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  exerted on the surface by the wind:  f  v   v z turbulence Viscous sublayer  Roughness z 0 In the viscous sublayer, v(z) is linear not logarithmic The roughness z 0 is appx. 1/30 of grain size The actual velocity v(z) is larger than v* and varies with height: where z 0 is a measure of the bed roughness

Initiation of sand transport v z turbulence Viscous sublayer Wind speed Grain diameter ~d 1/2 ~d -1 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  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: 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  =17  Pa s,  f =1.3 kg m -3,  s =2800 kg m -3 d t =200  m v*=3.5  /  f 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)

Threshold grain diameters BodyMediumViscosity (  Pa s) d t (  m) Fluid velocity at 1m (m/s) VenusQtz in CO TitanTar in N EarthQtz in air MarsQtz in CO (!) 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 Does this make sense?

Terminal velocity ss ff d Downwards force: Drag force: v C D is a drag coefficient, ~0.4 for turbulent flow Terminal velocity: 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: Whether viscous or turbulent effects dominated is controlled by the Reynolds number Re =  f 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: 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 Motion Sand flux q s Dune speed v d xx h  Large dunes move slower than small dunes. What are some of the consequences of this? Does this equation make sense? Dune modification timescale: = length:height ratio (~10)

Dune Motion on Mars Repeat imaging allows detection of dune motion Inferred flux ~5 m 2 /yr Similar to Antarctic dune fluxes on Earth Dune modification timescale ~10 3 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 dust devil caught in the act Martian dune features

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

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

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

Experimental Test Ping et al. Nature Geosci 2014

Summary - Wind Sediment transport –Initiation of motion – friction velocity v*, threshold grain size d t, turbulence and viscosity –Sinking - terminal velocity –Motion of sand-grains – saltation, sand flux, dune motion Aeolian landforms and what they tell us