Page 129 - Fundamentals of Physical Volcanology

9780632054435_4_008.qxd 12/10/2007 12:29PM Page 106

106 CHAPTER 8

Fig. 8.2 A Plinian eruption cloud
viewed obliquely from a direction
at right-angles to the direction of the
wind. A clast released from the edge
of the cloud is carried downwind from
its release point and travels a distance
that depends on the wind speed and
its terminal fall velocity.

entrainment in the gas-thrust region is dominated mass flux) can be used to predict the shape of the
by momentum transfer, and an analysis by a pioneer eruption column and the height to which a clast of
of fluid mechanics named Prandtl showed that this a given size and density will be carried. Then if the
should cause the edge of the eruption column to speed at which the clast will fall and the speed of
expand at a rate of one unit sideways for every eight the wind are known, it is possible to predict where
units of height gained. This pattern is close to what on the ground any given clast should land (Fig. 8.2).
has been seen in historic eruptions, especially if an The smaller the clast, the greater the height to
allowance is made for the fact that the bulk density which it is carried above the vent and thus, because
of the erupting jet of clasts and volcanic gas is the column expands with height, the greater the
greater than the density of the surrounding atmo- cross-wind distance it will land from the vent; also,

sphere. Higher up the eruption column, as discussed the greater the wind speed, the greater the down-
in Chapter 6, things become more complicated wind distance it will land. This description suggests
due to the expansion of entrained air, as a result of that there should be a unique relationship between
both heating by pyroclasts and the decreasing atmo- clast size and position in the final deposit. Unfor-
spheric pressure. The spreading rate increases, and tunately things are a little more complicated,
as a general approximation one can think of the because at any given height in an eruption column
lateral expansion rate as being 1 in 8 for the first a range of particle sizes will be released. The largest
quarter of the plume height, 1 in 4 for the second clast will, of course, be the one that is just sup-
quarter, 1 in 2 for the third quarter, and 1 in 1, i.e., ported in the column by the rising gases at that
a spreading angle of 45° from the vertical, near the height; but there will also be many smaller clasts
start of the umbrella region (Fig. 8.1). that would normally be carried to greater heights
A clast will only fall out from the eruption col- but that happen to be moved by turbulence to the
umn if it is carried to the edge of the column. Once edge of the column where the upward velocity is
it is released, it will be carried along by the wind, much smaller as the column grades into the bulk of
but this will only move it in the direction of the the atmosphere, and some of these smaller clasts
wind. Using the theoretical models of eruption will be released as well. This means that at every
cloud development described in Chapter 6, the erup- location a pyroclastic fall deposit will contain a
tion conditions (magma gas content and erupted range of grain sizes.