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STEADY EXPLOSIVE ERUPTIONS 87

Table 6.3 The terminal velocity, U , is given for three clasts fixed height above the surface while smaller parti-
T
of different sizes. These values were calculated from eqn 6.9 cles continue to stream upwards past it.
assuming clast and gas densities of 1000 and 0.5 kg m −3
respectively and a drag coefficient of 1.0. If the gas stream
in which the clasts are moving has an upward velocity of 6.6.2 Fallout of clasts from eruption plumes
−1
160ms then the net upward velocity (relative to the
Section 6.5 showed that the upward velocity of the
ground surface) of the clasts is (160 − U ).
T
plume decreases with height. Figure 6.8 shows two
−1
−1
Radius (m) U (m s ) Net upward velocity (m s ) examples of the variation in rise speed with height.
T
In each case the velocity is highest as the gas stream
0.02 30 130 exits the vent and then declines rapidly in the gas-
0.15 90 70
thrust region. The velocity remains fairly constant
0.48 160 0
through much of the convective region before
declining rapidly near the top of the plume
(Fig. 6.8). This variation in upward velocity of the
force exerted on the clast by the gas stream through gas in the plume has important implications for the
which it is moving. In practice a balance is reached fallout of clasts from it. Consider again the largest
between these two forces, and for a spherical clast clast in Table 6.3. This clast has been carried
this can be written: upward through a region in which the gas speed
−1
exceeded 160 m s . As the plume rises and its
1 π d σ g = 1 C ρ π d U 2 (6.8)
2
3
6 8 D g T
0 100 200 300 400
Gravity Drag 25 25
where d is the diameter of the clast, σ and ρ are
g 20 F 20
the densities of the clast and gas respectively, g is
the acceleration due to gravity, C is the drag D
D
coefficient and U is the terminal velocity of the 15 15
T
clast relative to the gas. Thus the terminal velocity, Height (km)
U , of the clast in the gas stream is E
T
10 1 10
U = 4 d σ g (6.9)
T 3 C ρ
D g 5 2 5
B
C
For a given clast density, eqn 6.9 shows that the A
bigger the clast, the greater the speed at which it 0 0
falls through the gas stream. The speed of the clast 0 100 200 300 400
–1
relative to the ground is, of course, its downward Eruption plume rise speed (m s )
speed through the gas plus the upward speed of the
Fig. 6.8 Two examples of the variation of eruption plume
gas relative to the ground. This just means that it is rise speed with height. The velocity is always highest as
harder for the gas stream to drag a large clast up the gas stream leaves the vent and then decreases rapidly
with it than it is to drag a smaller clast. This effect is through the gas-thrust region. The speed decreases slowly
shown by the example in Table 6.3, which demon- through much of the convective region before declining
rapidly towards the top of the plume. (Adapted from fig.
strates that the smallest clasts are carried upward at
5(b) in Wilson, L. & Walker, G.P.L. (1987) Explosive
the greatest velocity relative to the ground surface.
volcanic eruptions – VI. Ejecta dispersal in plinian
The largest clast in Table 6.3 has a terminal velocity
eruptions: the control of eruption conditions and
which exactly equals the velocity of the gas stream atmospheric properties. Geophys. J. Roy. Astron. Soc. 89,
and is thus suspended in the eruption plume at a 657–679, copyright Wiley-Blackwell Publishing Ltd.)