Last Week - 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
This week – “Water” Only three bodies: Earth, Mars, Titan Subsurface water – percolation, sapping Surface flow –Water discharge rates –Sediment transport – initiation, mechanisms, rates Channels Fluvial landscapes
Caveats 1. “Most geologic work is done by large, infrequent events” 2. Almost all sediment transport laws are empirical
Subsurface Flow On Earth, there is a water table below which the pores are occupied by fluid This fluid constitutes a reservoir which can recharge rivers (and is drained by wells) Surface flow happens if infiltration into the subsurface is exceeded by the precipitation rate
Flow in a permeable medium vdvd vdvd v d is the Darcy velocity (m/s) k is the permeability (m 2 ) is the viscosity (Pa s), typical value for water is 10 -3 Pa s Darcy velocity is the average flow velocity of fluid through the medium (not the flow velocity through the pores) Permeability controls how fast fluid can flow through the medium – intrinsic property of the rock. Permeable flows are almost always low Reynolds numbers – so what?
Permeability and porosity Permeability can vary widely Porosity is the volume fraction of rock occupied by voids High porosity usually implies high permeability Rock typePermeability (m 2 ) Gravel10 -9 – 10 -7 Loose sand10 -11 – 10 -9 Permeable basalt10 -13 – 10 -8 Fractured crystalline rock10 -14 – 10 -11 Sandstone10 -16 – 10 -12 Limestone10 -18 – 10 -16 Intact granite10 -20 – 10 -18
Porosity and permeability Grain size 2b, pore diameter 2a A unit cell includes 3 pore cylinders Porosity ( ): Permeability (k): Permeability increases with grain size b and porosity E.g. 1mm grain size, porosity 1% implies k~2x10 -12 m 2
Response timescale If the water table is disturbed, the response timescale depends on the permeability The hydraulic diffusivity (m 2 s -1 ) of the water table is k is permeability, is viscosity, P is the pressure perturbation Knowing allows us to calculate the time t it takes a disturbance to propagate a distance d: t=d 2 / Example: a well draws down the local water table by 10 m. If it takes 1 year for this disturbance to propagate 1 km, what value of k/ is implied? Does this make sense?
When does subsurface flow matter? Subsurface flow is generally very slow compared to surface flow, so it does much less geological work But at least on present-day Mars, water is not stable at the surface, while it is stable in the subsurface. So subsurface flow may matter on Mars. On Earth, it matters in regions with high permeability where the rock is soluble (e.g. limestone or chalk) Titan may also have regions where “rock” dissolution is important?
Groundwater sapping on Mars? Lamb et al. 2008 Do blunt amphitheatres necessarily indicate groundwater sapping? Or might they be a sign of ancient surface runoff?
Sediment transport At low velocities, bed-load dominates (saltation + traction + rotation) At intermediate velocities/low grain sizes, suspended load can be important At high velocities, entire bed moves (washload) Solution load is usually minor
Sediment Transport A column of water on a slope exerts a shear stress This stress will drive fluid motion h d ff If the fluid motion is rapid enough, it can also overcome gravity + cohesion and cause sediment transport The shear stress is a useful measure of whether sediment transport is likely
Transport Initiation Just like aeolian transport, we can define a friction velocity u* which is related to the shear stress The friction velocity u*=( / f ) 1/2 =(gh sin ) 1/2 The critical friction velocity required to initiate sediment transport depends on the grain size d The dimensionless constant is a function of u* and d and is a measure of how hard it is to initiate movement. A typical value of is 0.1 (see next page) Does this equation make sense?
Shields Curve =0.05-0.2 Sediment transport harder Small grains Low velocities Large grains High velocities Minimum grain size (as with aeolian transport)
Transport initiation Burr et al. 2006 Slope=0.001 Easiest on Titan – why?
Water and sediment discharge Water discharge rate (m 2 s -1 ) is well-established and depends on dimensionless friction factor f w : Sediment discharge rate (m 2 s -1 ) is not well-established. The formula below is most suitable for steep slopes. It also depends on a dimensionless friction factor f s : The friction factors are empirical but are typically ~0.05
Worked example: cobbles on Titan d=10cm so u*=11 cm/s (for =0.1) u*=(gh sin ) 1/2 so h=9 m (for sin = 0.001) Fluid flux = 20 m 2 s -1 For a channel (say) 100m wide, discharge rate = 2000 m 3 /s Catchment area of say 400 km 2, rainfall rate 18 mm/h Comments? 30 km g=1.3 ms -2, f =500 kgm -3, s =1000 kgm -3 f w =0.05
Braided vs. Meandering Channels Image 2.3 km wide. Why are the meanders high-standing? Braided channels are more common at high slopes and/or high discharge rates (and therefore coarse sediment load – why?) Meanders seem to require cohesive sediment to form – due to clays or plants on Earth, and clays or ice on Mars
Meanders on Venus (!) Image width 50 km Presumably very low viscosity lava Some channels extend for >1000 km Channels do not always flow “down- stream” – why?
Fluvial landscapes Valley networks on Mars Only occur on ancient terrain (~4 Gyr old) What does this imply about ancient Martian atmosphere? 30 km Valley network on Titan Presumably formed by methane runoff What does this imply about Titan climate and surface? 100 km
Fluvial Landscapes Stepinksi and Stepinski 2006 Martian networks resemble those of the Earth, suggesting prolonged lifetime – clement climate?
Large-scale fluvial features, indicating massive (liquid) flows, comparable to ocean currents on Earth Morphology similar to giant post- glacial floods on Earth Spread throughout Martian history, but concentrated in the first 1-2 Gyr of Martian history Source of water unknown – possibly ice melted by volcanic eruptions (jokulhaups)? Martian Outflow channels 50km flow direction 150km Baker (2001)
Martian Gullies A very unexpected discovery (Malin & Edgett, Science 283, 2330- 2335, 2000) Found predominantly at high latitudes (>30 o ), on pole-facing slopes, and shallow (~100m below surface) Inferred to be young – cover young features like dunes and polygons How do we explain them? Liquid water is not stable at the surface! Maybe even active at present day?
Alluvial Fans Schon et al. 2009 Consequence of a sudden change in slope – sediment gets dumped out Fans can eventually merge along-strike to form a continuous surface – a bajada
Martian sediments in outcrop Opportunity (Meridiani) Cross-bedding indicative of prolonged fluid flows
Lakes Titan, 140km across (false colour) Gusev, Mars 150km Clearwater Lakes Canada ~30km diameters Titan lakes are (presumably) methane/ethane and occur mainly near the poles – why? How do we know they are liquid-filled? Gusev crater shows little evidence for water, based on Mars Rover data
Summary Subsurface water – percolation, sapping Surface flow –Water discharge rates –Sediment transport – initiation, mechanisms, rates Channels – braided vs. meandering Fluvial landscapes
Erosion Erosion will remove small, near-surface craters But it may also expose (exhume) craters that were previously buried Erosion has recently been recognized as a major process on Mars, but the details are still extremely poorly understood The images below show examples of fluvial features which have been exhumed: the channels are highstanding. Why? Malin and Edgett, Science 2003 meander channel