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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - A. A. Barmin
AU  - O. E. Melnik
AU  - E. A. Vedeneeva
AU  - Yu. D. Tsvetkova
TI  - Effect of crystallization, heat exchange, and viscous dissipation on the dynamics of extrusive eruptions
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2013
SP  - 127
EP  - 136
VL  - 281
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2013_281_a9/
LA  - ru
ID  - TM_2013_281_a9
ER  - 
%0 Journal Article
%A A. A. Barmin
%A O. E. Melnik
%A E. A. Vedeneeva
%A Yu. D. Tsvetkova
%T Effect of crystallization, heat exchange, and viscous dissipation on the dynamics of extrusive eruptions
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2013
%P 127-136
%V 281
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2013_281_a9/
%G ru
%F TM_2013_281_a9
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/

[1] Cashman K.V., Blundy J., “Degassing and crystallization of ascending andesite and dacite”, Philos. Trans. R. Soc. London A, 358:1770 (2000), 1487–1513 | DOI

[2] Nakada S., Motomura Y., “Petrology of the 1991–1995 eruption at Unzen: effusion pulsation and groundmass crystallization”, J. Volcanol. Geotherm. Res., 89 (1999), 173–196 | DOI

[3] Slezin Yu.B., “Dinamika dispersionnogo rezhima vulkanicheskikh izverzhenii. 1: Teoreticheskoe opisanie dvizheniya magmy v kanale vulkana”, Vulkanologiya i seismologiya, 1983, no. 5, 9–17

[4] Slezin Yu.B., “Dinamika dispersionnogo rezhima vulkanicheskikh izverzhenii. 2: Uslovie neustoichivosti raskhoda i priroda katastroficheskikh eksplozivnykh izverzhenii”, Vulkanologiya i seismologiya, 1984, no. 1, 23–35

[5] Wilson L., “Relationships between pressure, volatile content and ejecta velocity in three types of volcanic explosion”, J. Volcanol. Geotherm. Res., 8 (1980), 297–313 | DOI

[6] Wilson L., Sparks R.S.J., Walker G.P.L., “Explosive volcanic eruptions. IV: The control of magma properties and conduit geometry on eruption column behaviour”, Geophys. J. R. Astron. Sos., 63:1 (1980), 117–148 | DOI

[7] Barmin A., Melnik O., Sparks R.S.J., “Periodic behavior in lava dome eruptions”, Earth Planet. Sci. Lett., 199 (2002), 173–184 | DOI

[8] Lejeune A.-M., Richet P., “Rheology of crystal-bearing silicate melts: An experimental study at high viscosities”, J. Geophys. Res., 100 (1995), 4215–4229 | DOI

[9] Melnik O., “Dynamics of two-phase conduit flow of high-viscosity gas-saturated magma: Large variations of sustained explosive eruption intensity”, Bull. Volcanol., 62 (2000), 153–170 | DOI

[10] Woods A.W., Koyaguchi T., “Transitions between explosive and effusive eruptions of silicic magmas”, Nature, 370 (1994), 641–644 | DOI

[11] Swanson D.A., Holcomb R.T., “Regularities in growth of the Mount St. Helens dacite dome, 1980–1986”, Lava flows and domes: Emplacement mechanisms and hazard implications, eds. J.H. Fink, Springer, Berlin, 1990, 3–24 | DOI

[12] Harris A.J.L., Rose W.I., Flynn L.P., “Temporal trends in lava dome extrusion at Santiaguito 1922–2000”, Bull. Volcanol., 65 (2003), 77–89

[13] Melnik O.E., “Nestatsionarnaya model dinamiki vulkanicheskogo izverzheniya s uchetom kristallizatsii i filtratsii gaza cherez magmu”, DAN, 377:5 (2001), 629–633

[14] Costa A., Melnik O., Sparks R.S.J., “Controls of conduit geometry and wallrock elasticity on lava dome eruptions”, Earth Planet. Sci. Lett., 260 (2007), 137–151 | DOI

[15] Hort M., “Abrupt change in magma liquidus temperature because of volatile loss or magma mixing: effects of nucleation, crystal growth and thermal history of the magma”, J. Petrol., 39:5 (1998), 1063–1076 | DOI

[16] Muskhelishvili N.I., Nekotorye osnovnye zadachi matematicheskoi teorii uprugosti: Osnovnye uravneniya. Ploskaya teoriya uprugosti. Kruchenie i izgib, Izd-vo AN SSSR, M., 1954 | MR | Zbl

[17] Elsworth D., Mattioli G., Taron J., Voight B., Herd R., “Implications of magma transfer between multiple reservoirs on eruption cycling”, Science., 322:5899 (2008), 246–248 | DOI

[18] Costa A., Melnik O., Vedeneeva E., “Thermal effects during magma ascent in conduits”, J. Geophys. Res. B, 112 (2007), 12205 | DOI

[19] Tsvetkova Yu.D., “Techenie magmy v kanale vulkana s uchetom neravnovesnoi kristallizatsii i teploobmena s okruzhayuschimi porodami”, Izv. RAN. Mekhanika zhidkosti i gaza, 2010, no. 5, 30–40 | Zbl