Modelling intrusions through quiescent and moving ambients

Abstract

Volcanic eruptions commonly produce buoyant ash-laden plumes that rise through the stratified atmosphere. On reaching their level of neutral buoyancy, these plumes cease rising and transition to horizontally spreading intrusions. Such intrusions occur widely in density-stratified fluid environments, and in this paper we develop a shallow-layer model that governs their motion. We couple this dynamical model to a model for particle transport and sedimentation, to predict both the time-dependent distribution of ash within volcanic intrusions and the flux of ash that falls towards the ground. In an otherwise quiescent atmosphere, the intrusions spread axisymmetrically. We find that the buoyancy-inertial scalings previously identified for continuously supplied axisymmetric intrusions are not realised by solutions of the governing equations. By calculating asymptotic solutions to our model we show that the flow is not self-similar, but is instead time-dependent only in a narrow region at the front of the intrusion. This non-self-similar behaviour results in the radius of the intrusion growing with time t as t 3/4 , rather than t 2/3 as suggested previously. We also identify a transition to drag-dominated flow, which is described by a similarity solution with radial growth now proportional to t 5/9 . In the presence of an ambient wind, intrusions are not axisymmetric. Instead, they are predominantly advected downstream, while at the same time spreading laterally and thinning vertically due to persistent buoyancy forces. We show that close to the source, this lateral spreading is in a buoyancy-inertial regime, whereas far downwind, the horizontal buoyancy forces that drive the spreading are balanced by drag. Our results emphasise the important role of buoyancy-driven spreading, even at large distances from the source, in the formation of the flowing thin horizontally extensive layers of ash that form in the atmosphere as a result of volcanic eruptions.

Sustained axisymmetric intrusions in a rotating system

“…This contrasts with other flows, such as intrusions generated by a sudden collapse of mixed fluid, in which internal waves can play a more significant role [9]. Large-scale experiments may be necessary to determine conclusively how internal waves and other disturbances to the ambient stratification interact with the volcanic intrusions that motivate this study [3].…”

“…A peculiarity of the second and third stages of the hybrid model is that r N varies with t, without apparently being subjected to a boundary condition. The reason for this is that a simplified balance of radial momentum (3) holds in the 'box' region of the second and third stages of the hybrid model. As we demonstrated in §2.3, when this radial momentum balance holds, the dynamic boundary condition (48) is satisfied by the introduction of a boundary layer is at the front of the flow, causing only a negligible perturbation to the leading-order solution in the bulk of the flow.…”

“…This implies that straightforward scaling, which is so often useful for this kind of motion, is misleading and leads to incorrect predictions of the behaviour of sustained axisymmetric flows [3]. In this study, our contributions are twofold.…”

“…Volcanic plumes rise from their source, mixing with the atmosphere, until their bulk density matches that of the surroundings. They then intrude, predominantly horizontally, at this level of neutral buoyancy with their motion driven at least in part by the perturbation they cause to the background distribution of density in the atmosphere [3].…”

A review of laboratory and numerical modelling in volcanology

“…Buoyant plume models describe the horizontal intrusion of volcanic plumes into the atmosphere as a gravity current (Bursik et al, 1992;Baines et al, 2008;Suzuki and Koyaguchi, 2009;Johnson et al, 2015). They are capable of reproducing both upwind dispersal (e.g.…”