Transcript PYTS 554 – Aeolian Processes I
PTYS 554 Evolution of Planetary Surfaces
Aeolian Processes I
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
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Suspension vs saltation PYTS 554 – Aeolian Processes I
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PYTS 554 – Aeolian Processes I
Suspension
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
Consider laminar flow around a falling sphere Drag from sphere affects air within a cylinder ~2d wide
Downward force from weight – buoyancy
F down
= p 6
d
3 ( r
s
r
a
)
g
Upward force from viscous drag
Stress ~ viscosity x strain rate Area affected is curved wall of cylinder …and ignoring some numerical factors
F up
= 3 p
d
2 h ( )
Equating the two gives the terminal velocity
v settle
= 1 18
d
2 ( r
s
h r
a
)
g
Stokes
’
law
r
a
3d d
r
s
Re = Re = s
inertial
s
viscous
r
a v d
h = h r
a v
2 ( )
v d
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PYTS 554 – Aeolian Processes I
Turbulent flow
As before downward force from weight – buoyancy
F down
= p 6
d
3 ( r
s
r
a
)
g
Falling particle is opposed by ram pressure
F up
= p 4
d
2 r
a v
2
Equating these to find the settling velocity – not very sensitive to particle size
v settle
= 2 3 æ è r
s
r
a
r
a
ö ø
gd
Low pressure d
r
s
High pressure
r
a
v
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PYTS 554 – Aeolian Processes I
Turbulent eddies have speeds ~0.2 the mean windspeed For suspension:
v settle
£ 1 5
u
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
In a planetary boundary layer
Drag of wind on surface produces a shear stress Measured with drag plates
t
We define a
‘
shear velocity
’
u * Just another way to quantify the shear stress
u
* = t r
a
= r
a
u
2
For a Newtonian fluid (like air):
t = h ¶
u z
In a thin laminar sub layer η is constant and a property of the fluid (and temperature)
u
= t h
z u u
* µ
z
d
where
d » 5 h r
a
u
*
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)
u u
* = 1 k ln æ è
z z
o
ö ø 7
PYTS 554 – Aeolian Processes I
Z 0 is the equivalent roughness height
1/30 th of the grain size for quiescent situations Otherwise it heights ’s empirically determined from several wind measurements at different
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Greeley, 1985
PYTS 554 – Aeolian Processes I
Two regimes
u u
* = 1 k ln æ è
z z
o
ö ø
Transition at: D ~ 0.7 δ
u
µ
z
d
where
d ~ 5 h r
a
u
*
Anderson and Anderson 2010 Small particles hide within the laminar zone, larger particles stick up into the turbulent zone Balance shear stresses with weight – buoyancy of particles
F down
= p 6
d
3 ( r
s
r
a
)
g F drag
= p 4
d
2 r
a u
* 2
At the threshold velocity, some component of drag force balances the particle weight
u
*
T
=
A
æ è r
s
r
a
r
a
ø
or
t
T
=
A
2 éë ( r
s
r
a
)
gd
ùû
A 2 often called θ A~0.1
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PYTS 554 – Aeolian Processes I
More detailed, gets you within a factor of 2 of deriving A
t
T
=
A
2 éë ( r
s
r
a
)
gd
ùû 10
Anderson and Anderson 2010
PYTS 554 – Aeolian Processes I
Define the frictional Reynolds number
A varies with this value
Re * = r
a u
* h
d A
µ Re * -
n
where n >>>1 Recall:
u
*
T
=
A
æ è r
s
r
a
r
a
ö ø
gd
A
A
@ 0.1
u
*
T
µ
d
1 2
~3.5
Small particles in laminar zone Re * Large particles in turbulent zone Laminar zone:
u
*
T
µ (
u
*
T d
) -
n d
1 2
u
*
T
µ
d
1 2 -
n n
+ 1
u
*
T
µ
d
1
for big n
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u T
u
*
T
µ
d
1
?
u
*
T
µ
d
1 2
d
PYTS 554 – Aeolian Processes I
‘A’ should be constant in the fully-turbulent case
Instead is depends on the fluid/particle density ratio A cautionary tale in using ‘dimensionless’ scaling from one planet to another…
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Quartz in water Basalt on Venus Ice on Titan Quartz on Earth Basalt on Mars Iversen et al.1987
PYTS 554 – Aeolian Processes I
Minimum exists when Re ~ 3.5
Re * = r
a u
* h
d u
*
T
=
A
æ è r
s
r
a
r
a
ö ø
gd
u T
u T
µ
d
1
u T
µ
d
1 2
?
u
* =
u
*
T
&
d
=
d
min
at
Re = 3.5
d
3.5
= r
a d
min h
A
è r
s
r
a
r
a
ö ø
gd
min
d
min = æ è 3.5
A
ö ø 2 3 éë h 2 ( r
s
r
a
) r
a g
~225 microns for Earth
ùû 1 3
Easiest particles to move depends on
Atm. viscosity Atm. density Particle weight (density and gravity)
Buoyancy effects minor (until we get to the fluvial processes lectures)
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PYTS 554 – Aeolian Processes I
Saltation threshold increases with particle size Particles classified by Udden-Wentworth scale
D
2
mm
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Easiest particles to move are sand-sized
Dust Sand-sized Gravel 0.1 mm 1mm 1cm Greeley, 1985
PYTS 554 – Aeolian Processes I
Necessary wind speed depends on atmospheric density
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PYTS 554 – Aeolian Processes I
Easy to move but not easy to suspend
Particles are launched off the surface, but re-impact a short time later – saltation!
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Greeley, 1985
PYTS 554 – Aeolian Processes I
Grains travel by saltation
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
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
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Kok, 2010 Kansas State University
Saltation length scales ~cm PYTS 554 – Aeolian Processes I
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Greeley, 1985
PYTS 554 – Aeolian Processes I
Bagnold
’
s description of momentum loss
Mass flux per unit length – q
Momentum change of grains mass x (u 2 -u 1 ) over a distance L, with u 2 >>u 1 Stress is:
t = ( 2 -
u
1 )
L
»
q u
2
L
Avg. horizontal velocity ~ 0.5 u 2 Time of flight is 2w 1 /g L = u 2 w 1 /g so: u 2 1 v 1
t »
q g w
1
L
Stress is also And w 1
t = r
~ u *
a
u
* 2 r
a
u
* 2
q
» r
a
»
g q g w
1
u
* 3
Sand flux per unit length is proportional to shear velocity cubed w 1 v 2
q
» r
a
u
* 3
C d d
o
g
Bagnold
’
s experimental work showed particle size is also a factor v 1 u 1
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PYTS 554 – Aeolian Processes I
There are many variations fit to empirical data
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Greeley, 1985
PYTS 554 – Aeolian Processes I
Density Kg m
-3
Gravity (m s
-2
) Dune material 71.92
8.9
Basalt 1.27
9.8
Quartz 0.027
3.7
Basalt
Titan
95% Zero Zero Zero 5% methane
5.3
1.35
Organics (lower density)
Dune Potential (All else being equal)
Venus Titan Earth Mars
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PYTS 554 – Aeolian Processes I
As usual – all else is not equal
Venus has very few dunes (two fields known)
Lack of weathering into small particles Detectability of dunes ? Low surface winds
Dune Potential (All else being equal)
Venus
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Fortuna-Meshkenet field Weitz et al. 1994
Titan Earth Mars
Mars has extensive dunefields
Very high wind speeds Lots of active weathering breaking up rocks
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
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