Rosso, Fabio

The paper deals with the mathematical modelling of a gas slug rising in a cylindrical duct filled with an incompressible liquid. This research is motivated by a phenomenon commonly observed during Strombolian eruptions at basaltic volcanoes, that is, mildly explosive events driven by a large bubble of magmatic gas (a slug) rising up the conduit and bursting at the surface. The model is compared with the laboratory experiments described in [15] and we prove that the constancy of the slug ascent velocity observed in these experiments is fully justifiable. The model is developed both in the case of a Newtonian fluid and in the case of a non-Newtonian power law fluid, more suitable for magmas, and applied to a volcanic scenario.

The paper describes a simplified mathematical model aimed at fitting available hydrographs of floods from subglacial lakes reaching their peak almost linearly in time, the so-called fast-risingjökulhlaups. The simplifying idea is that the glacier can be treated as a block with fixed width, length and thickness, confining a subglacial lake with a constant cross-sectional area and variable level. We do not consider the role of heat transfer as suggested by many authors for fast-rising events. The model consists of two ordinary differential equations: conservation equation for the lake water and motion equation for the glacier. The glacier vertical movement is supposed to be governed by its own weight, the water pressure generated by the lake and by the forces acting on the lateral sides due to interaction between the glacier and the surroundings. The model has three free parameters and reproduces satisfactorily eight historical hydrographs observed originated by eight jökulhlaups in the Skaftá river (Iceland). These floods, of fast-rising type, are sourced from two ice cauldrons, the Eastern one being responsible of the largest floods (up to 3500 m^3/s). On average, the cauldrons drain almost every two years due to persistent geothermal activity beneath Vatnajökull glacier. This periodicity has a simple mathematical interpretation and is used to obtain another validation of the model.