When a batch of magma reaches Earth’s surface, it forms a vent from which volcanic products are erupted. At many volcanoes, successive batches may open vents far away from previous ones, resulting in scattered, sometimes seemingly random spatial distributions. This exposes vast areas to volcanic hazards and makes forecasting difficult. Here, we show that magma pathways and thus future vent locations may be forecast by combining the physics of magma transport with a Monte Carlo inversion scheme for the volcano stress history. We validate our approach on a densely populated active volcanic field, Campi Flegrei (Italy), where we forecast future vents on an onshore semiannular belt located between 2.3 and 4.2 km from the caldera center. Our approach offers a mechanical explanation for the vent migration over time at Campi Flegrei and at many calderas worldwide and may be applicable to volcanoes of any type.

Eruptions at shield volcanoes often occur from radially aligned linear fissures fed by blade‐like magma‐filled cracks (dykes). The fissures of the 2018 Sierra Negra eruption were scattered on the flank of the volcano. Space‐borne radar interferometric data (interferometric synthetic aperture radar) revealed that, unexpectedly, part of the eruption was fed by a 15 km long, tortuous and flat‐lying crack (sill). Here we develop a framework that captures the full three‐dimensional (3D) kinematics of non‐planar intrusions. This includes both an analytical and comprehensive numerical scheme. We constrain the models such that they match the observed ground deformation at Sierra Negra. We show that the peculiar sill trajectory is due to the competing stress gradient magnitudes being close to one another throughout its propagation. By accounting for the interaction of all these factors, these 3D models open the possibility to understand and simulate the geometry of magma transport at volcanic systems.

Hydrofracturing is a routine industrial technique whose safety depends on fractures remaining confined within the target rock volume. Both observations and theoretical models show that, if the fluid volume is larger than a critical value, pockets of fluid can propagate large distances in the Earth's crust in a self‐sustained, uncontrolled manner. Existing models for such critical volumes are unsatisfactory; most are two‐dimensional and depend on poorly constrained parameters (typically the fracture length). Here we derive both analytically and numerically in three‐dimensional scale‐independent critical volumes as a function of only rock and fluid properties. We apply our model to gas, water, and magma injections in laboratory, industrial, and natural settings, showing that our critical volumes are consistent with observations and can be used as conservative estimates. We discuss competing mechanisms promoting fracture arrest, whose quantitative study could help to assess more comprehensively the safety of hydrofracturing operations.

The mechanism of trailing vortex wandering has long been debated and often attributed to either wind-tunnel effects or a self-induced instability. We remove the effect of wandering from a measured velocity field by averaging and, through a triple decomposition, recover the coherent wandering motion. Based on this wandering motion, the most energetic structures are computed using the proper orthogonal decomposition (POD) and exhibit a helical mode |m| = 1 whose kinetic energy grows with downstream progression. As such, we hypothesize that a vortex instability underlies the wandering motion, and test this hypothesis by performing a spatial stability analysis of a matched Batchelor vortex, which is devoid of wind-tunnel effects. The primary stability mode is marginally stable and is nearly identical, in size and structure, to the principal POD mode. The strikingly similar structure coupled with the measured energy growth supports the proposition that the vortex wandering is the result of an instability. The cause of the wandering is the non-zero radial velocity of the |m| = 1-mode on the vortex centerline, transversely displacing the trailing vortex as observed in experiments. However, the marginal nature of the stability mode prevents any conclusion regarding the specific type of instability.