Palabos Online Seminar Wednesday June 2nd 10:00 am CET

Dear Palabos users

At the Palabos Online Seminar Series, this Wednesday at 10:00 am CET, Jonathan Lemus (UniGe) will present the following topic:

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

The participation link is provided here: ). Everyone is welcome to attend.

The abstract of the presentation is:
Field observations and laboratory experiments have shown that volcanic ash sedimentation beneath eruptive clouds can be significantly affected by collective settling mechanisms such as aggregation and settling-driven gravitational instabilities. Both processes increase particle settling velocities and, therefore, promote premature ash deposition with important implications for associated impacts. Failing to accurately describe size-selective processes could underestimate tephra-sedimentation hazard in proximal areas and overestimate it in distal areas. Settling-driven gravitational instabilities result from a growing gravitationally-unstable particle boundary layer between volcanic ash cloud and the underlying atmosphere. Once this reaches a critical thickness, characterised by a dimensionless Grashof number, it destabilises, triggering the formation of rapid, downward-moving ash fingers. Despite their possible influence on ash deposition, these instabilities and the resulting ash fingers remain poorly characterised. In order to better understand this phenomenon, we consider a simplified configuration consisting of a buoyant particle suspension, analogue to the volcanic ash cloud, overlaying a denser ambient, analogue to the underlying atmosphere. This configuration is initially stably-stratified but, as particles settle into the lower layer, a gravitationally-unstable particle boundary layer grows downwards, triggering a Rayleigh-Taylor-like instability. 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 particle boundary layer and the non-linear dependence of the fingers’ vertical velocity on both the initial particle concentration and the particle diameter. Detailed examination of these relationships reveals that the critical Grashof number for the instability is approximately 10^4, about ten times larger than expected by analogy with thermal convection. Moreover, as in experiments, we report the existence of a particle diameter threshold above which no instability develops and particles instead settle individually. 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 settled individually. This suggests that real-time measurements of sedimentation rate from volcanic clouds may be able to distinguish finger sedimentation from individual settling. Our validated model therefore expands the parameter space within which settling-driven gravitational instabilities can be studied experimentally to encompass conditions representative of volcanic clouds and provides additional measurements of important quantities for field studies.