Geodesic
Effect of crystallization, heat exchange, and viscous dissipation on the dynamics of extrusive eruptions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 281 (2013), pp. 127-136

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The paper surveys mathematical models of magma flow in a volcanic conduit in the case of extrusive (nonexplosive) eruption that were developed in the group of dynamic volcanology at the Institute of Mechanics, Moscow State University, under the supervision of Professor A. A. Barmin. In the quasi-one-dimensional and two-dimensional formulations, the effect of crystallization, heat exchange, and viscous dissipation on the relationship between the magma discharge rate and the pressure difference between the magma chamber and atmosphere is analyzed. It is shown that there exist several steady-state solutions of the boundary value problem that differ in discharge rates by orders of magnitude. A transition between steady-state solutions may lead to cyclic variations in the magma discharge rate. Limitations of the hydraulic approach, which is based on the parameters averaged over the cross-section of a volcanic conduit, are revealed. 
@article{TM_2013_281_a9,
     author = {A. A. Barmin and O. E. Melnik and E. A. Vedeneeva and Yu. D. Tsvetkova},
     title = {Effect of crystallization, heat exchange, and viscous dissipation on the dynamics of extrusive eruptions},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {127--136},
     publisher = {mathdoc},
     volume = {281},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2013_281_a9/}
}
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A. A. Barmin; O. E. Melnik; E. A. Vedeneeva; Yu. D. Tsvetkova. Effect of crystallization, heat exchange, and viscous dissipation on the dynamics of extrusive eruptions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 281 (2013), pp. 127-136. http://geodesic.mathdoc.fr/item/TM_2013_281_a9/