Page 121 - Fundamentals of Physical Volcanology

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98 CHAPTER 7

Large blocks
start to follow
ballistic trajectories

Expansion
phase

Fig. 7.2 Diagram showing the
progressive fragmentation and
dispersal of the material originally
Vent plug
forming a plug in the vent as the
compressed trapped gas is released
by the explosion and expands and
accelerates. (Adapted from fig. 1
published in Icarus, Vol. 123, Fagents,
S.A. and Wilson, L., Numerical
modelling of ejecta dispersal from
transient volcanic explosions on Mars,
284–295, copyright Elsevier (1996).)

point of view it is useful to extend the model to These blocks now experience air drag in the nor-

predict the range of clasts ejected in transient mal way and this has to be taken into account in
explosions. To do this we need first to visualize order to work out the maximum distance to which
what happens during these explosions. they can be thrown. We make the analysis a bit eas-
During the initial phase of the explosion the ier by imagining that the blocks are spheres. The
gas is expanding and the gas and clasts making up drag force, F , acting on a sphere of radius R mov-
d
the ejected material move upwards and outwards ing at a high speed U through a gas of density ρ is
a
from the explosion point as a single mass (Fig. 7.2).
2
Towards the end of the gas expansion process, F = 0.5 ρ C π R U 2 (7.2)
d a d
however, the sharp boundary between the atmo-
sphere and the ejected material breaks down. Gas where C is a dimensionless number called the drag
d
from the explosion mixes with air and slows down coefficient and has a value between about 0.5 and
rapidly, and the smallest solid particles, which suf- 1.3 for real blocks depending on their shape and
fer a very large drag force from the gas, also slow roughness (and even on whether they are spinning
down. These particles share their heat with the air or not!) – an average value of 0.7 is used here. A sec-
and warm it up, so that a convecting eruption col- ond force acts on the block, its weight – gravity
umn forms – this is discussed in the next section. pulls it downward toward the Earth’s surface. The
Meanwhile the larger blocks of solid material carry gravitational force F acting on a block of density ρ
g b
on moving at high speed. and radius R is given by