ptys 554 evolution of planetary surfaces fluvial processes i
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PTYS 554
Evolution of Planetary Surfaces
Fluvial Processes IFluvial Processes I
PYTS 554 – Fluvial Processes I 2
Fluvial Processes I Rainfall and runoff Channelization and erosion Drainage networks Sediment transport – Shields curve Velocity and discharge, Manning vs Darcy Weisback
Fluvial Processes II Stream power and stable bedforms from ripples to antidunes Floodplains, Levees, Meanders and braided streams Alluvial fans and Deltas Wave action and shoreline Processes
Fluvial Processes III Groundwater tables Subterranean flow rates Springs and eruption of pressurized groundwater Sapping as an erosional mechanism
PYTS 554 – Fluvial Processes I 3
Earth Liquid = water Sediment=quartz
Mars Liquid = water Sediment=basalt
Titan Liquid = Methane (mostly) Sediment = organic stuff
PYTS 554 – Fluvial Processes I 4
Liquid water is fairly difficult to get in our solar system Earth is lucky Mars can have it – just about
Phase diagram shows only what is stable against phase changes… i.e. water on Mars can be stable against boiling and freezing That doesn’t mean water is in equilibrium! Evaporation rates depend on the partial pressure of water vapor in the atmosphere At 273 K, you need 6.1mb of water vapor in the atmosphere to have liquid survive
Stability of water
The problem for Mars… Molecular weight of CO2 is 44 Molecular weight of H2O is 18 i.e. water vapor is buoyant in a CO2
atmosphere Unlike the Earth it doesn’t rain so
liquid dries up fast Strong evaporation rates cause a lot
of cooling that can push water back into the solid phase
PYTS 554 – Fluvial Processes I 5
Lower gravity Slower flow …but easier to transport sediment
Fluid viscosity and density Affects particle buoyancy and settling velocity Water can carry bigger particles in suspension
PYTS 554 – Fluvial Processes I 6
Fluvial erosion starts with rainfall Rainsplash is similar to micrometeorite bombardment ‘Ejecta’ is preferentially transported downslope Diffusive smoothing where dominant Channel formation suppressed
Do
wn
hill
Growth of Drainage Features
PYTS 554 – Fluvial Processes I 7
Fluid mostly infiltrates surface Infiltration rate fast at first until near-surface pores are filled, constant rate thereafter set by
permeability
Fluid that doesn’t infiltrate the subsurface can run off Causes erosion
Surface with high infiltration rates are
very resistant to erosion
Melosh 2011
PYTS 554 – Fluvial Processes I 8
Permeability effects on erosion
Low permeability ash 5 months after eruption
High permeability cinders 50 Kyr after eruption
PYTS 554 – Fluvial Processes I 9
Flow thickness increases with distance from the divide
Shear stress depends on flow thickness
Transport of debris is a threshold process
No channelization where flow is thin Rainsplash smoothing suppresses rille formation
At some point transition from sheet flow to rille formation
PYTS 554 – Fluvial Processes I 10
If surface is eroded until stress falls below the threshold…
x is distance from drainage divide
Solving this gives a logarithmic profile
Result is a characteristic terrestrial hillshape
z = zo
PYTS 554 – Fluvial Processes I 11
Rilles combine to form networks E.g. Pinatubo ash deposit
Low permeability, high runoff A wet environment
5 months after the eruption
PYTS 554 – Fluvial Processes I 12
Drainage basins Range from a few m across to continental in scale Bounded by divides Area, length relation
Montgomery and Dietrich 1992
PYTS 554 – Fluvial Processes I 13
Networks characterized by Strahler number Stream order
1 – initial rilles 2 – combining 2 order 1 streams 3 – combining 2 order 2 streams etc…
Combining streams of different order gives a stream with the higher order – side branches
Some rivers can by up to 10th order (Mississippi) The nearby Gila river is 8th order
e.g. fifth order network
Turcotte 1997
PYTS 554 – Fluvial Processes I 14
Networks characterized by Branching ratio
Length order ratio
How space filling? Basin area filled with channels: More generally:
Networks are close to fully space filling
Pelletier and Turcotte 2000
PYTS 554 – Fluvial Processes I 15
Proceeds by: Abrasion from suspended sediment Plucking Cavitation
Bedrock abrasion on Titan Roughly as easy to do as on Earth Various properties of the two bodies and
materials involved cancel Abrasion of water ice is easier Lower kinetic energy on Titan
Big question is how much run-off there is and the nature of the debris
Bedrock stream erosion on Mars Harder than Earth – lower kinetic energy Equally hard rocks
Bedrock Erosion
Collins et al. 2005
PYTS 554 – Fluvial Processes I 16
Plucking requires jointed rocks Local vortices cause pressure lows above bed
Channeled scabland in eastern Washington state
Considered the best analogue for the Martian outflow channels
Glacially damned Lake Missoula Dam fails Lake catastrophically empties
Floods 100’s of meters deep at ~25 m/s
Discharge rates of ~ 107 m3s-1
Enormous by terrestrial standards!! Mississippi river ~ 3x104 m3s-1
PYTS 554 – Fluvial Processes I 17
How did the terrestrial outflow channels get so big?
Plucking of jointed basalt…
PYTS 554 – Fluvial Processes I 18
Plucking may have had a role in the martian outflow channels
Effects on Titan are unknown
THEMIS - V01786010
PYTS 554 – Fluvial Processes I 19
Cavitation is easier on Mars Very destructive implosion of bubbles within the fluid
Cavitation is hard on Earth and harder on Titan
=2
Collins et al. 2005
PYTS 554 – Fluvial Processes I 20
Moving material Bedload – saltating and rolling material Suspended load Washload
Very fine particles (essentially part of the fluid)
Washload
Sediment Transport
PYTS 554 – Fluvial Processes I 21
Transport threshold - The Shields curve
Define the shear velocity
Define the boundary Reynolds number
Motion when threshold shear stress is within some factor of the adjusted weight
This factor is the Shields criterion Function of Rayleigh number Empirically determined
Burr et al. 2006
PYTS 554 – Fluvial Processes I 22
All Re* and θt values along that line can be converted to u* and d U* is proportional to uave (constant depends on bed roughness)
Yields different threshold curves for different material parameters and gravity
Frictional velocities on Earth, Titan and Mars differ by only a factor of ~3
Burr et al. 2006
PYTS 554 – Fluvial Processes I 23
Hjulstrom diagram often used instead Uses dimensional velocity instead of shear velocity Curves are different for every depth Not as flexible as the Shields curve – not easily transferred to other planets
PYTS 554 – Fluvial Processes I 24
Suspended load Settling velocity…
Low Re, Stokes law:
High Re, turbulent:
See Burr et al., Icarus 2006 for details of how these regimes are combined
Non-dimensionalize both d and vsettle
Combine and then re-dimensionalize
Criteria for suspension Settling velocity vs flow velocity
k < 1-1.8 : suspended load k < 0.05-0.13 : washload
Burr et al. 2006
Stoke
s la
w
Non-Stokes
PYTS 554 – Fluvial Processes I 25
Putting it all together Fluvial landforms look pretty alike in all three cases
Washload
Burr et al. 2006
PYTS 554 – Fluvial Processes I 26
Open channel flow described by the manning equation: Rh is the hydraulic radius
Flow-cross-section / Wet-perimeter
i.e. for a rectangular trough
When w>>h then Rh ~ h
for a V-shaped channel
When w >>h then Rh ~ h/3
S is the dimensionless gradient (m/m) n is the Manning coefficient of roughness
Varies from:
~0.02 – smooth beds and straight plans
to
~0.08 – rough beds and sinuous plans
n is determined empirically
Empirically ‘discovered’ in 19th century by averaging a bunch of pre-existing flow laws
Problem is that ‘n’ has dimensions – can’t be generalized to other planets
Chezy’s law has the same problem:
w
h
w
h
Flow velocities and discharges
PYTS 554 – Fluvial Processes I 27
Darcy-Weisbach law Balance shear stress with friction
Downhill force per unit length Divided by surface in contact with fluid (2h+w): Friction with walls in terms of mean velocity: i.e.
So Flow velocity is:
Discharge is:
When w >> h then
Relation to manning’s law… Implies that
Use tabulated manning values to find fc or… Empirical relations that relate fc to
Grain-size of bed material Implies zo = D50/(2e) ~ D50 / 6
w
h
Julien et al. 2006Compare to eolian flow, law of the wall
PYTS 554 – Fluvial Processes I 28
Fluvial Processes I Rainfall and runoff Channelization and erosion Drainage networks Sediment transport – Shields curve Velocity and discharge, Manning vs Darcy Weisback
Fluvial Processes II Stream power and stable bedforms from ripples to antidunes Floodplains, Levees, Meanders and braided streams Alluvial fans and Deltas Wave action and shoreline Processes
Fluvial Processes III Groundwater tables Subterranean flow rates Springs and eruption of pressurized groundwater Sapping as an erosional mechanism