16
Applications– dune migration (2)
From: N.M. Vriend, M.L. Hunt, R.W. Clayton, GJI, 2012
17
Applications – booming sand dunes (1)

Music from the desert
An array of geophones:
wave propagation in
plane configuration
Microphone recording: Eureka
Dunes, Death Valley NP
18
Applications – booming sand dunes (2)

Source: shearing of grains in the avalanche

Constructive interference in a waveguide:



Amplification of sound
Setting the frequency
Frequency of sound:
nc1
fn 
, n  1,2,3,...
2
2 1/ 2
2 H (1  c1 / c2 )

for c0 = c2 and critical refraction
19
Applications - quicksand

Quicksand: sand, clay & salt water

Sensitive to small stress variations:




low stress: viscosity slowly changes
high stress: viscosity drops magnitudes
 liquid behavior  reduces friction
first liquefies, then collapses
Sinking mechanism:



trapping: liquefaction and sedimentation
 water and sand separates in fractions
 apparent viscosity increases
untrapping: add water to liquefy compacted sand
alternatively: low density humans prevents complete submersion!
From: Bonn et al., Nature, 2005
20
Applications – sand castles

Sandcastles: perfect composition?

Stiffness of sand:




dry: hardly supports own weight
wet: forms liquid bridges (ideal: 1%)
too wet: bridges form large liquid pockets
Stability of wet sand columns:



elastic buckling under own weight
critical height:
 column of R = 20 cm  hcrit = 2.5 m
increase height: compaction or density 
 use hydrophobic sand: water  air
From: Bonn et al., Nature, 2005, Moller & Bonn, EPL, 2007
21
Hillslope processes – avalanches (1)

Snow avalanches:

Erosion & deposition


Grain processes:



mass balance changes
segregation
levee formation
Velocity evolution:



start-up
steady-state
run-out
22
Hillslope processes – avalanches (2)
23
Hillslope processes – avalanches (3)
24