PTYS 554 Evolution of Planetary Surfaces Fluvial Processes I

PYTS 554 – Fluvial Processes I 2 l Fluvial Processes I n Rainfall and runoff n Channelization and erosion n Drainage networks n Sediment transport – Shields curve n Velocity and discharge, Manning vs Darcy Weisback l Fluvial Processes II n Stream power and stable bedforms from ripples to antidunes n Floodplains, Levees, Meanders and braided streams n Alluvial fans and Deltas n Wave action and shoreline Processes l Fluvial Processes III n Groundwater tables n Subterranean flow rates n Springs and eruption of pressurized groundwater n Sapping as an erosional mechanism

PYTS 554 – Fluvial Processes I 3 l Earth n Liquid = water n Sediment=quartz l Mars n Liquid = water n Sediment=basalt l Titan n Liquid = Methane (mostly) n Sediment = organic stuff

PYTS 554 – Fluvial Processes I 4 l Liquid water is fairly difficult to get in our solar system n Earth is lucky n Mars can have it – just about l Phase diagram shows only what is stable against phase changes… n i.e. water on Mars can be stable against boiling and freezing n That doesn’t mean water is in equilibrium! n Evaporation rates depend on the partial pressure of water vapor in the atmosphere n At 273 K, you need 6.1mb of water vapor in the atmosphere to have liquid survive Stability of water l The problem for Mars… n Molecular weight of CO 2 is 44 n Molecular weight of H 2 O is 18 n i.e. water vapor is buoyant in a CO 2 atmosphere n Unlike the Earth it doesn’t rain so liquid dries up fast n Strong evaporation rates cause a lot of cooling that can push water back into the solid phase

PYTS 554 – Fluvial Processes I 5 l Lower gravity n Slower flow n …but easier to transport sediment l Fluid viscosity and density n Affects particle buoyancy and settling velocity n Water can carry bigger particles in suspension

PYTS 554 – Fluvial Processes I 6 l Fluvial erosion starts with rainfall n Rainsplash is similar to micrometeorite bombardment n ‘Ejecta’ is preferentially transported downslope n Diffusive smoothing where dominant n Channel formation suppressed Downhill Growth of Drainage Features

PYTS 554 – Fluvial Processes I 7 l Fluid mostly infiltrates surface n Infiltration rate fast at first until near-surface pores are filled, constant rate thereafter set by permeability n Fluid that doesn’t infiltrate the subsurface can run off wCauses erosion n Surface with high infiltration rates are very resistant to erosion Melosh 2011

PYTS 554 – Fluvial Processes I 8 l Permeability effects on erosion Low permeability ash 5 months after eruption High permeability cinders 50 Kyr after eruption

PYTS 554 – Fluvial Processes I 9 l Flow thickness increases with distance from the divide n Shear stress depends on flow thickness n Transport of debris is a threshold process n No channelization where flow is thin n Rainsplash smoothing suppresses rille formation n At some point transition from sheet flow to rille formation

PYTS 554 – Fluvial Processes I 10 l If surface is eroded until stress falls below the threshold… n x is distance from drainage divide n Solving this gives a logarithmic profile n Result is a characteristic terrestrial hillshape z = z o

PYTS 554 – Fluvial Processes I 11 l Rilles combine to form networks n E.g. Pinatubo ash deposit wLow permeability, high runoff wA wet environment 5 months after the eruption

PYTS 554 – Fluvial Processes I 12 l Drainage basins n Range from a few m across to continental in scale n Bounded by divides n Area, length relation Montgomery and Dietrich 1992

PYTS 554 – Fluvial Processes I 13 l Networks characterized by Strahler number n Stream order w1 – initial rilles w2 – combining 2 order 1 streams w3 – combining 2 order 2 streams etc… wCombining streams of different order gives a stream with the higher order – side branches n Some rivers can by up to 10 th order (Mississippi) n The nearby Gila river is 8 th order e.g. fifth order network Turcotte 1997

PYTS 554 – Fluvial Processes I 14 l Networks characterized by n Branching ratio n Length order ratio n How space filling? wBasin area filled with channels: wMore generally: Networks are close to fully space filling Pelletier and Turcotte 2000

PYTS 554 – Fluvial Processes I 15 l Proceeds by: n Abrasion from suspended sediment n Plucking n Cavitation l Bedrock abrasion on Titan n Roughly as easy to do as on Earth n Various properties of the two bodies and materials involved cancel wAbrasion of water ice is easier wLower kinetic energy on Titan n Big question is how much run-off there is and the nature of the debris l Bedrock stream erosion on Mars n Harder than Earth – lower kinetic energy n Equally hard rocks Bedrock Erosion Collins et al. 2005

PYTS 554 – Fluvial Processes I 16 l Plucking requires jointed rocks n Local vortices cause pressure lows above bed l Channeled scabland in eastern Washington state n Considered the best analogue for the Martian outflow channels l Glacially damned Lake Missoula n Dam fails n Lake catastrophically empties l Floods 100’s of meters deep at ~25 m/s l Discharge rates of ~ 10 7 m 3 s -1 n Enormous by terrestrial standards!! n Mississippi river ~ 3x10 4 m 3 s -1

PYTS 554 – Fluvial Processes I 17 l How did the terrestrial outflow channels get so big? n Plucking of jointed basalt…

PYTS 554 – Fluvial Processes I 18 l Plucking may have had a role in the martian outflow channels l Effects on Titan are unknown THEMIS - V

PYTS 554 – Fluvial Processes I 19 l Cavitation is easier on Mars n Very destructive implosion of bubbles within the fluid l Cavitation is hard on Earth and harder on Titan =2 Collins et al. 2005

PYTS 554 – Fluvial Processes I 20 l Moving material n Bedload – saltating and rolling material n Suspended load n Washload wVery fine particles (essentially part of the fluid) Washload Sediment Transport

PYTS 554 – Fluvial Processes I 21 l Transport threshold - The Shields curve n Define the shear velocity n Define the boundary Reynolds number n Motion when threshold shear stress is within some factor of the adjusted weight n This factor is the Shields criterion wFunction of Rayleigh number wEmpirically determined Burr et al. 2006

PYTS 554 – Fluvial Processes I 22 l All Re * and θ t values along that line can be converted to u * and d n U * is proportional to u ave (constant depends on bed roughness) l Yields different threshold curves for different material parameters and gravity l Frictional velocities on Earth, Titan and Mars differ by only a factor of ~3 Burr et al. 2006

PYTS 554 – Fluvial Processes I 23 l Hjulstrom diagram often used instead n Uses dimensional velocity instead of shear velocity n Curves are different for every depth n Not as flexible as the Shields curve – not easily transferred to other planets

PYTS 554 – Fluvial Processes I 24 l Suspended load n Settling velocity… n Low Re, Stokes law: n High Re, turbulent: n See Burr et al., Icarus 2006 for details of how these regimes are combined wNon-dimensionalize both d and v settle wCombine and then re-dimensionalize l Criteria for suspension n Settling velocity vs flow velocity n k < : suspended load n k < : washload Burr et al Stokes law Non-Stokes

PYTS 554 – Fluvial Processes I 25 l Putting it all together n Fluvial landforms look pretty alike in all three cases Washload Burr et al. 2006

PYTS 554 – Fluvial Processes I 26 l Open channel flow described by the manning equation: n R h is the hydraulic radius Flow-cross-section / Wet-perimeter i.e. for a rectangular trough When w>>h then R h ~ h for a V-shaped channel When w >>h then R h ~ h/3 n S is the dimensionless gradient (m/m) n 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 n is determined empirically l Empirically ‘discovered’ in 19 th century by averaging a bunch of pre-existing flow laws l Problem is that ‘n’ has dimensions – can’t be generalized to other planets l Chezy’s law has the same problem: w h w h Flow velocities and discharges

PYTS 554 – Fluvial Processes I 27 l Darcy-Weisbach law n Balance shear stress with friction n Downhill force per unit length n Divided by surface in contact with fluid (2h+w): n Friction with walls in terms of mean velocity: n i.e. n So Flow velocity is: n Discharge is: n When w >> h then l Relation to manning’s law… Implies that n Use tabulated manning values to find f c or… n Empirical relations that relate f c to wGrain-size of bed material wImplies z o = D 50 /(2e) ~ D 50 / 6 w h Julien et al Compare to eolian flow, law of the wall

PYTS 554 – Fluvial Processes I 28 l Fluvial Processes I n Rainfall and runoff n Channelization and erosion n Drainage networks n Sediment transport – Shields curve n Velocity and discharge, Manning vs Darcy Weisback l Fluvial Processes II n Stream power and stable bedforms from ripples to antidunes n Floodplains, Levees, Meanders and braided streams n Alluvial fans and Deltas n Wave action and shoreline Processes l Fluvial Processes III n Groundwater tables n Subterranean flow rates n Springs and eruption of pressurized groundwater n Sapping as an erosional mechanism