Magma wagging and whirling : excitation by gas flux

Author Posting. © The Authors, 2018. This article is posted here by permission of The Royal Astronomical Society for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 215 (2018): 713–735, doi:10.1093/gji/ggy313.Gas flux in volcanic conduits is often associated with long-period oscillations known as seismic tremor (Lesage et al.; Nadeau et al.). In this study, we revisit and extend the ‘magma wagging’and ‘whirling’models for seismic tremor, in order to explore the effects of gas flux on the motion of a magma column surrounded by a permeable vesicular annulus (Jellinek & Bercovici; Bercovici et al.; Liao et al.). We find that gas flux flowing through the annulus leads to a Bernoulli effect, which causes waves on the magma column to become unstable and grow. Specifically, the Bernoulli effects are associated with torques and forces acting on the magma column, increasing its angular momentum and energy. As the displacement of the magma column becomes large due to the Bernoulli effect, frictional drag on the conduit wall decelerates the motions of the column, restoring them to small amplitude. Together, the Bernoulli effect and the damping effect contribute to a self-sustained wagging-and-whirling mechanism that help explain the longevity of long-period seismic tremor.This work was supported by National Science Foundation grants EAR-1344538 and EAR-164505

Two-phase dynamics of volcanic eruptions: compaction, compression and the conditions for choking

International audienceVolcanic eruptions involve high-speed turbulent flows of gas and magma mixtures in which peak gas velocities often approach 600 m s−1. Such speeds are well in excess of the slow mixture sound speeds of approximately 150 m s−1 predicted by pseudo-gas theory, in which the gas and magma phases are assumed to be locked to each other; eruptions thus appear to be highly super-sonic. Indeed, flow in the volcanic conduit will choke when it reaches the sound speed and to attain supersonic velocities one must invoke special conduit nozzle shapes. However, the pseudo-gas approximation is a long-wavelength assumption, while choking and acoustic shocks are a short-wavelength effect; thus, the approximation is likely inapplicable for the choking phenomenon. To allow for non-pseudo-gas effects, such as phase separation, in the short-wavelength limit requires a more complete treatment of two-phase eruptions. We therefore develop and explore a model for two-phase, high Reynolds number flow of a compacting suspension of magma particles in a compressible gas. Flow properties, such as mixture density, are controlled both by gas content as well as gas compressibility, both of which vary according to different processes of compaction and compression, respectively. The two phases of the mixture separate because of their different densities, and the interaction forces (turbulent drag and inertial exchange) can be complex. The model is used to examine acoustic-porosity wave propagation and the development of shocks or choking structures in a volcanic conduit. Sound waves in separable mixtures are highly dispersive with fast waves propagating at the pure gas sound speed at small wavelengths, slow waves travelling at the pseudo-gas speed at long wavelengths, and pure attenuation and sound blocking at intermediate wavelengths. As shock fronts in gas density develop they become increasingly short wavelength features and thus will only cause choking if the maximum speed in the flow reaches the pure gas sound speed. Non-linear, finite-amplitude steady-state models of eruptions in a volcanic conduit show that compaction occurs over the magma particle gravitational deceleration height, and either suppresses gas expansion for fast eruptions, or isopycnally collapses the gas volume near the base of the erupting column for slow eruptions. Once compaction ceases, the gas expands toward a shock structure or choking point, which is coincident with a rapid gas acceleration and a high-speed vent eruption. Increased turbulent drag between the gas and particles suppresses compaction effects but greatly sharpens the shock front at the choking point. Although the standard pseudo-gas models predict such choking to occur at low velocities, the full two-phase theory always has choking occur when the gas reaches the pure gas sound speed, in keeping with the sound-speed dispersion analysis. Therefore, the full two-phase theory predicts choking to occur at the pure gas sound speed, which (for water vapour at the relevant high temperatures) is about 700 m s−1. Eruption velocities of 600 m s−1 are therefore fully consistent with the limit imposed by this choking condition, and no special conditions to obtain supersonic eruptions, such as nozzled conduit geometries, are necessary

A mechanism for mode selection in melt band instabilities

The deformation of partially molten mantle in tectonic environments can lead to exotic structures, which potentially affect both melt and plate-boundary focussing. Examples of such structures are found in laboratory deformation experiments on partially molten rocks. Simple-shear and torsion experiments demonstrate the formation of concentrated melt bands at angles of around 20° to the shear plane. The melt bands form in the experiments with widths of a few to tens of microns, and a band spacing roughly an order of magnitude larger. Existing compaction theories, however, cannot predict this band width structure, let alone any mode selection, since they infer the fastest growing instability to occur for wavelengths or bands of vanishing width. Here, we propose that surface tension in the mixture, especially on a diffuse interface in the limit of sharp melt-fraction gradients, can mitigate the instability at vanishing wavelength and thus permit mode selection for finite-width bands. Indeed, the expected weak capillary forces on the diffuse interface lead to predicted mode selection at the melt-band widths observed in the experiments

Melt-band instabilities with two-phase damage

Deformation experiments on partially molten rocks in simple shear form melt bands at 20° to the shear plane instead of at the expected 45° principal compressive stress direction. These melt bands may play an important role in melt focusing in mid-ocean ridges. Such shallow bands are known to form for two-phase media under shear if strongly non-Newtonian power-law creep is employed for the solid phase, or anisotropy imposed. However laboratory experiments show that shallow bands occur regardless of creep mechanism, even in diffusion creep, which is nominally Newtonian. Here we propose that a couple of forms of two-phase damage allow for shallow melt bands even in diffusion creep

Plate generation in a simple model of lithosphere–mantle flow with dynamic self-lubrication.

Abstract One of the more enigmatic features of the Earth's style of mantle convection is plate tectonics itself, in particular the existence of strike-slip, or toroidal, motion. Toroidal motion is uncharacteristic of basic thermal convection, but necessarily forms through the interaction of convective flow and nonlinear rheological mechanisms. Recent studies have implied that the empirically determined power-law rheologies of mantle silicates are not sufficient to generate the requisite toroidal motion. A simple source-sink model of mantle or lithospheric flow shows that dynamic self-lubrication, which arises through the coupling of viscous heating and temperature-dependent viscosity, is highly successful at generating strike-slip motion. In particular, as the viscosity of the fluid system becomes more temperature dependent, the toroidal flow field makes an abrupt transition from a state of weak, unplate-like motion to a state with intense and extremely focused structure. In essence, the fluid dynamical model develops strike-slip faults

Generation of plate tectonics from lithosphere-mantle flow and void-volatile self-lubrication,

Abstract The formation of plate tectonics from mantle convection necessarily requires nonlinear rheological behavior. Recent studies suggest that self-lubricating rheological mechanisms are most capable of generating plate-like motion out of fluid flows. The basic paradigm of self-lubrication is nominally derived from the feedback between viscous heating and Ž temperature-dependent viscosity. Here, we propose a new idealized self-lubrication mechanism based on void e.g., pore . Ž . andror microcrack generation and volatile e.g., water ingestion. We test this void-volatile self-lubrication mechanism in Ž . a source-sink flow model; this leads to a basic nonlinear system which permits the excitation of strike-slip toroidal motion Ž . Ž . a necessary ingredient of plate-like motion out of purely divergent i.e., poloidal or characteristically convective flow. Ž With relatively inviscid void-filling volatiles, the void-volatile mechanism yields a state of highly plate-like motion i.e., . with uniformly strong ''plate'' interiors, weak margins, and extremely focussed strike-slip shear zones . Moreover, the void-volatile model obeys a chemical diffusion time scale that is typically much longer than the thermal convection time scale; the model thus complies with the observation that plate boundaries are long lived and survive even while inactive. The void-volatile model of self-lubrication therefore predicts self-focussing shear zones, plate generation, and plate-boundary longevity through what has long been suspected to be a key ingredient for the existence of plate tectonics, i.e., water. q 1998 Elsevier Science B.V

The effects of degassing on magmatic gas waves and long period eruptive precursors at silicic volcanoes

Author Posting. © American Geophysical Union, 2020. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Solid Earth 125 (10), (2020): e2020JB019755, https://doi.org/10.1029/2020JB019755Cyclical ground deformation, associated seismicity, and elevated degassing are important precursors to explosive eruptions at silicic volcanoes. Regular intervals for elevated activity (6–30 hr) have been observed at volcanoes such as Mount Pinatubo in the Philippines and Soufrière Hills in Montserrat. Here, we explore a hypothesis originally proposed by Michaut et al. (2013, https://doi.org/10.1038/ngeo1928) where porosity waves containing magmatic gas are responsible for the observed periodic behavior. We use two‐phase theory to construct a model where volatile‐rich, bubbly, viscous magma rises and decompresses. We conduct numerical experiments where magma gas waves with various frequencies are imposed at the base of the model volcanic conduit. We numerically verify the results of Michaut et al. (2013, https://doi.org/10.1038/ngeo1928) and then expand on the model by allowing magma viscosity to vary as a function of dissolved water and crystal content. Numerical experiments show that gas exsolution tends to damp the growth of porosity waves during decompression. The instability and resultant growth or decay of gas wave amplitude depends strongly on the gas density gradient and the ratio of the characteristic magma extraction rate to the characteristic magma degassing rate (Damköhler number, Da). We find that slow degassing can lead to a previously unrecognized filtering effect, where low‐frequency gas waves may grow in amplitude. These waves may set the periodicity of the eruptive precursors, such as those observed at Soufrière Hills Volcano. We demonstrate that degassed, crystal‐rich magma is susceptible to the growth of gas waves which may result in the periodic behavior.J. S. J. and D. B. were supported by NSF grant EAR‐1645057. C. M. has received financial support of the IDEXLyon Project of the University of Lyon in the frame of the Programme Investissements dAvenir (ANR‐16‐IDEX‐0005)

Tectonic plate generation and two-phase damage: void growth versus grainsize reduction

The two-phase theory for compaction and damage employs a nonequilibrium relation between interfacial surface energy, pressure, and viscous deformation, thereby providing a model for damage (void generation and microcracking) and a continuum description of weakening, failure, and shear localization. Here we examine the application of this theory to the problem of generating plate-like behavior from convective-type divergent (poloidal) motion through a source-sink formulation. We extend the previous damage theory to consider two possible damage effects: (1) growth and nucleation of voids associated with dilation of the host matrix, and (2) increasing fineness (i.e., reducing coarseness) of the mixture by, for example, grainsize reduction. Void-generating damage is found to be poor at plate generation because of the predominance of dilational motion that is adverse to the development of plate-like flow. Finenes-generating damage is found to be very efficient at generating plate-like behavior if we assume that the matrix viscosity is a simple function of grain/void size, as is typical for diffusion creep. The implied grainsize reduction mechanism is different than that of dynamic recrystallization, and appears more capable of generating the requisite shear-localization for forming tectonic plates from mantle flow