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8/10/2019 Particle fall throught the atmosphere
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Particle Fall through theatmosphere
Lecture #5
Ashfall Class 2009
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Distance dtravelled by an object falling for
time t:
Time ttaken for an object to fall distance d:
Instantaneous velocity viof a falling object
after elapsed time t:
Instantaneous velocity viof a falling object
that has travelled distance d:
Average velocity vaof an object that has
been falling for time t(averaged over time):
Average velocity vaof a falling object that
has travelled distance d(averaged overtime):
use g= 9.8 m/s(metres per second squared; which might be thought
of as "metres per second, per second. Assuming SI units, gis measured
in metres per second squared, so dmust be measured in metres, tin
seconds and vin metres per second.
air resistance is neglected--- quite inaccurate after only 5 seconds
http://en.wikipedia.org/wiki/International_System_of_Unitshttp://en.wikipedia.org/wiki/International_System_of_Units8/10/2019 Particle fall throught the atmosphere
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Particle Fallout
After a very short time, ~4 seconds, particles
will reach a terminal velocityin 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).
http://hyperphysics.phy-astr.gsu.edu/hbase/airfri2.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/airfri2.html8/10/2019 Particle fall throught the atmosphere
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Reynolds Number
Re
Reynolds number is a dimensionless number(i.e. it has no units) that is a measure of thetype of flow through a fluid. In the case of
falling particles, this describes the way that airflows around the particle. There are threebasic types:
laminarwhere Re < 0.4,
intermediate where 0.4 < Re < 500, and
turbulent where Re > 500.
http://www-pgss.mcs.cmu.edu/Publications/Volume16/physics/Turb/Turb-II.htmlhttp://www-pgss.mcs.cmu.edu/Publications/Volume16/physics/Turb/Turb-II.htmlhttp://www-pgss.mcs.cmu.edu/Publications/Volume16/physics/Turb/Turb-II.htmlhttp://www-pgss.mcs.cmu.edu/Publications/Volume16/physics/Turb/Turb-II.html8/10/2019 Particle fall throught the atmosphere
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Laminar flow;
RN = 10-2Turbulent flow;
RN = 106RN = 20 RN = 40 RN = 104
Fast-falling
Large
Pyroclasts
Fluid dynamics applies dimensionless analysis of fall of spheres in the
atmosphere, which shows that experience with large pyroclasts might not applyto smaller ones which fall much more slowly
RN =dvt/
Medium and
small pyroclasts
10
m/s
D =
1mmD =1m
.01
cm/
s
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8
Conventional Wisdom:
Particle Settling
particle accelerates due to gravity
Drag force:
(i) viscous drag(friction betweenthe fluid and the
particle surface)(ii) form drag(inertial forcecaused by theacceleration offluid around theparticle as it falls)
Particle Reynoldsnumber, Rep:
ratio of inertial forceto viscous force perunit mass
Rep= Vtd/ v
Vt= particle terminal
fall velocity;d= particle diameter;v= fluid kinematic viscosity
Rep:
> 500 turbulent
1-500 transitional
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Larger pyroclasts,
those >2mm in
diameter, fall in aturbulent flow
regime (Re> 500)
through the
atmosphere. Smallpyroclasts,
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10
Particle Terminal Fall Velocity
For large particles (Rep> 500)
inertial forces dominate:
fd
fp
CgdtV
)(34
d = particle diameter
p= particle density
f= fluid density
g = acceleration due to gravity
Cd= dimensionless drag coefficient
For small particles(Rep< 1)-viscous forces dominate:
18
2
gdV pt
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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12
Particle Terminal Fall Velocity
100 microndiameter
particle hasVtof ~4-7
ms-1
Mean particle sizeat ~330 km fromMSH (Ritzville,WA) was 20
microns; Vt~0.2-
0.4 ms-1
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13
Atmospheric Structure
Environmental parameters determined from the radiosonde sounding takenat 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 3. Digital elevation map produced from stereo-pair in Figure 2.
Figure 2 Typical stereo-pair taken at 8otilt angle.
Owen P Mills, MSthesis, Michigan Tech,
2007
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Ash is NOT
spherical!
Riley et al., 2003
Augustine ash P Izbekov
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Riley et al., 2003
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Rose W I, C M Riley and S Dartevelle, 2003, J Geology, 111:115-124.
http://www.geo.mtu.edu/~raman/papers/Nebraska.pdfhttp://www.geo.mtu.edu/~raman/papers/Nebraska.pdfhttp://www.geo.mtu.edu/~raman/papers/Nebraska.pdfhttp://www.geo.mtu.edu/~raman/papers/Nebraska.pdf8/10/2019 Particle fall throught the atmosphere
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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, 111:115-124.
http://www.geo.mtu.edu/~raman/papers/Nebraska.pdfhttp://www.geo.mtu.edu/~raman/papers/Nebraska.pdfhttp://www.geo.mtu.edu/~raman/papers/Nebraska.pdfhttp://www.geo.mtu.edu/~raman/papers/Nebraska.pdf8/10/2019 Particle fall throught the atmosphere
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Rose W I, C M Riley and S Dartevelle, 2003, J Geology, 111:115-124.
http://www.geo.mtu.edu/~raman/papers/Nebraska.pdfhttp://www.geo.mtu.edu/~raman/papers/Nebraska.pdfhttp://www.geo.mtu.edu/~raman/papers/Nebraska.pdfhttp://www.geo.mtu.edu/~raman/papers/Nebraska.pdf8/10/2019 Particle fall throught the atmosphere
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Riley et al., 2003