A. A. Barmin

Periodic behavior in lava dome eruptions

Lava dome eruptions commonly display fairly regular alternations between periods of high activity and periods of low or no activity. The time scale for these alternations is typically months to several years. Here we develop a generic model of magma discharge through a conduit from an open-system magma chamber with continuous replenishment. The model takes account of the principal controls on flow, namely the replenishment rate, magma chamber size, elastic deformation of the chamber walls, conduit resistance, and variations of magma viscosity, which are controlled by degassing during ascent and kinetics of crystallization. The analysis indicates a rich diversity of behavior with periodic patterns similar to those observed. Magma chamber size can be estimated from the period with longer periods implying larger chambers. Many features observed in volcanic eruptions such as alternations between periodic behaviors and continuous discharge, sharp changes in discharge rate, and transitions from effusive to catastrophic explosive eruption can be understood in terms of the non-linear dynamics of conduit flows from open-system magma chambers. The dynamics of lava dome growth at Mount St. Helens (1980–1987) and Santiaguito (1922–2000) was analyzed with the help of the model. The best-fit models give magma chamber volumes of ∼0.6 km3 for Mount St. Helens and ∼65 km3 for Santiaguito. The larger magma chamber volume is the major factor in explaining why Santiaguito is a long-lived eruption with a longer periodicity of pulsations in comparison with Mount St. Helens.

Depressurization of fine powders in a shock tube and dynamics of fragmented magma in volcanic conduits

Abstract Samples of fine glass beads (mean grain size equal to 38 and 95 μm) have been depressurized within a vertical shock tube. These short-lived, rapid decompressions resemble discrete, cannon-like vulcanian explosions and produce two-phase flows that are inhomogeneous in density in both vertical and horizontal directions because of the presence of bubble-like heterogeneities. We suggest that also volcanic flows may present similar inhomogeneities in density. In the experimental apparatus the flow velocities increase from approximately 1 to 13 m/s when the pressure drop increases from approximately 200 to 900 mbar. A physical model of the initial velocities of expansions in the shock tube has been applied to a range of volcanic overpressures between 0.1 and 20 MPa, suggesting initial velocities of volcanic flows caused by the removal of a rock plug in volcanic conduits between 25 and 400 m/s. During the experiments at large pressure drops, as the mixture expands and moves up the tube, the flow front becomes highly irregular and bubble-like heterogeneities form. The shape of these bubbles becomes distorted and stretched in the turbulent flow. During the experiments at relatively small pressure drops, the sample oscillates when the particles, after the expansion, flow back and bounce upward again. Jets with diameter smaller than that of the tube are ejected from the oscillating samples generating independent pulses. Large bubble-like heterogeneities whose diameter is a significant fraction of the tube diameter can also discretize the flows. Similar mechanisms in real volcanoes may produce pulse-like ejections of gas–particle mixtures out of the vent.

Eruption dynamics of high-viscosity gas-saturated magmas

A model of eruption, which is a variant of that described in [4] and takes into account the disequilibrium of the pressure in the bubble and in the liquid in the absence of total solidification is proposed. The fragmentation zone is simulated by a disintegration wave with allowance for the velocity and temperature nonequilibrium of the particles of the gas suspension formed and its polydispersity. On the basis of the model constructed steady-state magma flow calculations are made for a given pressure difference and channel length. The results of the calculations show that taking pressure nonequilibrium into account leads to a qualitatively new dependence of the flow rate on the governing parameters and makes it possible to propose a catastrophic eruption intensification mechanism different from that proposed in [3].

Interaction of interplanetary shocks with the heliospheric termination shock: Two‐dimensional magnetohydrodynamic model

The two-dimensional problem of the oblique interaction between an interplanetary shock (IPS) and the termination shock (TS) with allowance for the effect of the interplanetary magnetic field is studied within the framework of the ideal magnetohydrodynamic model and a steady model of the solar wind interaction with the local interstellar medium. The self-consistent axisymmetric model proposed by Baranov and Malama, which takes into account the processes of resonant charge exchange between H atoms and protons, is used. The electron number density and the solar wind velocity VSW ahead of TS depends on the parameters of this model. The postinteraction configuration consists of a new moving TS′, a transmitted IPS′, a set of Alfven and slow magnetohydrodynamic waves, and a contact discontinuity which can change as functions of five dimensionless governing parameters and the specific heat ratio γ. The maximum electron number density ne is usually reached behind the new termination shock TS′ for an oblique (θ ≠ 0) impingement of IPS on TS rather than for the head-on collision (θ = 0). Nevertheless, the maximum calculated values of ne are lower than those corresponding to plasma frequencies ωp ≅ 2 kHz observed by the Voyager spacecraft. It is found that all the quantities considered depends radically on the angle ψTS between the front of TS and the vector of the interplanetary magnetic field strength BSW.

Structure of a steady-state ionization front in the plasma accelerator channel

A theoretical approach to studying ionizable gas flows with the formation of an ionization front in the plasma accelerator channel is proposed. The study is based on the MHD equations supplemented with the ionization and recombination kinetics equation. As a result, the structure of an ionization front is investigated.

Effect of Crystallization, Heat Exchange, and Viscous Dissipation on the Dynamics of Extrusive Eruptions

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 steadystate 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.