Modelling Settling-Driven Gravitational Instabilities at the Base of Volcanic Clouds Using the Lattice Boltzmann Method

Abstract

Field observations and laboratory experiments have shown that ash sedimentation can be significantly affected by collective settling mechanisms that promote premature ash deposition, with important implications for dispersal and associated impacts. Among these mechanisms, settling-driven gravitational instabilities result from the formation of a gravitationally-unstable particle boundary layer (PBL) that grows between volcanic ash clouds and the underlying atmosphere. The PBL destabilises once it reaches a critical thickness characterised by a dimensionless Grashof number, triggering the formation of rapid, downward-moving ash fingers that remain poorly characterised. We simulate this process by coupling a Lattice Boltzmann model, which solves the Navier-Stokes equations for the fluid phase, with a Weighted Essentially Non Oscillatory (WENO) finite difference scheme which solves the advection-diffusion-settling equation describing particle transport. Since the physical problem is advection dominated, the use of the WENO scheme reduces numerical diffusivity and ensures accurate tracking of the temporal evolution of the interface between the layers. We have validated the new model by showing that the simulated early-time growth rate of the instability is in very good agreement with that predicted by linear stability analysis, whilst the modelled late-stage behaviour also successfully reproduces quantitative results from published laboratory experiments. The results show that the model is capable of reproducing both the growth of the unstable PBL and the non-linear dependence of the fingers’ vertical velocity on both the initial particle concentration and the particle diameter. Our validated model is used to expand the parameter space explored experimentally and provides key insights into field studies. Our simulations reveal that the critical Grashof number for the instability is about ten times larger than expected by analogy with thermal convection. Moreover, as in the experiments, we found that instabilities do not develop above a given particle threshold. Finally, we quantify the evolution of the mass of particles deposited at the base of the numerical domain and demonstrate that the accumulation rate increases with time, while it is expected to be constant if particles settle individually. This suggests that real-time measurements of sedimentation rate from volcanic clouds may be able to distinguish finger sedimentation from individual particle settling.

Measuring binary fluidization of nonspherical and spherical particles using machine learning aided image processing

“…This shift is possibly due to collective settling mechanism induced by the increase of wood particle mass loadings. The collective effects enhancing the settling velocity due to local particle concentration increase have been observed in many particle‐laden flow systems 41–44 …”

Particle Sedimentation in Numerical Modelling: A Case Study from the Puyehue-Cordón Caulle 2011 Eruption with the PLUME-MoM/HYSPLIT Models

“…Differences in total mass between model and deposit are especially high between 20 and 60 km from vent. An explanation for such a difference (in addition to human/automatic inaccuracies in isomass drawing) could be linked to the non-consideration (in HYSPLIT) of near-vent sedimentation mechanisms (e.g., sediment waves [39]; two-way coupling effect [7]; and settling-driven gravitational instabilities [72]). In this view, an increase in particle sedimentation in the surrounding of the vent (i.e., up to 1 km, where field data are also possibly underestimated) by considering such phenomena within the model could reduce the amount of particles deposited in the subsequent transects.…”

Two-way coupling Eulerian numerical simulations of particle clouds settling in a quiescent fluid

“…Thus, in this study we adopt an equilibrium Eulerian approach [4] to model our settling particle clouds at reasonably low numerical cost, while still accounting for the two essential ingredients of (i) the feedback of particles on the fluid through a drag term which forces the flow, and (ii) a differential motion between water and settling particles through a gravitational drift, a formalism already used in the literature to model particle-laden flows [26][27][28][29][30]. The latter effect is quantified by a Rouse number which is about R = 0.3 for the optimum growth rate in experiments, and which lies below unity for most of our clouds.…”