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
turbulence
The actual velocity v(z) is larger
than v* and varies with height:
z
v
Roughness
z0
Viscous sublayer
d
 z 
v( z ) = 5.75v log10  
 z0 
*
where z0 is a measure of the bed
roughness
In the viscous sublayer, v(z) is linear not logarithmic
The roughness z0 is appx. 1/30 of grain size
turbulence
z
Viscous sublayer
v

d
rf
d
Wind speed
Initiation of sand transport
~d-1
~d1/2
Grain diameter
Small grains are stranded in the viscous sublayer – velocities are low
Big grains are too large to move easily
There is an intermediate grain size dt at which required speed is a minimum



dt  10

r
(
r

r
)
g
 f s

f
2
1/ 3
 is the viscosity of air.
Does this equation make sense?
We can then use this grain size to infer the wind speed required
Same analysis can also be applied to water flows.
In theory, sand deposits should consist of a single grain-size
What speed is required?
• Bagnold derived an empirical criterion which has not
really been improved upon:

v  3.5
r f dt
*
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



dt  10

 r f ( r s  r f ) g 
2
• Quartz sand on Earth
• =17 mPa s, rf=1.3 kg m-3, rs=2800 kg m-3
• dt=200 mm
• v*=3.5/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)
1/ 3
Threshold grain diameters
Body
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
v*
l
g
Does this make
sense?
Terminal velocity
d
rs
v
Downwards force:
rf
Drag force:

6
d 3 (rs  r f )g
CD
Terminal velocity:
r f d 2 v 2
4
4 ( r s  r f )dg
v=
3
r f CD
CD is a drag
coefficient, ~0.4
for turbulent flow
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
24
turbulence, and is given by:
CD =
r f vd
Whether viscous or turbulent effects dominated is controlled by the Reynolds
number Re=rf vd/. A Reynolds number >1000 indicates turbulence dominates.
Sand Fluxes
Another empirical expression from Bagnold – the mass
flux (kg s-1 m-1) of (saltating) sand grains:
qs = C
rfv
*3
C is a constant
g
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 Motion
Sand
flux qs
Dune speed vd
h
Dx
a
qs
vd =
rsh
Does this equation
make sense?
Large dunes move slower than small dunes.
What are some of the consequences of this?
Dune modification timescale:
t d = h
2
rs
qs
 = 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
Martian dune features
Image of a dust
devil caught in
the act
30km
Aeolian features (elsewhere)
Namib desert, Earth
few km spacing
Longitudinal dunes, Earth (top),
Titan (bottom), ~ 1 km spacing
Longitudinal dunes
Mead crater, Venus
Wind directions
Venus
Mars (crater diameter 90m)
Wind streaks, Venus
Global patterns of wind
direction can be compared
with general circulation
models (GCM’s)
Bidirectional wind transport
=D/S
Dominant
Subordinate
Bedform-normal transport
is maximized at:
D
S
tana =
 cos
sin 
a
Rubin & Hunter 1987
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



dt  10

 r f ( r s  r f ) g 
2
1/ 3
qs = C
r f v*3
g
4 ( r s  r f )dg
v=
3
r f CD
• Aeolian landforms and what they tell us