EART163 Planetary Surfaces. Francis Nimmo

Transcription

1 EART163 Planetary Suraces Francis Nimmo

2 Last Week Mass Movements Downhill creep is diusive: z t 2 z 2 x Resitance to sliding depends on pore pressure: s c ( p) tan Angle o repose is independent o gravity Eective riction coeicient o long-runout landslides is very low n K

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

4 Wind speed and riction velocity Wind speed varies in the near-surace (due to drag) The riction velocity v* is a measure o the stress t exerted on the surace by the wind: tr v* 2 turbulence z Viscous sublayer d v Roughness z 0 The actual velocity v(z) is larger than v* and varies with height: v( z) 5.75v * log 10 z z where z 0 is a measure o the bed roughness In the viscous sublayer, v(z) is linear not logarithmic Viscous sublayer thickness d is ~1 mm (Earth) The roughness z 0 is appx. 1/30 o grain size 0

5 Wind speed turbulence z Initiation o sand transport v d r ~d -1 ~d 1/2 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 d t at which required speed is a minimum d t 2 10 r ( rs r ) g 1/3 is the viscosity o air. Does this equation make sense? We can then use this grain size to iner the wind speed required Same analysis can also be applied to water lows. In theory, sand deposits should consist o a single grain-size

6 What speed is required? Bagnold derived an empirical criterion which has not really been improved upon: v 3.5 r * Does this make sense? d t This criterion says that there is a rough balance between viscous and turbulent eects 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 2 10 r ( rs r ) g =17 mpa s, r =1.3 kg m -3, r s =2800 kg m -3 d t =200 mm v*=3.5/r d t = 0.23 m/s Velocity at 1m height = 5.75 v* log 10 (z/z 0 )=4.9 m/s (taking z 0 =0.2 mm) d t 1/3

8 Threshold grain diameters Body Medium Viscosity (mpa s) d t (mm) Venus Qtz in CO Titan Tar in N Earth Qtz in air Fluid velocity at 1m (m/s) Mars Qtz in CO (!) Ease o transport is Venus Titan Earth Mars These dierences are due mostly to atmospheric density r Mars sand grains are diicult to transport because the very low r 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 o mass lux Creep generally minor component l v* g Does this make sense?

10 v Terminal velocity 3 d Downwards orce: d ( rs r ) g 6 r s r Drag orce: C D r d 4 2 v 2 C D is a drag coeicient, ~0.4 or turbulent low Terminal velocity: v 4 (r s r ) dg 3 r C D Does this make sense? The terminal velocity is important because it determines how long a dust/sand grain can stay alot, and hence how ar dust/sand can be transported. For very small grains, the drag coeicient is dominated by viscous eects, not turbulence, and is given by: 24 C D r vd Whether viscous or turbulent eects dominated is controlled by the Reynolds number Re=r vd/. A Reynolds number >1000 indicates turbulence dominates.

11 Sand Fluxes Another empirical expression rom Bagnold the mass lux (kg s -1 m -1 ) o (saltating) sand grains: r v *3 q C s g C is a constant Note that the sand lux goes as the riction velocity cubed sand is mostly moved by rare, high wind-speed events. This makes predicting long-term luxes rom short-term records diicult.

12 Sand lux q s h Dx Dune Motion Dune speed vd Large dunes move slower than small dunes. What are some o the consequences o this? v d qs r h s a Does this equation make sense? s d h r 2 Dune modiication timescale: t = length:height ratio (~10) qs

13 Dune Motion on Mars Repeat imaging allows detection o dune motion Inerred lux ~5 m 2 /yr Similar to Antarctic dune luxes on Earth Dune modiication timescale ~10 3 times longer (dunes are larger) Bridges et al. Nature 2012

14 Aeolian Landorms Known on Earth, Venus, Mars and Titan Provide inormation on wind speed & direction, availability o sediment One o the ew time-variable eatures

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 surace o Mars appears to have a very homogenous composition) Occasionally get global dust-storms (hazardous or spacecrat) Rates o deposition/erosion (almost) unknown Image o a dust devil caught in the act Martian dune eatures 30km

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

17 Mount Sharp and Bagnold dunes

18 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 Delation? Cosmogenic dating suggests recent erosion rate o ~0.1 mm/year

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

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

21 =D/S Bidirectional wind transport Dominant tana Subordinate Bedorm-normal transport is maximized at: D cos S sin a Rubin & Hunter 1987

22 Experimental Test Ping et al. Nature Geosci 2014

23 Sediment transport d t Summary - Wind Initiation o motion riction velocity v*, threshold grain size d t, turbulence and viscosity Sinking - terminal velocity Motion o sand-grains saltation, sand lux, dune motion 2 10 r ( rs r ) g 1/3 q Aeolian landorms and what they tell us s r v C g *3 v 4 (r s r ) dg 3 r C D

24 Wind speed Grain diameter