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Particle Fall through the atmosphere. Lecture #5 Ashfall Class 2009. Distance d travelled by an object falling for time t : . Time t taken for an object to fall distance d : . Instantaneous velocity v i of a falling object after elapsed time t : .

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Particle fall through the atmosphere

Particle Fall through the atmosphere

Lecture #5

Ashfall Class 2009


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


Particle fallout
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).


Reynolds number re
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 < 0.4,

  • intermediate where 0.4 < Re < 500, and

  • turbulent where Re > 500.


RN =dvt/

Medium and small pyroclasts

Fast-falling Large Pyroclasts

D = 1mm

D = 1µm

.01 cm/s

10 m/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…


Conventional wisdom particle settling
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:

> 500 turbulent

1-500 transitional

<1 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


Larger pyroclasts, those >2mm in diameter, fall in a turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.


Particle terminal fall velocity
Particle Terminal Fall Velocity turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.

  • For large particles (Rep > 500) – inertial forces dominate:

  • For small particles(Rep< 1)

    -viscous forces dominate:

d = particle diameter

ρp = particle density

ρf = fluid density

g = acceleration due to gravity

Cd = dimensionless drag coefficient

ρp = particle density

g = acceleration due to gravity

d = particle diameter

v = kinematic viscosity


Fall of spherical particles in earth s atmosphere
Fall of spherical particles in earth’s atmosphere turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.

Schneider et al., 1999, J Geophys Res 104 4037-4050


Particle terminal fall velocity1
Particle Terminal Fall Velocity turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.

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


Atmospheric structure
Atmospheric Structure turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.

Environmental parameters determined from the radiosonde sounding taken at Spokane International Airport at 1800 UTC on 18 May 1980.


Bonadonna et al., 1998 turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.


Bonadonna et al., 1998 turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.


Bonadonna et al., 1998 turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.


Bonadonna et al., 1998 turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.


Bonadonna et al., 1998 turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.


Bonadonna et al., 1998 turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.


Bonadonna et al., 1998 turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.


Bonadonna et al., 1998 turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.


Figure 2 Typical stereo-pair taken at 8 turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional. o tilt angle.

Owen P Mills, MS thesis, Michigan Tech, 2007

Figure 3. Digital elevation map produced from stereo-pair in Figure 2.


Ash is not spherical

Augustine ash P Izbekov turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.

Ash is NOT spherical!

Riley et al., 2003


Riley turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional. et al., 2003


Rose W I, C M Riley and S Dartevelle, 2003, turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional. J Geology, 111:115-124.


Riley turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional. et al., 2003


Riley turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional. et al., 2003


Riley turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional. et al., 2003


Riley turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional. et al., 2003


Rose W I, C M Riley and S Dartevelle, 2003, turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional. J Geology, 111:115-124.


Rose W I, C M Riley and S Dartevelle, 2003, turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional. J Geology, 111:115-124.


Riley turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional. et al., 2003


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