EART163 Planetary Surfaces

1. EART163 Planetary Surfaces Francis Nimmo

2. Last Week – Impact Cratering • Why and how do impacts happen? • Impact velocity, comets vs. asteroids • Crater morphology • Simple,complex,peak-ring,multi-ring • Crateringand ejectamechanics • Contact, compression, excavation, relaxation • Scaling of crater dimensions • Strength vs. gravity, melting • Cratered landscapes • Saturation, modification, secondaries, chronology • Planetary Effects

3. 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

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=rfv*2 • The actual velocity v(z) is larger than v* and varies with height: z turbulence v Roughness z0 Viscous sublayer • where z0 is a measure of the bed roughness d In the viscous sublayer, v(z) is linear not logarithmic The roughness z0 is appx. 1/30 of grain size

5. Initiation of sand transport z 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 dtat 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/rfdt = 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 • 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 (!)

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 Downwards force: rs CD is a drag coefficient, ~0.4 for turbulent flow Drag force: rf 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 numberRe=rfvd/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. a Dune Motion Sand flux qs 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? l = length:height ratio (~10) Dune modification timescale:

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

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

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

19. Experimental Test Ping et al. Nature Geosci2014

20. 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