Fluid Dynamics, Vol. 38, No. 5, 2003, pp. 742–751. Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2003, pp. 95–105. Original Russian Text Copyright  2003 by Barmin, Mel’nik, and Starostin. Simulation of the Effect of Water Injection on Volcanic Conduit Flow A. A. Barmin, O. E. Mel’nik, and A. B. Starostin Received February 13, 2003 Abstract — The effect on the eruption process of water or steam injection into a volcanic conduit from an adjacent water-saturated stratum is studied. Both steady-state and unsteady processes are considered. The physical characteristics of these eruptions are identified. A mathematical model of such an eruption is proposed for the first time. Keywords: multiphase flows, flow through a porous medium, volcanic magma flow, fragmentation front. Magma flow in a volcanic conduit during an eruption is a complex process. Firstly, magma is a mul- tiphase medium: melt, gas bubbles (mainly steam), crystals, and dissolved gas. Secondly, the mechanical properties of the magma, such as the viscosity, depend strongly on its state, in particular, on the dissolved gas content. Thirdly, as the magma ascends, the pressure in it varies by several orders (from 10 8 to 10 5 Pa) so that a homogeneous liquid can go over into a gas suspension. The amount of the dissolved in the magma significantly affects the nature of the eruption. If this amount is fairly large (≈ 7%), then the transition from a quiet (extrusive) type of eruption, in which a lava dome is slowly extruded, to a blast (explosive) type, when a gas-suspension jet flows out from the volcanic pipe and the flow rate increases by orders of magnitude, can occur. At present, there are many mathematical models describing various movements of high-viscosity gas- saturated magmas. These models take into account the dependence of the viscosity on the magma param- eters, escape of the gas separated from the magma through a system of connected bubbles (porous liquid medium) [1], nonequilibrium between the gas bubbles and the melt with respect to the pressure [1, 2], crys- tallization during the ascent [2], and a number of other effects. As a result of numerical experiments, many processes occurring in eruptions have been identified and explained on the basis of these models. In par- ticular, the possibility of two types of eruption, namely, explosive and extrusive, was noted. The transition from one solution to the other was explained and the reasons for the cyclic variation of the flow rate in the process of eruption were discovered. In the present study, using models constructed earlier, we consider the case in which, in the process of eruption, water (steam) flows into the volcanic conduit from an adjacent water-saturated stratum. Such eruptions are called phreatic-magmatic. When water (steam) is injected into a hot magma, many physico- chemical processes leading to changes in the properties of the magma and its parameters take place. This can lead to a change in the nature of the eruption, including a sharp increase in the flow rate, although the mass fraction of the water injected amounts to a few percent of the flow rate. The models described below take the processes of interaction between the water and the magma integrally into account and even this shows that significant changes in the nature of the eruption are possible. Mathematical models of these eruptions have not previously been considered. 0015–4628/03/3805–0742$25.00  2003 Plenum Publishing Corporation