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

TL;DR

This study models the formation of gravitational instabilities in volcanic ash clouds using a coupled Lattice Boltzmann and WENO scheme, providing insights into ash sedimentation and instability growth.

Contribution

It introduces a novel coupled simulation approach combining Lattice Boltzmann and WENO methods to accurately model settling-driven gravitational instabilities in volcanic clouds.

Findings

Model accurately predicts early-time instability growth rates.

Simulation reproduces late-stage behaviour observed in lab experiments.

Coupled model reduces numerical diffusivity for better interface tracking.

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 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, 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.