×

zbMATH — the first resource for mathematics

A mathematical model of magma transport in the asthenosphere. (English) Zbl 0568.76100
We present a mathematical model for the flow of a partial melt through its solid phase. The model is based on the conservation laws of two-phase flow, which reduce to a generalization of porous flow in a permeable medium, when the solid matrix deforms very slowly. The continuity equation for the melt contains a source term (due to melting), which is determined by the energy equation. In addition, the melt fraction is unknown, and a new equation, representing conservation of pore space, is introduced. This equation may also be thought of as a constitutive law for the melt pressure (which is not lithostatic).

MSC:
76T99 Multiphase and multicomponent flows
86A99 Geophysics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ahern J. L., Earth & Planet. Sci. Lett. 45 pp 115– (1979) · doi:10.1016/0012-821X(79)90113-4
[2] Anderson O. L., Rev. Geophys. & Space Phys. 15 pp 77– (1977) · doi:10.1029/RG015i001p00077
[3] Angevine C. L., EOS 65 pp 273– (1984)
[4] Barnes P., Nature 210 pp 878– (1966) · doi:10.1038/210878a0
[5] Batchelor G. K., An Introduction to Fluid Dynamics (1967) · Zbl 0152.44402
[6] Carrigan C. R., J. Volcanol. Geotherm. Res. 16 pp 279– (1983) · doi:10.1016/0377-0273(83)90034-3
[7] Drew D. A., Annu. Rev. Fluid Mech. 15 pp 261– (1983) · doi:10.1146/annurev.fl.15.010183.001401
[8] Duval P., IAHS Publ. 118 pp 29– (1977)
[9] Elliott C. M., Weak and Variational Methods for Moving Boundary Problems (1982) · Zbl 0476.35080
[10] Fleitout L., EOS 65 pp 272– (1984)
[11] Fowler A. C., Phys. Earth & Planet. Inter. 31 pp 83– (1983) · doi:10.1016/0031-9201(83)90069-9
[12] Fowler A. C., Geophys. & Astrophys. Fluid Dyn. 29 pp 99– (1984) · Zbl 0616.76118 · doi:10.1080/03091928408222846
[13] Frank F. C., Nature 220 pp 350– (1968) · doi:10.1038/220350a0
[14] Hills R. N., Q. J. Mech. Appl. Math. 36 pp 505– (1983) · Zbl 0549.73002 · doi:10.1093/qjmam/36.4.505
[15] Hubbert M. K., Bull. Geol. Soc. Am. 70 pp 115– (1959) · doi:10.1130/0016-7606(1959)70[115:ROFPIM]2.0.CO;2
[16] Ishii M., Thermo-fluid Dynamic Theory of Two-phase Flow (1975) · Zbl 0325.76135
[17] Kamb W. B., J. Geophys. Res. 66 pp 259– (1961) · doi:10.1029/JZ066i001p00259
[18] Kirby S. H., Rev. Geophys. & Space Phys. 21 pp 1458– (1983) · doi:10.1029/RG021i006p01458
[19] Kynch G. I., Trans. Farad. Soc. 48 pp 166– (1952) · doi:10.1039/tf9524800166
[20] Lacey A. A., IMA J. Appl. Math. 30 pp 303– (1983) · Zbl 0531.35076 · doi:10.1093/imamat/30.3.303
[21] La Chapelle E., J. Glacial. 7 pp 183– (1968)
[22] Marsh B. D., Philos. Trans. R. Soc. 288 pp 611– (1978) · doi:10.1098/rsta.1978.0037
[23] McKenzie D. P., J. Petrol. 25 pp 713– (1984) · doi:10.1093/petrology/25.3.713
[24] Morris S., J. Fluid Mech. 124 pp 1– (1982) · Zbl 0514.76023 · doi:10.1017/S0022112082002389
[25] Nye J. F., Proc. R. Soc. London 219 pp 477– (1953) · doi:10.1098/rspa.1953.0161
[26] Nye J. F., J. Glacial. 17 pp 181– (1976)
[27] Nye J. F., Hydrology of the intergranular veins in a temperature glacier pp 157– (1969)
[28] Ribe N. M., J. Volcanol. Geotherm. Res. 16 pp 221– (1983) · doi:10.1016/0377-0273(83)90031-8
[29] Rubenstein L., Control Cybernet. 10 pp 187– (1981)
[30] Rudnicki J. W., Ann. Rev. Earth & Planet. Set. 8 pp 489– (1980) · doi:10.1146/annurev.ea.08.050180.002421
[31] Scott D. R., Geophys. Res. Lett. 11 pp 1161– (1984) · doi:10.1029/GL011i011p01161
[32] Scott D. R., EOS 64 pp 849– (1983)
[33] Shankland T. J., Rev. Geophys. & Space Phys. 19 pp 394– (1981) · doi:10.1029/RG019i003p00394
[34] Shaw H. R., Physics of Magmatic Processes pp 201– (1980)
[35] Spence D. A., EOS 65 pp 273– (1984)
[36] Spence D. A., J. Geophys. Res. 90 pp 575– (1985) · doi:10.1029/JB090iB01p00575
[37] Stevenson D. J., Proc. 13th Lunar Planet. Sci. Conf. pp 768– (1982)
[38] Thompson J., Proc. R. Soc. 11 pp 473– (1860)
[39] Turcotte D. L., J. Volcanol. Geotherm. Res. 10 pp 267– (1981) · doi:10.1016/0377-0273(81)90079-2
[40] Turcotte D. L., J. Geophys. Res. 83 pp 767– (1978) · doi:10.1029/JB083iB02p00767
[41] Weertman J., J. Geophys. Res. 76 pp 1171– (1971) · doi:10.1029/JB076i005p01171
[42] Weertman J., J. Geophys. Res. 76 pp 8544– (1971) · doi:10.1029/JB076i035p08544
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.