[1] The current paradigm for normal eruptions at Stromboli volcano and Strombolian‐type activity more generally posits that each eruption represents the burst of a large pocket of gas, commonly referred to as slug, at the free surface of themagma column. This slug model has been investigated and refined primarily through analog fluid dynamical experiments at the laboratory scale. There is no doubt that these studies have advanced our understanding of Strombolian eruptions considerably. However, given the very fundamental status of the slug model for our current thinking about Strombolian‐type eruptions, it is paramount to carefully assess all underlying assumptions of the model. One important uncertainty lies in the scaling behavior of the observed slug dynamics in the laboratory. Scale invariance requires all nondimensional numbers to be identical, but it is generally not feasible to match all of the nondimensional numbers characterizing the volcanic conduit exactly in a laboratory experiment. Numerical computations offer a means of directly comparing slug dynamics at drastically different scales [Suckale et al., 2010b]. We find that the very large slugs in volcanic conduits are more prone to dynamic instabilities and breakup than the comparatively small slugs in laboratory settings. This finding in itself does of course not ‘disprove’ the slug model: it merely points to potentially important differences in slug stability at volcanic scales as opposed to laboratory scales. [2] Being careful and critical of the errors and interpretations of numerical simulations is important; similarly, the appropriateness of laboratory analogs must also be examined. James et al. [2011] raise a valid point asking whether our simulations are capable of reproducing stable slug rise in water. Figure 1 shows a computation performed for the experimental parameters provided by James et al. [2011]. In agreement with the analog experiments, we do indeed find that this slug rises stably in water, i.e., the slug ascends buoyantly within the conduit without experiencing ‘catastrophic’ breakup as defined by Suckale et al. [2010b]. Thus the experiments by James et al. [2011] do not appear to contradict our computations. We also reproduce computationally stable slug flow at finite Reynolds number (Re) shown in the experiment specified by Jaupart and Vergniolle [1989] [Suckale et al., 2010b]. It is worth noting that in both cases, the set of nondimensional numbers characterizing the experiment are not identical to those thought to be representative of the volcanic conduit and thus potential differences in the fluid dynamical behavior are not unexpected. [3] That we observe stable slugs in water but not in magma supports an argument raised by James et al. [2011], namely that Re is an insufficient parameter for comparing slug dynamics at different spatial scales. We welcome their discussion of the drawbacks of using a single Re to describe slugs. Focusing on Re to characterize our computations was a purely pragmatic decision: First, Re is commonly used for the purpose of comparing fluid dynamical computations at different scales. Second, we were able to use estimates for Re characterizing Strombolian slugs based on observational data measured at Stromboli [Vergniolle and Brandeis, 1996]. Third, we observed a correlation between Re and breakup within the regime we investigated, which is not unexpected since Re is an indirect measure of the size of a gas bubble or slug. That being said, a more comprehensive set of nondimensional numbers is undoubtedly needed to evaluate scaling behavior of slugs for different fluid dynamical regimes, including nondimensional criteria that capture the wavelength of potential interface instabilities in relation to the curvature of the interface and the time scale associated with instability growth to the time scale associated with advection of the instability along the interface. Our study is a first step toward gaining a better understanding of slug stability. [4] From a theoretical point of view, very large and dynamic gas volumes are not expected to be indefinitely stable. The light gas slug moves underneath a column of very heavy magma and this unstable density stratification is prone to the formation of Rayleigh‐Taylor instabilities at the essentially flat upper surface of the slug. Grace et al. [1978] developed a semiempirical rationalization of this process that affords rough estimates of maximum stable sizes as listed in Table 1 of Suckale et al. [2010b]. The appeal of this model lies primarily in its simplicity, but this very simplicity also Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA. Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada.
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Dec 8, 2015
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