Can lava flow like water? Assessing applications of critical flow theory to channelized basaltic lava flows

Abstract

Flowing lava and water have dramatically different physical properties but can form similar hydraulic structures, including undular hydraulic jumps, or standing wave trains. In water flows, undular hydraulic jumps are evidence of critical flow (Froude number ∼1) and open-channel hydraulic theory provides a powerful tool for estimating flow depth and velocity. Monitoring these parameters in an active lava channel is inherently challenging, but essential for calculating lava discharge (effusion rate), a primary control on the rate of flow front advance and ultimate flow runout distance. We analyze undular hydraulic jumps in both water and lava flows to assess the conditions under which they form and, by extension, the potential use of critical flow theory to estimate, in real time, lava flow velocity, depth, and discharge. Experimental data for water flows show that these structures mark the transition from supercritical to subcritical flow. Undular hydraulic jumps in the near-vent lava channel of the 2018 lower East Rift Zone eruption of Kīlauea, Hawaiʻi also reflect critical flow conditions; their wavelengths scale with flow depth and velocity, consistent with hydraulic theory. Calculated lava effusion rates are similar to estimates made using more traditional approaches (Jeffreys', 1925, https://doi.org/10.1080/14786442508634662, equation based on lava viscosity, density, and channel slope) and with lava volumes derived from topographic-change mapping. From this we conclude that critical flow phenomena show great potential to track flow dynamics and inform hazard assessment for a wide range of geophysical fluids. Plain Language Summary: Flowing water and lava have very different physical properties, but under certain flow conditions, each will form arrays of evenly spaced standing waves (wave trains). In water, these are known to form at “critical flow” when there is a specific ratio between flow depth and flow velocity. However, conditions for forming standing wave trains in lava have not been measured. We investigated the relationship between the spacing of waves in a train, and the flow speed and depth, using both data from experiments with water and measurements made during the 2018 lava flow at Kīlauea volcano. We found that waves form in each fluid at the same ratio of flow speed and depth, and that the spacing of waves in a train shows a fixed mathematical relationship to these parameters. There is considerable practical importance to this finding. During a volcanic eruption, direct measurement of flow speed is difficult and dangerous, and depth is impossible, and yet both are needed to predict how far and how fast lava will travel. The critical flow characteristics of lava, and potentially other hazardous flows such as mudflows, allow assessment of flow behavior and potential hazards in real time.

Citation

Dietterich, H. R.; Grant, G. E.; Fasth, B.; Major, J. J.; Cashman, K. V. 2022. Can lava flow like water? Assessing applications of critical flow theory to channelized basaltic lava flows. Journal of Geophysical Research: Earth Surface. 127(9): 357-383. https://doi.org/10.1029/2022JF006666.