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

vzturbulence

Viscous sublayer d

Roughness z0

010

* log75.5)(z

zvzv

In the viscous sublayer, v(z) is linear not logarithmicThe roughness z0 is appx. 1/30 of grain size

The actual velocity v(z) is larger than v* and varies with height:

where z0 is a measure of the bed roughness

Initiation of sand transportv

zturbulence

Viscous sublayer

Win

d sp

eed

Grain diameter

~d1/2

~d-1

Small grains are stranded in the viscous sublayer – velocities are lowBig grains are too large to move easilyThere is an intermediate grain size dt at which required speed is a minimum

3/12

)(10

gd

fsft

h is the viscosity of air. Does this equation make sense?

We can then use this grain size to infer the wind speed requiredSame analysis can also be applied to water flows.In theory, sand deposits should consist of a single grain-size

f

d

What speed is required?• Bagnold derived an empirical criterion which has not

really been improved upon:

tf dv

5.3* 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• 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)

3/12

)(10

gd

fsft

Threshold grain diametersBody 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

g

vl

* Does this make

sense?

Terminal velocity

rsrf

d Downwards force: gd fs )(6

3

Drag force:4

22vdC f

D

v

CD is a drag coefficient, ~0.4 for turbulent flow

Terminal velocity:Df

fs

C

dgv

)(

3

4 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:

vdC

fD

24

Whether viscous or turbulent effects dominated is controlled by the Reynolds number Re=rf vd/h. A Reynolds number >1000 indicates turbulence dominates.

Sand Fluxes

g

vCq f

s

3*

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 MotionSand flux qs Dune speed vd

Dx

h

h

qv

s

sd

a

Large dunes move slower than small dunes.What are some of the consequences of this?

Does this equation make sense?

s

sd q

h 2Dune modification timescale: l = 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

30km

Image of a dustdevil caught inthe act

Martian dune features

Aeolian features (elsewhere)Namib desert, Earthfew km spacing

Longitudinal dunesMead crater, Venus

Longitudinal dunes, Earth (top),Titan (bottom), ~ 1 km spacing

Wind directionsVenus

Wind streaks, Venus

Global patterns of wind direction can be compared with general circulation models (GCM’s)

Mars (crater diameter 90m)

Bidirectional wind transportDominant

Subordinate

Rubin & Hunter 1987

sin

costan

S

D

Bedform-normal transport is maximized at:

=D

/S

a

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

• Aeolian landforms and what they tell us

g

vCq f

s

3*

3/12

)(10

gd

fsft

Df

fs

C

dgv

)(

3

4