EART163 Planetary Surfaces Francis Nimmo. Last Week – Impact Cratering Why and how do impacts...
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Transcript of EART163 Planetary Surfaces Francis Nimmo. Last Week – Impact Cratering Why and how do impacts...
EART163 Planetary Surfaces
Francis Nimmo
Last Week – Impact Cratering• Why and how do impacts happen?
– Impact velocity, comets vs. asteroids
• Crater morphology– Simple,complex,peak-ring,multi-ring
• Cratering and ejecta mechanics– Contact, compression, excavation, relaxation
• Scaling of crater dimensions– Strength vs. gravity, melting
• Cratered landscapes– Saturation, modification, secondaries, chronology
• Planetary Effects
This week - Wind
• Sediment transport– Initiation of motion– Sinking (terminal velocity)– Motion of sand-grains
• Aeolian landforms and what they tell us• Guest lecture on Thurs – Dr Dave Rubin
• WARNING: many of the relationships shown here are empirical and not theoretically derived
Wind speed and friction velocity• Wind speed varies in the near-surface (due to drag)• The friction velocity v* is a measure of the stress t
exerted on the surface by the wind: =t rf v*2
vzturbulence
Viscous sublayer d
Roughness z0
010
* log75.5)(z
zvzv
In the viscous sublayer, v(z) is linear not logarithmicThe roughness z0 is appx. 1/30 of grain size
The actual velocity v(z) is larger than v* and varies with height:
where z0 is a measure of the bed roughness
Initiation of sand transportv
zturbulence
Viscous sublayer
Win
d sp
eed
Grain diameter
~d1/2
~d-1
Small grains are stranded in the viscous sublayer – velocities are lowBig grains are too large to move easilyThere is an intermediate grain size dt at which required speed is a minimum
3/12
)(10
gd
fsft
h is the viscosity of air. Does this equation make sense?
We can then use this grain size to infer the wind speed requiredSame analysis can also be applied to water flows.In theory, sand deposits should consist of a single grain-size
f
d
What speed is required?• Bagnold derived an empirical criterion which has not
really been improved upon:
tf dv
5.3* Does this make sense?
• This criterion says that there is a rough balance between viscous and turbulent effects when sand grain motion starts
• Given v* and a roughness, we can then calculate the actual wind speeds required to initiate transport
Worked Example
• Quartz sand on Earth• h=17 mPa s, rf=1.3 kg m-3, rs=2800 kg m-3
• dt=200 mm
• v*=3.5h/rf dt = 0.23 m/s
• Velocity at 1m height = 5.75 v* log10(z/z0)=4.9 m/s
(taking z0=0.2 mm)
3/12
)(10
gd
fsft
Threshold grain diametersBody Medium Viscosity
(mPa s)dt
(mm)Fluid velocity at 1m (m/s)
Venus Qtz in CO2 33 94 0.4
Titan Tar in N2 6 160 0.5
Earth Qtz in air 17 200 4.9
Mars Qtz in CO2 11 1100 70 (!)
• Ease of transport is Venus – Titan – Earth – Mars• Mars sand grains are difficult to transport because the very
low atmospheric density results in a large viscous sublayer thickness
• The high wind velocities required at Mars create problems – “kamikaze grains”
• Note that gas viscosity does not depend on pressure (!)
Sand Transport
• Suspension – small grains, turbulent velocity >> sinking velocity
• Saltation – main component of mass flux
• Creep – generally minor component
g
vl
* Does this make
sense?
Terminal velocity
rsrf
d Downwards force: gd fs )(6
3
Drag force:4
22vdC f
D
v
CD is a drag coefficient, ~0.4 for turbulent flow
Terminal velocity:Df
fs
C
dgv
)(
3
4 Does this make
sense?
The terminal velocity is important because it determines how long a dust/sand grain can stay aloft, and hence how far dust/sand can be transported.
For very small grains, the drag coefficient is dominated by viscous effects, not turbulence, and is given by:
vdC
fD
24
Whether viscous or turbulent effects dominated is controlled by the Reynolds number Re=rf vd/h. A Reynolds number >1000 indicates turbulence dominates.
Sand Fluxes
g
vCq f
s
3*
Another empirical expression from Bagnold – the mass flux (kg s-1 m-1) of (saltating) sand grains:
C is a constant
Note that the sand flux goes as the friction velocity cubed – sand is mostly moved by rare, high wind-speed events. This makes predicting long-term fluxes from short-term records difficult.
Dune MotionSand flux qs Dune speed vd
Dx
h
h
qv
s
sd
a
Large dunes move slower than small dunes.What are some of the consequences of this?
Does this equation make sense?
s
sd q
h 2Dune modification timescale: l = length:height ratio (~10)
Dune Motion on Mars• Repeat imaging allows
detection of dune motion• Inferred flux ~5 m2/yr• Similar to Antarctic dune
fluxes on Earth• Dune modification
timescale ~103 times longer (dunes are larger)
Bridges et al. Nature 2012
Aeolian Landforms• Known on Earth, Venus, Mars and Titan• Provide information on wind speed &
direction, availability of sediment• One of the few time-variable features
Aeolian Features (Mars)• Wind is an important process on Mars at the present day (e.g.
Viking seismometers . . .)• Dust re-deposited over a very wide area (so the surface of
Mars appears to have a very homogenous composition)• Occasionally get global dust-storms (hazardous for spacecraft)• Rates of deposition/erosion (almost) unknown
30km
Image of a dustdevil caught inthe act
Martian dune features
Aeolian features (elsewhere)Namib desert, Earthfew km spacing
Longitudinal dunesMead crater, Venus
Longitudinal dunes, Earth (top),Titan (bottom), ~ 1 km spacing
Wind directionsVenus
Wind streaks, Venus
Global patterns of wind direction can be compared with general circulation models (GCM’s)
Mars (crater diameter 90m)
Bidirectional wind transportDominant
Subordinate
Rubin & Hunter 1987
sin
costan
S
D
Bedform-normal transport is maximized at:
=D
/S
a
Experimental Test
Ping et al. Nature Geosci 2014
Summary - Wind• Sediment transport
– Initiation of motion – friction velocity v*, threshold grain size dt, turbulence and viscosity
– Sinking - terminal velocity– Motion of sand-grains – saltation, sand flux, dune
motion
• Aeolian landforms and what they tell us
g
vCq f
s
3*
3/12
)(10
gd
fsft
Df
fs
C
dgv
)(
3
4