Multiphase turbulent flow explains lightning rings in volcanic plumes

The January 15, 2022, eruption of the Hunga Tonga-Hunga Ha'apai (HTHH) submarine volcano was a momentous event, generating the most intense volcanic lightning ever documented, exceeding 400,000 strokes within 6 hours. This unprecedented electrical activity manifested in distinct concentric ring patterns around the volcanic vent, a phenomenon not previously observed with such regularity and scale in meteorological lightning. The eruption also produced a 57-58 km high plume, an umbrella cloud reaching 400 km in diameter within an hour, and global geophysical waves. Analyses of these waves suggest multiple eruption bursts over several hours, although the opaque ash cloud obstructed direct satellite observation of vent activity, making it difficult to fully constrain the eruptive sequence. Understanding the origin of the lightning rings is crucial, as it may provide insights into the eruption's dynamics and the generation of hazardous impacts, such as tsunamis and atmospheric disturbances. This study investigates the hypothesis that particle clustering within the turbulent volcanic plume is the primary mechanism responsible for the formation of these lightning rings.

Volcanic lightning generation is primarily attributed to triboelectrification—charge separation due to collisions between ash particles of varying sizes. The presence of hydrometeors (ice particles and water droplets) also contributes to electrification, particularly in submarine eruptions where magma fragmentation by water contact enhances water vaporization. Previous studies have noted gaps in lightning activity within thunderstorms, interpreted as "lightning holes," associated with localized strong updrafts. However, the symmetric, extensive, and periodic lightning rings observed in HTHH are unique and require further investigation. Turbulence, known to efficiently mix fluids and particles, can under certain conditions also lead to particle clustering or preferential concentration, increasing collision rates. While existing plume models incorporate complexities like gas-particle relative motion, supersonic expansion, and entrainment mechanisms, simpler models may be sufficient to isolate the essential physics governing lightning ring formation.

This study employs three-dimensional numerical simulations of a turbulent plume with solid particles in a stably stratified atmosphere. The simulations utilize the Boussinesq approximation for a single-phase incompressible fluid within a linearly stratified atmosphere. Passive heavy particles with linear drag model the particle-laden flow. The focus is on identifying the physical conditions that generate the ring structure in a convective plume, rather than precisely replicating the HTHH eruption. Four sets of particles with varying inertia (Stokes numbers St = 1, 0.1, 0.01) were used. Three sets were initially positioned in a thin layer at the bottom, to be advected upwards by the plume. A fourth set of particles (St = 1) was initially suspended homogeneously at higher altitudes to simulate pre-existing atmospheric particles. The simulations tracked particle accumulation as a function of radius and time, using the particle density as a proxy for collision probability. The probability of collisions between different particle species was estimated using cross-correlations of densities, and a quantity proportional to the product of densities and characteristic velocities (Equation 1). The simulation parameters, including the Brunt-Väisälä frequency (N = 0.01 s⁻¹), upward velocity, turbulent velocity, and particle Stokes numbers, were chosen to reflect realistic atmospheric conditions and particle properties. The impact of gravity and particle settling was also examined. The expansion behavior of the ring structures was compared with theoretical plume models and observational data.

The simulations successfully reproduced the key features of the observed lightning rings. Particles, regardless of their initial inertia, accumulated in the central core of the plume and in a ring-like region at a radius of approximately 40 km. This annular structure correlated with regions of high turbulence intensity. The cross-correlations of particle densities indicated that the collision probability between particles was significantly enhanced in both the central core and the ring. The ring initially expanded with the plume at a rate proportional to time (t), then at a rate proportional to t⁰·⁷, and later decelerated to t⁰·⁴. This behavior is consistent with the expansion of a gravity current spreading horizontally after the plume reaches its level of neutral buoyancy. The initial linear expansion might suggest an accelerating supply rate. The simulations showed that the ring structure oscillated around a mean radius even with a constant buoyancy flux at the source. Analysis of the particle velocity power spectrum revealed that horizontal displacements were dominated by turbulent motions, while gravity waves influenced particle accumulation through vertical confinement. The addition of gravity to the simulations enhanced clustering, particularly in turbulent regions, although it caused particles in calmer areas to settle. Comparing simulation results with the observational data of HTHH lightning suggests the occurrence of significant explosions at approximately 4:14, 4:51, 5:34, and 8:33 UTC on January 15, 2022. These timings correlate with seismic events and infrasound/hydroacoustic data.

The simulations demonstrate that turbulence-induced particle clustering in the buoyant volcanic plume is a plausible mechanism for generating the observed lightning rings. The annular gap between the central core and the ring is explained by the distribution of turbulence intensity. The simulations effectively captured the expansion and oscillation of the ring structure, demonstrating that these phenomena can occur even with a constant buoyancy flux. This contrasts with thunderstorm lightning where lightning holes are associated with localized updraft surges. The study's findings highlight the potential of lightning ring dynamics as a valuable proxy for inferring otherwise inaccessible eruption parameters. The repeated expansion and contraction of the ring structure, not simply attributable to new injections of buoyant material, reflects the complex interplay between turbulence and atmospheric stratification. The inferred timings of significant explosions, otherwise hidden by the expanding plume, underscores the utility of lightning ring observations in understanding the full eruption sequence.

This research presents a compelling case for turbulence-induced particle clustering as the mechanism responsible for the formation of lightning rings in volcanic plumes. The simplified, yet realistic model successfully reproduced key observational features, providing a framework for interpreting volcanic lightning data. Future research should incorporate more complex models that include factors like vapor condensation, more detailed atmospheric conditions, supersonic flow at the vent, and time-dependent mass discharge to improve the accuracy and predictive capabilities of simulations. The ability to infer eruption parameters and timing of successive explosions using the characteristics of lightning rings has significant implications for hazard assessment and eruption monitoring.

The model employed several simplifying assumptions, including the Boussinesq approximation, linear density stratification, and the use of passive, non-interacting point particles. The simulations did not explicitly account for compressibility effects or vapor condensation and ice crystal formation. The energy input rate in the simulations is comparable to a typical eruption but may not precisely reflect the conditions during the HTHH eruption. While the study successfully demonstrates the potential of using lightning ring dynamics for estimating eruption parameters, further validation is needed through more detailed and realistic simulations.