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some models continuing fragmentation of the magma is
included in the model, but in others constant particle siz-
es are assumed. A model by Melnik et al (2002) includes
the following Flow regimes and boundaries:
Magma flow regime
Homogeneous from magma
chamber until gas saturation
pressure exceeds fluid pres-
sure.
Constant density, viscosity
and laminar velocity.
Bubble regime
Vesiculated magma from ho-
mogeneous till magma frag-
mentation.
Bubbles grow due to exsolu-
tion of the gas with fluid pres-
sure drop.
Velocity and viscosity in-
creases.
Flow is laminar with sharp
gradients before fragmenta-
tion due to viscous friction.
Fragmented flow regime (or surface).
Fragmentation criteria applied.
Gas-particle dispersive flowfrom fragmentation till level
to the vent.
Turbulent flow, velocities large and accelerating.
In steady flow, velocities are subsonic, in transient flow
supersonic.
Following assumptions are for the flow:
Magma, 3-phase system - melt, crystals and gas.
Viscous liquid, viscosity depends on concentrations of
dissolved gas and crystals.
Permeable flow through the magma.
Pressure difference between melt and bubbles is ac-
counted for.
Fragmentation happens when overpressure in the melt
reaches critical value.
2 particle sizes after fragmentation.
The equation system includes mass conservation, mo-
mentum balance, bubble growth, gas particle dispersion
and fragmentation wave conservation laws. With a shock
wave in the vent, this model gives the following approxi-
mative results for the ereuption discharge in the magma
chamber pressure range 80 - 230 Mpa.
Q (kg/sec) = 2997928 e0015248908 PP in MPa
The physical properties of the conduit are L = 8 km and
d = 50 m for conduit length and diameter in this model
result. Magma chamber temperature is T 850°C and ini-
tial water content 5,85%. In lceland this data would cor-
respond to an overburden pressure of 130 - 230 MPa.
Many other conduit models exist on eruptive conduit
flow with various degrees of sophistication. Vergniolle
and Jaupart, (1986), Dobran, (1992), Papale and Dobran,
(1993) (separated flow between magma and, gas), Pa-
pale and Dobran, (1993), (variations in viscosity, density,
and gas solubility with melt composition), Proussevitch
and Sahagian, (1998) (transient conduit flow) and Papale
(2001) (incomplete fragmentation).
A plume rise model
Many such models exist. Fig 2 shows an output screen
from one of the simpler ones. It is available free on the
internet. By close inspection of Fig. 2 all 3 phases of the
plume may be seen.
Fig 2. Screen from the Erupt3 plume model by Dr.
Ken Wohletz, LosAlamos National Laboratory; http:H
www.eesl 1 .lanl.gov/EES11 /Staff/Wohletz/wohletz.
html
Translatory floods from subglacial
eruptions
These floods, the jokelhlaups, are very dangerous, Elias-
son etal (2007). In order to estimate their strength, plume
models are very helpful. Take for instance the output from
the model by Melnik et al (2003), the range 107- 108 kg/
s of can create 50.000 - 500.000 m3/sec of meltwater.
Fig. 3 shows a computer simulation of a jokulhlaup
down the Markarfljot valley in lceland, Eliasson et al
(2007). The water discharge is 300.000 m3/sec. In the po-
sition shown the flood is best described as a wall of wa-
ter, travelling down the valley with a velocity of 20 m/s,
or 72 km/hour. The flood will devastate the valley com-
pletely. The lcelandic civil defense force has worked out a
major contingency plan to meet this catastrophe if it ever
occurs. The probability of this event is about 1 % in the
next 15 years Eliasson et al (2006)
Fig. 3 Acomputer simulation by Vatnaskil of the
jokulhlaup down Markarfljot.
References
Dobran, F., Nonequilibrium flow in volcanic conduits and appli-
cation to the eruptions of Mt. St. Helens on May 18, 1980, and
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