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.
Highlights
Explosive volcanic eruptions can inject large quantities of ash into the atmosphere, generating multiple hazards at various spatial and temporal scales (Blong, 2000; Bonadonna et al, 2021)
Various studies have highlighted the need to take these processes into account by revealing discrepancies between field measurements and numerical models (Scollo et al, 2008), premature sedimentation of fine ash leading to bimodal grainsize distributions related to particle aggregation (Bonadonna et al, 2011; Manzella et al, 2015; Watt et al, 2015) and significant depletion of airborne fine ash close to the source (Gouhier et al, 2019)
This paper presents an innovative method to implement a continuum model by coupling the Lattice Boltzmann Method (LBM) with a low-diffusivity finite difference (FD) scheme
Summary
Explosive volcanic eruptions can inject large quantities of ash into the atmosphere, generating multiple hazards at various spatial and temporal scales (Blong, 2000; Bonadonna et al, 2021). Alongside particle aggregation, settling-driven gravitational instabilities contribute to the early deposition of fine ash with similar outcomes (e.g., grainsize bimodality, premature sedimentation of fine ash). These instabilities generate downward-moving ash columns (fingers) which grow from the base of the ash cloud (Figure 1) (Carazzo and Jellinek, 2012; Manzella et al, 2015; Scollo et al, 2017). This phenomenon has the potential to enhance the sedimentation rate of fine ash beyond the terminal fall velocity of individual particles, reducing the residence time of fine ash in the atmosphere. A rigorous understanding of these processes is important in order to build a comprehensive parametrisation that can be included in dispersal models (Scollo et al, 2010; Bonadonna et al, 2012; Folch, 2012; Durant, 2015)
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