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STEADY EXPLOSIVE ERUPTIONS 89

will fall back to the ground surface in a continuous
stream forming a kind of enormous fountain over
the vent. This effect is usually referred to as col-
umn collapse, although it would be much better
described as column instability. The resulting sys-
tem can be thought of as similar to an ornamental r
water fountain, in which the rise of water above the
ground surface is driven purely by the initial high
speed at which the water is ejected. The rise of the
x
water droplets continues only until all their kinetic
energy is converted into potential energy, at which
point they must fall back to the ground. We refer
to the volcanic version as a pyroclastic fountain.

6.7.2 Causes of column instability
It appears that, in many cases, eruption plumes
in steady eruptions are initially stable but can, in
certain circumstances, become unstable at a later
Fig. 6.9 Diagram of a “control volume” used to relate the
stage. There are two main reasons why an eruption
flux of atmospheric gas entrained into an eruption plume
column might become unstable as the eruption to the flux of gas and pyroclasts already rising in the plume.
continues: the mass flux may increase significantly
or the exsolved gas content of the erupting magma
may decrease. gas–magma mixture has not entrained enough air
Take the increasing mass flux case first. The mass by the time it reaches the top of the gas-thrust re-
flux, M , is given by gion to be buoyant. In such a situation the eruption
f
plume will cease to be stable and will collapse. This
2
M = π r ρ u (6.10) effect can be seen in the example in Fig. 6.10a.
B
f
Here a Plinian eruption starts from a vent with a
where r is the vent radius, ρ is the bulk density of radius of ∼12 m. As the eruption continues the mass

B
the gas–magma mixture and u is the exit velocity of flux progressively increases as erosion widens the
the gas–magma mixture. Thus the mass flux is pro- vent, and the plume height also increases because
2
portional to r . As the gas–magma mixture emerges more heat is being provided to the plume (see
from the vent it begins to entrain air around its section 6.5.2). Eventually a point is reached, in this
margins. The surface area, A, over which air can be case when the vent radius reaches ∼350 m, where
entrained is the mass flux has become so great that not enough
entrainment can occur to allow the plume to be-
A = 2 π rx (6.11) come thermally buoyant. The initially stable Plinian
eruption plume then collapses from its peak height
where x is the vertical distance moved by the gas jet of ∼40 km and a pyroclastic fountain forms over
in one second (Fig. 6.9). Thus the surface area over the vent. The fountain is driven solely by the initial
which air can be entrained is proportional to the momentum of the erupted material, and so is less
vent radius. Because the increasing mass flux of than 10 km in height (Fig. 6.10a).
volcanic material gets larger in proportion to r 2 We saw in eqn 6.2 and Table 6.4 that the bulk
whereas the amount of surrounding atmosphere density of the gas–magma mixture depends on the
entrained only increases in proportion to r, entrain- amount of gas exsolved from the magma and, there-
ment does not keep pace with the increasing mass fore, the initial gas content of the magma. Thus, if
flux. So, a situation may be reached in which the the gas content of the erupting magma decreases