6th Grade presentation

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Extending models of granular avalanche flows
and if you see my reflection in the snow covered
hills well the landslide will bring it down the
landslide will bring it down M. Fleetwood
Bruce Pitman The University at Buffalo
GEOPHYSICAL GRANULAR PARTICLE-LADEN FLOWS
Newton Institute _at_ Bristol 28 October 2003
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Interdisciplinary team Camil Nichita (Math)
Abani Patra, Kesh Kesavadas, Eliot Winer,
Andy Bauer (MAE) Mike Sheridan, Marcus Bursik
(Geology) Chris Renschler (Geography) and a cast
of students Long Le (Math)
Supported by NSF
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(No Transcript)
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Casita disaster, Nicaragua
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Model System Dry Flow

• 2D - depth averaged equations, dry flow
• two parameters internal and basal friction

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TITAN 2D

• Simulation environment, currently for dry flow
  only
• Integrate GRASS GI data for topographical map
• High order numerical solver, adaptive mesh,
  parallel computing
• Extension to include erosion (Bursik)

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Little Tahoma Peak, 1963 avalanche

• several avalanches, total of 107 m3 of broken
  lava blocks and other debris
• 6.8 km horizontal and 1.8 km vertical run
• estimate pile run-up on terminal moraine gives
  reasonable comparison with mapped flow we miss
  the run-up on Goat Island Mt.

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Little Tahoma Peak, 1963 avalanche
Tahoma peak (deposit area extent)
Tahoma peak, Mount Rainier (debris avalanche,
1963)
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Debris Flows

• Mass flows containing fluid ubiquitous and
  important
• Iverson (97) 1D Mixture model Iverson and
  Denlinger 2D mixture model and simulations
• How to model fluid/pore pressure motion?

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2-Fluid Approach

• Model equations used in engineering literature
• Continuum balance laws of mass and momentum for
  interpenetrating solids and fluid
• Drag terms transfer momentum

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2-Fluid Approach
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2-Fluid Approach

• Decide constitutive relations for solid and fluid
  stresses (frictional solids, Newtonian fluid)
• Phenomenological volume-fraction dependent
  function in drag
• Depth average introduces
• errors that we will examine (and live with)

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Free boundary and basal surface
Upper free surface Fs(x,t)
s(x,y,t) z 0, Basal material surface
Fb(x,t) b(x,y) z 0 Kinematic BC
flowing mass
ground
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Scales

• Characteristic length scales (mm to km)
• e.g for Mount St. Helens (mudflow 1985)
• Runout distance ? 31,000 m
• Descent height ? 2,150 m
• Flow length(L) ? 100-2,000
• Flow thickness(H) ? 1-10 m
• Mean diameter of sediment material 10-3-10 m
• Scale e-H/L several terms small and are
  dropped
• (data from Iverson 1995, Iverson Denlinger 2001)

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Model System-Depth Average Theory 2D to 1D

• Depth average
• solids conservation
• where

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Model System 1D
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Model System 1D
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Model System 1D
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Errors in modeling
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Special Solutions
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Special Solutions
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Special Solutions
hf constant (lower curve) h evolves in time
(upper curve)
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Special Solutions
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Special Solutions
constant velocities u,v hf faster h slower
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Time Evolution

• Mixed hyperbolic-parabolic system

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Time Evolution
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Time Evolution

• On inclined plane, volume fraction changes small
• special solution
• Interaction with topography induces variation
  in f

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Modeling questions

• Evolution equation for fluid velocity?
• Efficient methods for computing 2D system
  including realistic topography

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Comments on model

• Continuum model
• In situ, there is a distribution of particle
  sizes. Models are operating at the edge where the
  discreteness of solids particles cannot be
  ignored
• Depth averaged velocity
• Are recirculation and basal slip velocity
  important?
• There is no simple scaling arguments from
  tabletop experiments to real debris avalanches
  (No Re, Ba, Sa)