One‐dimensional, time‐dependent, homogeneous, two‐phase flow in volcanic conduits

Ramos, J. I.

doi:10.1002/fld.1650210306

Cited by 25 publications

(8 citation statements)

References 26 publications

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“…Consideration of time‐dependent behavior adds further complexity. Such behavior may occur over many different timescales due to changes in conduit size, nonlinear behavior associated with gas exsolution and crystal growth, or a time‐varying magma chamber pressure [ Ramos , 1995; Barmin et al , 2003; Proussevitch and Sahagian , 2005; Starostin et al , 2005; Melnik and Sparks , 2005, 2006; Mason et al , 2006]. Time‐dependent models with complex interactions may provide insight into the short‐to intermediate‐period oscillatory behavior often observed during eruptions.…”

Section: Previous Studiesmentioning

confidence: 99%

“…The time‐dependent term in equation (2) may be neglected only when magma ascent times are significantly shorter than the times associated with changes in eruption dynamics [ Ramos , 1995; Melnik and Sparks , 2006]. Changes in eruption dynamics can be slow for effusive dome‐building eruptions, but magma ascent rates are low and residence times are thus long.…”

Section: Model Designmentioning

confidence: 99%

See 1 more Smart Citation

Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes

Anderson¹,

Segall²

2011

J. Geophys. Res.

115

154

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[1] We present a model of effusive silicic volcanic eruptions which relates magma chamber and conduit physics to time-dependent data sets, including ground deformation and extrusion rate. The model involves a deflating chamber which supplies Newtonian magma through a cylindrical conduit. Solidification is approximated as occurring at fixed depth, producing a solid plug that slips along its margins with rate-dependent friction. Changes in tractions acting on the chamber and conduit walls are used to compute surface deformations. Given appropriate material properties and initial conditions, the model predicts the full evolution of an eruption, allowing us to examine the dependence of observables on initial chamber volume, overpressure, and volatile content. Employing multiple data sets in combination with a physics-based model allows for better constraints on these parameters than is possible using kinematic idealizations. Modeling posteruptive deformation provides an improved constraint on the rate of influx into the magma chamber from deeper sources. We compare numerical results to analytical approximations and to data from the 2004-2008 eruption of Mount St. Helens. For nominal parameters the balance between magma chamber pressure and frictional resistance of the solid plug controls the evolution of the eruption, with little contribution from the fluid magma below the idealized crystallization depth. While rate-dependent plug friction influences the timedependent evolution of the eruption, it has no control on the final chamber pressure or extruded volume.Citation: Anderson, K., and P. Segall (2011), Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes,

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Section: Previous Studiesmentioning

confidence: 99%

Section: Model Designmentioning

confidence: 99%

Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes

Anderson¹,

Segall²

2011

J. Geophys. Res.

115

154

View full text Add to dashboard Cite

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“…For the cases where the effects of magma viscosity and gravity are neglected, the fundamental features of the above situation, such as generation of shock wave and velocity of magma‐air contact, have been analytically investigated on the basis of the classical shock tube theory [e.g., Turcotte et al , 1990; Woods , 1995]. Although the effect of viscosity has been included in some numerical models [e.g., Ramos , 1995], the physics how magma viscosity influences the fragmentation process has not been fully understood. We, therefore, focus on this problem.…”

Section: Introductionmentioning

confidence: 99%

A theoretical model for fragmentation of viscous bubbly magmas in shock tubes

Koyaguchi

2005

J. Geophys. Res.

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[1] A coupled model for one-dimensional time-dependent compressible flow and bubble expansion is developed to investigate fragmentation mechanisms of viscous bubbly magmas in shock tubes. Initially a bubbly magma at a high pressure is separated from air at the atmospheric pressure by a diaphragm. As the diaphragm is ruptured, a shock wave propagates into the air, and a rarefaction wave propagates into the bubbly magma. As a result, the bubbly magma is decompressed and expands. Gas overpressure and hoop stress around expanding bubbles are calculated by applying the cell model. It is assumed that the magma fragments and the flow changes from bubbly flow to gas-pyroclast dispersion when the hoop stress or the gas volume fraction reaches a given threshold. Two types of fragmentation mechanisms are recognized: (1) high-viscosity magma fragments as the hoop stress reaches the tensile strength of the melt (stress fragmentation) and (2) the hoop stress does not grow in low-viscosity magma so that fragmentation occurs after bubble expansion when the gas volume fraction reaches a threshold (expansion fragmentation). During stress fragmentation a zone of steep pressure gradient forms just behind the fragmentation surface, which propagates into the magma together with the fragmentation surface. Analytical considerations suggest that the self-sustained stress fragmentation process can be described by a combination of a traveling-wave-type solution in the bubbly flow region and a self-similar solution in the gas-pyroclast flow region. Some simple formulae to predict the fragmentation speed (downward propagation velocity of the fragmentation surface) are derived on the basis of these solutions. The formulae are applied to recent experimental results using shock tube techniques as well as Vulcanian explosions in nature.Citation: Koyaguchi, T., and N. K. Mitani (2005), A theoretical model for fragmentation of viscous bubbly magmas in shock tubes,

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“…Another model was also presented in on the basis of microscopic particle dynamics simulations to explore non‐equilibrium behavior of volcanoes. In , an isothermal model was developed to investigate magma ascent in volcanic eruptions. Although these are some remarkable studies in understanding the volcanic two‐phase flow processes, they are limited to mechanical, thermal, and velocity equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Application of a thermodynamically compatible two‐phase flow model to the high‐resolution simulations of compressible gas–magma flow

Zeidan

Touma

Slaouti³

2014

Numerical Methods in Fluids

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SUMMARYThis paper reports on the application and development of a fully hyperbolic and fully conservative two‐phase flow model for the simulation of gas and magma flow within volcanic processes. The model solves a set of mixture conservation equations for the gas and magma two‐phase flow with velocity non‐equilibrium. In this model, the effect of the relative velocity is introduced by a kinetic constitutive equation with other equations for volume and mass fractions of the gas phase. The model is examined numerically by the widely used finite volume Godunov methods of centered‐type. Using the Riemann problem, we numerically simulate wave propagation and the development of shocks and rarefactions in volcanic eruptions. These simulations are of magma fragmentation type where the relative velocity continues to dominate. A series of test cases whose solution contains features relevant to gas–magma mixtures are conducted. In particular, numerical results indicate that the model implementation predicts key features of the relative velocity within volcanic processes without any mathematical or physical simplifications. Simulation results are sharply and accurately provided without any spurious oscillations in all of the flow variables. The numerical methods and results are also compared with other numerical methods available in the literature. It is found that the provided resolutions are more accurate for the considered test cases. Copyright © 2014 John Wiley & Sons, Ltd.

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One‐dimensional, time‐dependent, homogeneous, two‐phase flow in volcanic conduits

Cited by 25 publications

References 26 publications

Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes

Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes

A theoretical model for fragmentation of viscous bubbly magmas in shock tubes

Application of a thermodynamically compatible two‐phase flow model to the high‐resolution simulations of compressible gas–magma flow

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