1. EART163 Planetary Surfaces
Francis Nimmo

2. Last Week – Mass Movements
Downhill creep is diffusive:
Resitance to sliding depends on pore pressure:
Angle of repose is independent of gravity
Effective friction coefficient of long-runout landslides is very low

3. This week - Wind Sediment transport
Initiation of motion
Sinking (terminal velocity)
Motion of sand-grains
Aeolian landforms and what they tell us
WARNING: many of the relationships shown here are empirical and not theoretically derived

4. 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
The actual velocity v(z) is larger than v* and varies with height: z
turbulence v
Roughness z0
Viscous sublayer d
where z0 is a measure of the bed roughness
In the viscous sublayer, v(z) is linear not logarithmic
Viscous sublayer thickness d is ~1 mm (Earth)
The roughness z0 is appx. 1/30 of grain size

5. Initiation of sand transportz
turbulence v
~d-1
Wind speed
~d1/2
Viscous sublayer d
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
h 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

6. What speed is required?
Bagnold derived an empirical criterion which has not really been improved upon:
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

7. 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)

8. 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 11
1100
70 (!)
Ease of transport is Venus – Titan – Earth – Mars
These differences are due mostly to atmospheric density rf
Mars sand grains are difficult to transport because the very low rf 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 (!)

9. Sand Transport
Suspension – small grains, turbulent velocity >> sinking velocity
Saltation – main component of mass flux
Creep – generally minor component
Does this make sense?

10. Terminal velocity d rs rf v Downwards force:
CD is a drag coefficient, ~0.4 for turbulent flow rf
Drag force: v
Does this make sense?
Terminal velocity:
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:
Whether viscous or turbulent effects dominated is controlled by the Reynolds number Re=rf vd/h. A Reynolds number >1000 indicates turbulence dominates.

11. Sand Fluxes
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.

12. Dune Motion Sand flux qs a Dune speed vd h
Does this equation make sense? Dx
Large dunes move slower than small dunes.
What are some of the consequences of this?
Dune modification timescale:
l = length:height ratio (~10)

13. 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

14. 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

15. 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

16. Gale Crater (Mars) Day & Kocurek 2016 Curiosity Landing Site
Mount Sharp
Bagnold dunes

17. Mount Sharp and Bagnold dunes

18. Deflation? Mount Sharp is higher than the crater rim!
This could be due to large-scale deposition and then erosion
Implied erosion rate is only ~1 mm/year
Cosmogenic dating suggests recent erosion rate of ~0.1 mm/year

19. Aeolian features (elsewhere)
Namib desert, Earth
few km spacing
Longitudinal dunes, Earth (top),
Titan (bottom), ~ 1 km spacing
Longitudinal dunes
Mead crater, Venus

20. Wind directions
Venus
Wind streaks, Venus
Mars (crater diameter 90m)
Global patterns of wind direction can be compared with general circulation models (GCM’s)

21. Bidirectional wind transport
Dominant
=D/S
Subordinate
Bedform-normal transport is maximized at:
Rubin & Hunter 1987 a

22. Experimental Test
Ping et al. Nature Geosci 2014

23. 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

24. Wind speed
Grain diameter