The effect of volatile bubble growth rate on the periodic dynamics of shallow volcanic systems (original) (raw)
Related papers
Journal of Geophysical Research, 1994
Sparks [this issue] has made several insightful and important comments on our paper [Proussevitch et al., 1993]. We are glad to have this opportunity to respond for the purposes of clarifying some of the model conditions and numerical techniques employed in our work, as well as for elaborating on the interpretation of our model results. Sparks is quite correct in suggesting that the present calculations must be thoroughly understood before more complex models can be reliably constructed. In general, the interpretation of our model results in the context of real volcanic systems is necessarily limited by the conditions imposed on the model. One condition was that of instantaneous decompression, while another required the variation of each parameter independently of all others, so that its effect on the results could be most uniquely quantified. An example of the artificial conditions imposed for our simple model is the variation of viscosity while holding diffusivity, initial volatile concentration, and temperature constant. Clearly, this is not a natural scenario, but it determines the effect of viscosity alone. In real systems, these parameters are not independent but are rather a part of a complex set of interactions and positive and negative feedbacks. Our continuing work is directed at quantifying the nature of these relationships (for various decompression histories) and should provide results which will be applicable to to a broader range of natural systems. A major point raised by Sparks is the interpretation of the "time delay" indicated in our model results. He calls this a period of "accelerating growth" which may be a more appropriate term for the phenomenon under some conditions. We agree that the sigmoidal shape of the bubble growth curve warrants further discussion. It should be noted that in many cases with basaltic melts, the "normal" parabolic growth curve is observed when plotted on linear axes (not logarithmic), in agreement with "classical" results [Scriven, 1959]. However, in other cases, the sigmoidal curve is real and may shed some light on the processes of early degassing and bubble growth. In our paper, we did not venture to explain the cause of the sigmoidal pattern other than to suggest that surface tension pressure may play a role for bubbles close to nuclear size. In this case, there is a time delay caused by elevated bubble tNow at Institute for the Study of the Earth, Oceans, and Space,
Dynamics and energetics of bubble growth in magmas: Analytical formulation and numerical modeling
Journal of Geophysical Research, 1998
We have developed a model of diffusive and decompressive growth of a bubble in a finite region of melt which accounts for the energetics of volatile degassing and melt deformation as well as the interactions between magmatic system parameters such as viscosity, volatile concentration, and diffusivity. On the basis of our formulation we constructed a numerical model of bubble growth in volcanic systems. We conducted a parametric study in which a saturated magma is instantaneously decompressed to one bar and the sensitivity of the system to variations in various parameters is examined. Variations of each of seven parameters over practical ranges of magmatic conditions can change bubble growth rates by 2-4 orders of magnitude. Our numerical formulation allows determination of the relative importance of each parameter controlling bubble growth for a given or evolving set of magmatic conditions. An analysis of the modeling results reveals that the commonly invoked parabolic law for bubble growth dynamics R -t 1/2 is not applicable to magma degassing at low pressures or high water oversaturation but that a logarithmic relationship R -log(t) is more appropriate during active bubble growth under certain conditions. A second aspect of our study involved a constant decompression bubble growth model in which an initially saturated magma was subjected to a constant rate of decompression. Model results for degassing of initially water-saturated rhyolitic magma with a constant decompression rate show that oversaturation at the vent depends on the initial depth of magma ascent. On the basis of decompression history, explosive eruptions of silicic magmas are expected for magmas rising from chambers deeper than 2 km for ascent rates > 1-5 m s-1.
Earth, Planets and Space, 2013
We numerically simulate volcanic inflation caused by magma ascent in a shallow conduit at volcanoes which repeatedly erupt, in order to understand the effect of volatile behavior on magma from geodetic data. Considering magma in which the relative velocities between melt and gas bubbles are negligible, we model magma flow in a one-dimensional open conduit with diffusive gas bubble growth. We calculate the ground displacements and tilts caused by spatio-temporal changes of magma pressure in the conduit. Our simulations show that magma without volatiles causes decelerated changes in volcanic inflation. Magma with gas bubble growth inflates the volcano with a constant, or accelerated, rate. Temporal changes of volcanic deformation are also affected by the magma pressure at the bottom of the conduit. When the pressure is small, the displacements and tilts increase in proportion to the 1.5th power of time. This time rate is similar to that predicted from a basic gas bubble growth model. When the pressure equals the lithostatic pressure, the effects of gas bubble growth relatively decrease and the displacements and tilts increase linearly with time.
Coupling of viscous and diffusive controls on bubble growth during explosive volcanic eruptions
Earth and Planetary Science Letters, 2001
The coupling of viscosity and diffusivity during explosive volcanic degassing is investigated using a numerical model of bubble growth in rhyolitic melts. The model allows melt viscosity and water diffusivity to vary spatially and temporally with water content. We find that the system is highly sensitive to the distribution of volatiles around the bubble, primarily as a consequence of the
Journal of Geophysical Research, 2010
1] This is the second paper of two that examine numerical simulations of buoyancydriven flow in the presence of large viscosity contrasts. In the first paper, we demonstrated that a combination of three numerical tools, an extended ghost fluid type method, the level set approach, and the extension velocity technique, accurately simulates complex interface dynamics in the presence of large viscosity contrasts. In this paper, we use this threefold numerical method to investigate bubble dynamics in the conduits of basaltic volcanos with a focus on normal Strombolian eruptions. Strombolian type activity, named after the famously episodic eruptions at Stromboli volcano, is characterized by temporally discrete fountains of incandescent clasts. The mildly explosive nature of normal Strombolian activity, as compared to more effusive variants of basaltic volcanism, is related to the presence of dissolved gas in the magma, yielding a complex two-phase flow problem. We present a detailed scaling analysis allowing identification of the pertinent regime for a given flow problem. The dynamic interactions between gas and magma can be classified into three nondimensional regimes on the basis of bubble sizes and magma viscosity. Resolving the fluid dynamics at the scale of individual bubbles is not equally important in all three regimes: As long as bubbles remain small enough to be spherical, their dynamic interactions are limited compared to the rich spectrum of coalescence and breakup processes observed for deformable bubbles, in particular, once inertia ceases to be negligible. One key finding in our simulations is that both large gas bubbles and large conduit-filling gas pockets ("slugs") are prone to dynamic instabilities that lead to their rapid breakup during buoyancy-driven ascent. We provide upper bound estimates for the maximum stable bubble size in a given magmatic system and discuss the ramifications of our results for two commonly used models of normal Strombolian type activity, the rise-speed-dependent model and the collapsing foam model. Citation: Suckale, J., B. H. Hager, L. T. Elkins-Tanton, and J.-C. Nave (2010), It takes three to tango: 2. Bubble dynamics in basaltic volcanoes and ramifications for modeling normal Strombolian activity,
Frequency and magnitude of volcanic eruptions controlled by magma injection and buoyancy
Nature Geoscience, 2014
Super-eruptions are extremely rare events. Indeed, the global frequency of explosive volcanic eruptions is inversely proportional to the volume of magma released in a single event 1,2 . The rate of magma supply, mechanical properties of the crust and magma, and tectonic regime are known to play a role in controlling eruption frequency and magnitude 3-7 , but their relative contributions have not been quantified. Here we use a thermomechanical numerical model of magma injection into Earth's crust and Monte Carlo simulations to explore the factors controlling the recurrence rates of eruptions of different magnitudes. We find that the rate of magma supply to the upper crust controls the volume of a single eruption. The time interval between magma injections into the subvolcanic reservoir, at a constant magma-supply rate, determines the duration of the magmatic activity that precedes eruptions. Our simulations reproduce the observed relationship between eruption volume and magma chamber residence times and replicate the observed correlation between erupted volumes and caldera dimensions 8,9 . We also find that magma buoyancy is key to triggering super-eruptions, whereas pressurization associated with magma injection is responsible for relatively small and frequent eruptions. Our findings help improve our ability to decipher the long-term activity patterns of volcanic systems.
Journal of Geophysical Research, 2011
This is the second paper of two that examine numerical simulations of buoyancydriven flow in the presence of large viscosity contrasts. In the first paper, we demonstrated that a combination of three numerical tools, an extended ghost fluid type method, the level set approach, and the extension velocity technique, accurately simulates complex interface dynamics in the presence of large viscosity contrasts. In this paper, we use this threefold numerical method to investigate bubble dynamics in the conduits of basaltic volcanos with a focus on normal Strombolian eruptions. Strombolian type activity, named after the famously episodic eruptions at Stromboli volcano, is characterized by temporally discrete fountains of incandescent clasts. The mildly explosive nature of normal Strombolian activity, as compared to more effusive variants of basaltic volcanism, is related to the presence of dissolved gas in the magma, yielding a complex two-phase flow problem. We present a detailed scaling analysis allowing identification of the pertinent regime for a given flow problem. The dynamic interactions between gas and magma can be classified into three nondimensional regimes on the basis of bubble sizes and magma viscosity. Resolving the fluid dynamics at the scale of individual bubbles is not equally important in all three regimes: As long as bubbles remain small enough to be spherical, their dynamic interactions are limited compared to the rich spectrum of coalescence and breakup processes observed for deformable bubbles, in particular, once inertia ceases to be negligible. One key finding in our simulations is that both large gas bubbles and large conduit-filling gas pockets ("slugs") are prone to dynamic instabilities that lead to their rapid breakup during buoyancy-driven ascent. We provide upper bound estimates for the maximum stable bubble size in a given magmatic system and discuss the ramifications of our results for two commonly used models of normal Strombolian type activity, the rise-speed-dependent model and the collapsing foam model.
Temporal evolution of flow conditions in sustained magmatic explosive eruptions
The temporal evolution of fundamental flow conditions in the magma chamber plus conduit system–such as pressure, velocity, mass flow-rate, erupted mass, etc.–during sustained magmatic explosive eruptions was investigated. To this aim, simplified one-dimensional and isothermal models of magma chamber emptying and conduit flow were developed and coupled together. The chamber model assumed an homogeneous composition of magma and a vertical profile of water content. The chamber could have a cylindrical, elliptical or spherical rigid geometry. Inside the chamber, magma was assumed to be in hydrostatic equilibrium both before and during the eruption. Since the timescale of pressure variations at the conduit inlet–of the order of hours–is much longer than the travel time of magma in the conduit–of the order of a few minutes–the flow in the conduit was assumed as at steady-state. The one-dimensional mass and momentum balance equations were solved along a circular conduit with constant diameter assuming choked-flow conditions at the exit. Bubble nucleation was considered when the homogeneous flow pressure dropped below the nucleation pressure given the total water content and the solubility law. Above the nucleation level, bubbles and liquid magma were considered in mechanical equilibrium. The same equilibrium assumption was made above the fragmentation level between gas and pyroclasts. Due to the hydrostatic hypothesis, the integration of the density distribution in the chamber allowed to obtain the total mass in the chamber as a function of pressure at the chamber top and, through the conduit model, as a function of time. Simulation results pertaining to rhyolitic and basaltic magmas defined at the Volcanic Eruption Mechanism Modeling Workshops (Durham, NH, 2002; Nice, France, 2003) are presented. Important flow variables, such as pressure, density, velocity, shear stress in the chamber and conduit, are discussed as a function of time and magma chamber and conduit properties. Results indicate that vent variables react in different ways to the pressure variation of the chamber. Pressure, density and mass flow-rate show relative variations of the same order of magnitude as the conduit inlet pressure, whereas velocity is more constant in time. Sill-like chambers produce also significantly longer and more voluminous eruptions than dike-like chambers. Water content stratification in the chamber and the increase of chamber depth significantly reduce the eruption