Abstract
The behaviour of a lava flow is reproduced by a two-dimensional model of a Bingham liquid flowing down a uniform slope. Such a liquid is described by two rheological parameters, yield stress and viscosity, both of which are strongly temperature-dependent. Assuming a flow rate and an initial temperature of the liquid at the eruption vent, the temperature decrease due to heat radiation and the consequent change in the rheological parameters are computed along the flow. Both full thermal mixing and thermal unmixing are considered. The equations of motion are solved analytically in the approximation of a slow downslope change of the flow parameters. Flow height and velocity are obtained as functions of the distance from the eruption vent; the time required for a liquid element to reach a certain distance from the vent is also computed. The gross features of observed lava flows are reproduced by the model which allows us to estimate the sensitivity of flow dynamics to changes in the initial conditions, ground slope and rheological parameters. A pronounced increase in the rate of height increase and velocity decrease is found when the flow enters the Bingham regime. The results confirm the observation according to which lava flows show an initial rapid advance, followed by a marked deceleration, while the final length of a flow is such that the Graetz number is in the order of a few hundreds.
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References
Archambault C, Tanguy JC (1976) Comparative temperature measurements on Mount Etna lavas: problems and techniques. J Volcanol Geotherm Res 1:113–125
Baloga S, Pieri D (1986) Time-dependent profiles of lava flows. J Geophys Res 91:9543–9552
Borgia A, Linneman S, Spencer D, Morales LD, Andre JB (1983) Dynamics of lava flow fronts, Arenal Volcano, Costa Rica. J Volcanol Geotherm Res 19:303–329
Daneš ZF (1972) Dynamics of lava flows. J Geophys Res 77:1430–1432
Dragoni M, Bonafede M, Boschi E (1986) Downslope flow models of a Bingham liquid: implications for lava flows. J Volcanol Geotherm Res 30:305–325
Emerman SH, Turcotte DL (1983) A fluid model for the shape of accretionary wedges. Earth Planet Sci Lett 63:379–384
Hulme G (1974) The interpretation of lava flow morphology. Geophys JR Astr Soc 39:361–383
Hulme G (1982) A review of lava flow processes related to the formation of lunar sinuous rilles. Geophys Surv 5:245–279
Hulme G, Fielder G (1977) Effusion rates and rheology of lunar lavas. Phil Trans R Soc A285:227–234
Huppert HE (1982) Flow and instability of a viscous current down a slope. Nature 300:427–429
Johnson AM (1970) Physical processes in geology. Freeman-Cooper, San Francisco
Johnson AM, Pollard DD (1973) Mechanics of growth of some laccolithic intrusions in the Henry Mountains, Utah, I. Tectonophysics 18:261–309
Landau L, Lifchitz E (1971) Méchanique des fluides. Éditions MIR, Moscow, pp 670
Lockwood JP, Banks NG, English TT, Greenland LP, Jackson DB, Johnson DJ, Koyanagi RY, McGee KA, Okamura AT, Rhodes JM (1985) The 1984 eruption of Mauna Loa Volcano, Hawaii. Eos 66:169–171
Malin MC (1980) Lengths of Hawaiian lava flows. Geology 8:306–308
McBirney AR, Murase T (1984) Rheological properties of magmas. Ann Rev Earth Planet Sci 12:337–357
McBirney AR, Noyes RM (1979) Crystallization layering of the Skaergaard intrusion. J Petrol 20:487–554
Murase T, McBirney AR (1970) Viscosity of lunar lavas. Science 167:1491–1493
Park S, Iversen JD (1984) Dynamics of lava flow: thickness growth characteristics of steady two-dimensional flow. Geophys Res Lett 11:641–644
Pieri DC, Baloga SM (1986) Eruption rate, area and length relationships for some Hawaiian lava flows, J Volcanol Geotherm Res 30:29–45
Pinkerton H, Sparks RSJ (1976) The 1975 sub-terminal lavas, Mount Etna: a case history of the formation of a compound lava field. J Volcanol Geotherm Res 1:167–182
Pinkerton H, Sparks RSJ (1978) Field measurements of the rheology of lava. Nature 276:383–385
Robson GR (1967) Thickness of Etnean lavas. Nature 216:251–252
Scarfe CM (1973) Viscosity of basic magmas at varying pressure. Nature 241:101–102
Shaw HR (1969) Rheology of basalt in the melting range. J Petrol 10:510–534
Shaw HR, Wright TL, Peck DL, Okamura R (1968) The viscosity of basaltic magma: an analysis of field measurements in Makaopuhi Lava Lake, Hawaii. Am J Sci 266:225–264
Skelland AHP (1967) Non-newtonian flow and heat transfer. Wiley, New York, pp 469
Sparks RSJ, Pinkerton H (1978) Effect of degassing on rheology of basaltic lava. Nature 276:385–386
Sparks RSJ, Pinkerton H, Hulme G (1976) Classification and formation of lava levees on Mount Etna, Sicily. Geology 4:269–271
Spera FJ, Yuen DA, Kirschvink SJ (1982) Thermal boundary layer convection in silicic magma chambers: effects of temperature-dependent rheology and implications for thermo-gravitational chemical fractionation. J Geophys Res 87:8755–8767
Wadge G (1978) Effusion rate and the shape of aa lava flow-fields on Mount Etna. Geology 6:503–506
Walker GPL (1967) Thickness and viscosity of Etnean lavas. Nature 213:484–485
Walker GPL (1973) Lengths of lava flows, Philos. Trans R Soc A 274:107–118
Wilson L, Head JW III (1983) A comparison of volcanic eruption processes on Earth, Moon, Mars, Io and Venus. Nature 302:663–669
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Dragoni, M. A dynamical model of lava flows cooling by radiation. Bull Volcanol 51, 88–95 (1989). https://doi.org/10.1007/BF01081978
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DOI: https://doi.org/10.1007/BF01081978