PTYS 554
Evolution of Planetary Surfaces
Aeolian Processes I
PYTS 554 – Aeolian Processes I
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Aeolian Processes I
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Entrainment of particles – settling timescales
Threshold friction speeds
Suspension vs. saltation vs. reptation vs. creep
Dependences on gravity, densities of particle/air
Aeolian Processes II
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Migration rates
Dune types
Dunefield pattern formation
Ripples vs. dunes
Ventifact, yardang erosion
Dust-devils and wind streaks
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PYTS 554 – Aeolian Processes I
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Suspension vs saltation
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PYTS 554 – Aeolian Processes I
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Suspension
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s inertial
ra v 2
Re =
=
s viscous h (v d )
All particles eventually settle out of a quiescent atmosphere
Reynolds number quantifies whether an atmosphere is quiescent
 Re > 10s means turbulent flow (viscosity doesn’t damp eddies)
 High velocity flows are more turbulent
 Low viscosity fluids are more turbulent
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Consider laminar flow around a falling sphere
Drag from sphere affects air within a cylinder ~2d wide
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Downward force from weight – buoyancy
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Fdown =

p
6
d 3 ( rs - ra ) g
Fup = 3pd h(v d)
2
Equating the two gives the terminal velocity
1 d ( rs - ra ) g
18
h
2
v settle =

ra v d
h
3d
Upward force from viscous drag
 Stress ~ viscosity x strain rate
 Area affected is curved wall of cylinder
 …and ignoring some numerical factors

Re =
Stokes’ law
ra
d
d
rs
v
PYTS 554 – Aeolian Processes I
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Low pressure
Turbulent flow

As before downward force from weight – buoyancy
Fdown =

p
6
d 3 ( rs - ra ) g
Falling particle is opposed by ram pressure
Fup =

5
p
4
d 2 ra v 2
Equating these to find the settling velocity – not very
sensitive to particle size
v settle
2 æ rs - ra ö
=
ç
÷gd
3 è ra ø
d
rs
High pressure
v
ra
PYTS 554 – Aeolian Processes I
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Turbulent eddies have speeds ~0.2 the mean windspeed
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For suspension: v settle £ 15 u
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For dust sized particles: Mars, Venus and Titan are effective at suspending particles
…but Venus (and Titan?) probably doesn’t have high near-surface winds
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PYTS 554 – Aeolian Processes I
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In a planetary boundary layer
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Drag of wind on surface produces a shear stress
Measured with drag plates
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We define a ‘shear velocity’ u*
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 Just another way to quantify the shear stress
u* =
t = ra u 2
t
ra
¶u
t =h
¶z
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For a Newtonian fluid (like air):
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In a thin laminar sub-layer η is constant and a property of the fluid (and temperature)
u=
t
z
h
u z
µ
u* d

where d » 5 h
rau*
Above this layer, turbulence dominates, η is a property of the flow and varies with height and u
 Empirically – law of the wall… (κ is Von Karman’s constant ~ 0.41)
æzö
u 1
= k lnç ÷
u*
è zo ø
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PYTS 554 – Aeolian Processes I
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Z0 is the equivalent roughness height
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1/30th of the grain size for quiescent
situations
Otherwise it’s empirically determined from
several wind measurements at different
heights
Greeley, 1985
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PYTS 554 – Aeolian Processes I
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Two regimes
æzö
u 1
= k lnç ÷
u*
è zo ø
Transition at: D ~ 0.7 δ
Neither approach works well in the transition zone
uµ
z
d
where d ~ 5 h
rau*
Anderson and Anderson 2010
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Small particles hide within the laminar zone, larger particles stick up into the turbulent zone
Balance shear stresses with weight – buoyancy of particles
Fdown =

p
6
d 3 ( rs - ra ) g
Fdrag =
p
4
d 2 ra u*2
At the threshold velocity, some component of drag force balances the particle weight
æ r - ra ö
u*T = A ç s
÷gd
r
è
ø
a
or
t T = A2 éë( rs - ra ) gd ùû
A2 often called θ
A~0.1
PYTS 554 – Aeolian Processes I
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More detailed, gets you within a factor of 2 of deriving A
t T = A éë( rs - ra ) gd ùû
2
Anderson and Anderson 2010
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PYTS 554 – Aeolian Processes I
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Define the frictional Reynolds number
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A varies with this value
-n
A µRe*
Re* =
11
ra u* d
h
where n >>>1
æ r - ra ö
u*T = A ç s
÷gd
r
è
ø
a
Recall:
A
Turbulent zone:
A @ 0.1
~3.5
Small particles
in laminar zone
Laminar zone:
Re*
u*T µ d
-n
u*T µ d
uT
u*T µ d
-1
2
u*T µ ( u*T d ) d
u*T µ d
Large particles in
turbulent zone
1
1
2
1 2-n
n+1
-1
for big n
u*T µ d
?
d
1
2
PYTS 554 – Aeolian Processes I
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‘A’ should be constant in the fully-turbulent case
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Instead is depends on the fluid/particle density ratio
A cautionary tale in using ‘dimensionless’ scaling from one planet to another…
Basalt on
Venus
Quartz
in
water
Ice on Titan
Quartz
on
Earth
Iversen et al.1987
Basalt
on Mars
PYTS 554 – Aeolian Processes I
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Minimum exists when Re ~ 3.5
Re* =
uT
uT µ d
-1
uT µ d
1
2
æ rs - ra ö
u*T = A ç
÷gd
è ra ø
u* = u*T
?
d
ra u* d
h
3.5 =
& d = dmin at Re = 3.5
æ r - ra ö
ra dmin
A ç s
÷ gdmin
h
è ra ø
2
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Easiest particles to move depends on
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1
æ 3.5 ö 3
dmin = ç ÷ éëh 2 ( r s - ra ) ra gùû 3
è Aø
~225 microns for Earth
Atm. viscosity
Atm. density
Particle weight (density and gravity)
Buoyancy effects minor (until we get to the fluvial processes lectures)
PYTS 554 – Aeolian Processes I
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Saltation threshold increases with particle size
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Particles classified by Udden-Wentworth scale
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D  2 m m
Easiest particles to move
are sand-sized
Dust
Sand-sized
0.1 mm
1mm
Gravel
1cm
Greeley, 1985
PYTS 554 – Aeolian Processes I
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Necessary wind speed depends on atmospheric density
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PYTS 554 – Aeolian Processes I
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Easy to move but not easy to suspend
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Particles are launched off the surface, but re-impact a short time later – saltation!
Greeley, 1985
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PYTS 554 – Aeolian Processes I
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Grains travel by saltation
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Impacting grains can dislodge new particles (reptation)
Impacting grains can push larger particles (creep)
Impacting grains knock finer particles into suspension
Impact vs fluid threshold
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It’s easier to keep saltation going than start it
Impact threshold is ~0.8 times the fluid threshold for
Earth
…but ~0.1 times the fluid threshold for Mars
 This is what makes martian saltation possible
Kok, 2010
Kansas State University
PYTS 554 – Aeolian Processes I
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Saltation length scales ~cm
Greeley, 1985
PYTS 554 – Aeolian Processes I
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Bagnold’s description of momentum loss
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Mass flux per unit length – q
Momentum change of grains mass x (u2-u1) over a distance L, with u2>>u1
Stress is:
t =q u -u L »qu L
(
2
1)
Avg. horizontal velocity ~ 0.5 u2
Time of flight is 2w 1/g
L = u2 w1/g
w1
v2
so: u2/L = g/w1
t » q g w1
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
L
Stress is also t = ra u*
And w1 ~ u* (ignoring factors ~1)
2
r a u* 2 » q g w1
ra 3
q»
q»
g
ra
g
u*
u* 3 C d do
u1
2
v1
Sand flux per unit length is
proportional to shear velocity cubed
Bagnold’s experimental work showed
particle size is also a factor
v1
PYTS 554 – Aeolian Processes I
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There are many variations fit to empirical data
Greeley, 1985
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PYTS 554 – Aeolian Processes I
Titan
95%
Dune Potential
(All else being equal)
Zero
Zero
Venus
Zero
5% methane
Density Kg m-3
71.92
1.27
0.027
5.3
Gravity (m s-2)
8.9
9.8
3.7
1.35
Dune material
Basalt
Quartz
Basalt
Organics
(lower
density)
Titan
Earth
Mars
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PYTS 554 – Aeolian Processes I
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As usual – all else is not equal
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Venus has very few dunes (two fields known)
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Lack of weathering into small particles
Detectability of dunes ?
Low surface winds
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Dune Potential
(All else being equal)
Venus
Titan
Earth
Fortuna-Meshkenet field
Weitz et al. 1994
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Mars has extensive dunefields
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Very high wind speeds
Lots of active weathering breaking up rocks
Mars
PYTS 554 – Aeolian Processes I

Aeolian Processes I





Entrainment of particles – settling timescales
Threshold friction speeds
Suspension vs. saltation vs. reptation vs. creep
Dependences on gravity, densities of particle/air
Aeolian Processes II






Migration rates
Dune types
Dunefield pattern formation
Ripples vs. dunes
Ventifact, yardang erosion
Dust-devils and wind streaks
23