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Pulsing in the Ahu‘ail$\bar{{\textbf{a}}}$‘au pond–spillway system during the 2018 K$\unicode{x012B}$lauea eruption: a dynamical systems perspective

Published online by Cambridge University Press:  10 May 2024

David M.R. Hyman Open the ORCID record for David M.R. Hyman [Opens in a new window] ,
Roger P. Denlinger ,
Hannah R. Dietterich  and
Matthew R. Patrick
David M.R. Hyman*
Affiliation:
Center for the Study of Active Volcanoes, University of Hawai‘i at Hilo, Hilo, HI 96720, USA US Geological Survey, Cascades Volcano Observatory, Vancouver, WA 98683, USA
Roger P. Denlinger
Affiliation:
US Geological Survey, Cascades Volcano Observatory, Vancouver, WA 98683, USA
Hannah R. Dietterich
Affiliation:
US Geological Survey, Alaska Volcano Observatory, Anchorage, AK 99508, USA
Matthew R. Patrick
Affiliation:
US Geological Survey, Hawaiian Volcano Observatory, Hilo, HI 96720, USA
*
†Email address for correspondence: dhyman@usgs.gov
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Abstract

During the 2018 K$\unicode{x012B}$lauea lower East Rift Zone eruption, lava from 24 fissures inundated more than 8000 acres of land, destroying more than 700 structures over three months. Eruptive activity eventually focused at a single vent characterized by a continuously fed lava pond that was drained by a narrow spillway into a much wider, slower channelized flow. The spillway exhibited intervals of ‘pulsing’ behaviour in which the lava depth and velocity were observed to oscillate on time scales of several minutes. At the time, this was attributed to variations in vesiculation originating at depth. Here, we construct a toy fluid dynamical model of the pond–spillway system, and present an alternative hypothesis in which pulsing is generated at the surface, within this system. We posit that the appearance of pulsing is due to a supercritical Hopf bifurcation driven by an increase in the Reynolds number. Asymptotics for the limit cycle near the bifurcation point are derived with averaging methods and compare favourably with the cycle periodicity. Because oscillations in the pond were not observable directly due to the elevation of the cone rim and an obscuring volcanic plume, we model the observations using a spatially averaged Saint-Venant model of the spillway forced by the pond oscillator. The predicted spillway cycle periodicity and waveforms compare favourably with observations made during the eruption. The unusually well-documented nature of this eruption enables estimation of the viscosity of the erupting lava.

JFM classification

Geophysical and Geological Flows: Magma and lava flow Nonlinear Dynamical Systems: Bifurcation Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 986 , 10 May 2024 , A37
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Creative Commons
To the extent this is a work of the US Government, it is not subject to copyright protection within the United States. Published by Cambridge University Press.
Copyright
© U.S. Geological Survey, 2024.

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