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Large volcanic plumes
Introduction
Volcanic plumes are a hydrodynam-
ic phenomenon of great complexity.
In general a plume, volcanic or not,
has 3 phases: Jet Phase is dominat-
ed by upward momentum, Convec-
tive Phase is where the plume rises
by buoyant convection and Umbrel-
la Phase is where the plume spreads
out. In the jet phase the momen-
tum of the emitted mixture is the
governing force. In the buoyant
convection phase the momentum
has become constant and it is the
relative density difference between
the plume and the ambient air that
controls the upward flow. While in
the umbrella phase this density dif-
ference has become zero, a mush-
room cloud has formed and the
spreading of this cloud is controled
by the inflow from below.
In volcanic plumes the process is much more complex.
The velocity of the emitted mixture may be supersonic,
this causes an immediate expansion, large loss of kinetic
energy and temperature drop in the plume. Once in the
air, the heavier components of the mixture are subjected
to negative boyancy and will tend to be seperated from
the plume, especially through the boundary layer to the
ambient air. When this seperation phase is most active,
the center column of the plume will grow less dense and
flow faster because of increased boyancy. Eventually, is-
entropic cooling in the center will neutralise the boyancy
forces, but then the plume may have reached the incred-
ible height of 80 km. Plume heights 15 - 30 km are com-
mon when great volcanoes erupt.
The plume is a mixture of particles and gases emitted
by an eruption. In order to estimate the parameters of
the plume, particle concentration and gas flow, one has
to start deep down in the ground where the molten mag-
ma is, that is the only place where appropriate boundary
conditions can be found. Then
there may be 2 or 3 critical sections
on the flowpath up the tube, the
first one where the volcanic gas
flow has fragmented the magma
and gets supersonic due to expan-
sion, just as gas flow in a pipe. The
next critical section may come if the
temperature suddenly drops due to
intruding water, the flow becomes
subsonic just after the intrusion and
later supersonic due to expansion
as before. Then there is a normal
shock when the plume exits the
vent as a jet into the ambient air.
Here at last we can estimate the
properties of the plume. The veloc-
ity through the shock is indepen-
dent of the atmospheric pressure,
but when the flow is subsonic,
there is no shock wave and the ve-
locity depends on the pressure gradient in the conduit.
This process is much too complex to treat in an analyti-
cal manner. There exists however a number of numerical
models to deal with the plume problem. Experience
shows that the magma fragmentation process and the
flow resistance in the conduit have to be included. The
models can therefore be divided in two categories, con-
duit models and plume models.
Conduit models
A model that might fit lcelandic volcanoes where there is
no water influx into the conduit during the eruption may
look somthing like fig. 1. Here the flow into the conduit
starts from a magma chamber where the pressure, tem-
perature and the mechanical properties of the magma
are assumed known. First the gas is only bubbles released
from the magma and they travel with the same velocity
as the magma. Due to decreasing conduit pressure in the
upwards flow the magma will fragment and from here
the gas flows much faster than the magma fragments. In
Jónas Elíasson, Ph. D.
Prófessor við Umhverfis- og
byggingarverkfræðiskor
Háskóla íslands.
Fræðasvið: Straumfræði, vatnafræði,
umhverfisverkfræði
Þ. Þorgrímsson & Co
Byggingavöruverslun

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