Open AccessA mathematical model of vulcanian eruptions
Author(s) -
Turcotte D. L.,
Ockendon H.,
Ockendon J. R.,
Cowley S. J.
Publication year - 1990
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1990.tb01763.x
Subject(s) - volcano , magma , geology , explosive eruption , vulcanian eruption , explosive material , constant (computer programming) , mass fraction , petrology , vapours , thermodynamics , mineralogy , geophysics , mechanics , seismology , chemistry , physics , organic chemistry , computer science , programming language , neuroscience , biology
SUMMARY The problem of an expansion wave propagating into a saturated magma is solved and used as a model of a vulcanian eruption. In our model for an explosive eruption we assume that a drop in pressure leads to the exsolution of magmatic volatiles. Initially the exsolved vapours create bubbles in the magma. We model the subsequent part of the exsolution process in which a foam is created; this is believed to be an essential feature of explosive volcanic eruptions. The foam also has the advantage that it can be modelled as a mixture or ‘pseudo‐gas’ without slippage between the phases. Eventually the foam breaks up and becomes volcanic ash. Assuming that the exsolution of vapour is given by Henry's law, that the temperature is constant, that the magma and vapour have equal velocities, and neglecting wall friction and gravitational effects, an analytic solution for pressure, velocity, and vapour fraction is obtained for the expanding mixture in a constant area duct. The exit velocity u for the mixture is u = (ø 0 RT 0 ) 1/2 In( P 0 / p ), where ø 0 is the original mass fraction of dissolved vapour, R is the gas constant for the vapour, T 0 the constant temperature, and p 0 / p the pressure ratio across the expansion. With ø 0 = 1 per cent, T 0 = 1000°K, and p 0 / p = 100 we find u 0 = 300ms ‐1 , consistent with observations for vulcanian eruptions.