Particle Fall through the atmosphere

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Particle Fall through the atmosphere

• Lecture 5
• Ashfall Class 2009

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Distance d travelled by an object falling for
time t
Time t taken for an object to fall distance d
Instantaneous velocity vi of a falling object
after elapsed time t
Instantaneous velocity vi of a falling object
that has travelled distance d
Average velocity va of an object that has been
falling for time t (averaged over time)
Average velocity va of a falling object that has
travelled distance d (averaged over time)
use g 9.8 m/s² (metres per second squared
which might be thought of as "metres per second,
per second. Assuming SI units, g is measured in
metres per second squared, so d must be measured
in metres, t in seconds and v in metres per
second.
air resistance is neglected--- quite inaccurate
after only 5 seconds
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Particle Fallout

• After a very short time, 4 seconds, particles
  will reach a terminal velocity in earth's
  atmosphere, with their gravitational attraction
  to the earth balanced by air resistance. Small
  particles have dominant air resistance (fall
  slowly) while large particles have dominant
  gravity (fall rapidly).

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Reynolds NumberRe

• Reynolds number is a dimensionless number (i.e.
  it has no units) that is a measure of the type of
  flow through a fluid. In the case of falling
  particles, this describes the way that air flows
  around the particle. There are three basic types
  
• laminar where Re lt 0.4,
• intermediate where 0.4 lt Re lt 500, and
• turbulent where Re gt 500.

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RN dvt?/? Medium and small pyroclasts
Fast-falling Large Pyroclasts
D 1mm
D 1µm
10 m/s
.01 cm/s
Laminar flow RN 10-2
Turbulent flow RN 106
RN 20
RN 40
RN 104
Fluid dynamics applies dimensionless analysis of
fall of spheres in the atmosphere, which shows
that experience with large pyroclasts might not
apply to smaller ones which fall much more slowly
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Conventional Wisdom Particle Settling
Particle Reynolds number, Rep ratio of inertial
force to viscous force per unit mass Rep Vtd /
v Vt particle terminal fall velocity
d particle diameter v fluid
kinematic viscosity Rep gt 500 turbulent
1-500 transitional lt1 laminar
Drag force (i) viscous drag (friction between
the fluid and the particle surface) (ii) form
drag (inertial force caused by the acceleration
of fluid around the particle as it falls)
From Sparks et al. 1997
particle accelerates due to gravity
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Larger pyroclasts, those gt2mm in diameter, fall
in a turbulent flow regime (Regt 500) through the
atmosphere. Small pyroclasts, lt1/16 mm (62 µm or
4 F), fall in laminar flow regime (Relt0.4).
Intermediate size particles are transitional.
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Particle Terminal Fall Velocity

• For large particles (Rep gt 500) inertial forces
  dominate

• For small particles (Rep lt 1)
• - viscous forces dominate

d particle diameter ?p particle density ?f
fluid density g acceleration due to
gravity Cd dimensionless drag coefficient
?p particle density g acceleration due to
gravity d particle diameter v kinematic
viscosity
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Fall of spherical particles in earths atmosphere
Schneider et al., 1999, J Geophys Res 104
4037-4050
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Particle Terminal Fall Velocity
Mean particle size at 330 km from MSH
(Ritzville, WA) was 20 microns Vt 0.2-0.4 ms-1
100 micron diameter particle has Vt of 4-7 ms-1
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Atmospheric Structure
Environmental parameters determined from the
radiosonde sounding taken at Spokane
International Airport at 1800 UTC on 18 May 1980.
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Bonadonna et al., 1998
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Bonadonna et al., 1998
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Bonadonna et al., 1998
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Bonadonna et al., 1998
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Bonadonna et al., 1998
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Bonadonna et al., 1998
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Bonadonna et al., 1998
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Bonadonna et al., 1998
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Figure 2 Typical stereo-pair taken at 8o tilt
angle.
Owen P Mills, MS thesis, Michigan Tech, 2007
    Figure 3. Digital elevation map produced
from stereo-pair in Figure 2.  
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Augustine ash P Izbekov

• Ash is NOT spherical!

Riley et al., 2003
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Riley et al., 2003
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Rose W I, C M Riley and S Dartevelle, 2003, J
Geology, 111115-124.
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Riley et al., 2003
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Riley et al., 2003
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Riley et al., 2003
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Riley et al., 2003
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Rose W I, C M Riley and S Dartevelle, 2003, J
Geology, 111115-124.
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Rose W I, C M Riley and S Dartevelle, 2003, J
Geology, 111115-124.
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Riley et al., 2003