Can Lava Flow Like Water? Assessing Applications of Critical Flow Theory to Channelized Basaltic Lava Flows

Abstract

The two great geophysical liquids present at Earth's surface-water and molten lava-share common features. Despite orders of magnitude differences in viscosity and temperature (water = 8.9 × 10 −4 Pa s at 25°C; basaltic lava = 50 Pa s at 1200°C), both liquids form gravity currents that, under the right circumstances, exhibit flow features such as turbulence, eddies, standing waves, and hydraulic jumps. In water flows, the full complement of these features occurs in channels with steep slopes (S) > 0.01 m/m (∼0.6°), such as those in mountain or canyon rivers, where flow velocities reach 1-10 m/s and complex flow features manifest as whitewater rapids. These features are often triggered by external influences, such as step changes in channel-bed elevation or channel width, substantive changes in slope, large boulders, or other conditions that cause abrupt changes in flow velocity. The circumstances that promote these same flow features in lava are not well constrained but observations show that they are most common close to volcanic vents where lava temperatures and flow velocities are high,

The Yih Instability in Layered Lava Flow May Initiate the Pāhoehoe to ‘a‘ā Lava Transition

“…The next step would be to compare the model to active lava flows as documented in Dietterich et al. (2022) and Cashman et al. (1999), ideally once the model has been generalized to include temperature and nonlinear effects.…”

“…We make an attempt to test our model results against solidified lava flows while keeping in mind that this comparison is inevitably flawed. The next step would be to compare the model to active lava flows as documented in Dietterich et al (2022) and Cashman et al (1999), ideally once the model has been generalized to include temperature and nonlinear effects. With the deployment of new technologies that track activity in Kılauea, Hawai'i and other volcanoes (Thompson & Ramsey, 2020) and more direct observations of active lava flows (e.g., Dietterich et al, 2022), new opportunities might soon arise to conduct further, more rigorous testing of our ideas.…”

“…(1999), ideally once the model has been generalized to include temperature and nonlinear effects. With the deployment of new technologies that track activity in Kı̄lauea, Hawai'i and other volcanoes (Thompson & Ramsey, 2020) and more direct observations of active lava flows (e.g., Dietterich et al., 2022), new opportunities might soon arise to conduct further, more rigorous testing of our ideas.…”

Toward Next‐Generation Lava Flow Forecasting: Development of a Fast, Physics‐Based Lava Propagation Model

“…We make no effort in this demonstration to refine our model inputs beyond what might be available in the first hours of an eruption such as fissure geometry and location, total eruption rate, vent temperature, and possibly an early rough estimate of viscosity using Jeffreys equation from rough estimates of flow depth and speed (e.g., Dietterich et al, 2021Dietterich et al, , 2022. Although early observations noted four fountaining centers feeding these flows, some of these centers fed the same initial flows and thus we represent the source term in this model as two linear fissures sharing the total eruption rate (400 m 3 s −1 ) equally: one extending 200 m to the northeast from the eventual "Flow 1" vent, and another extending 800 m east from the end of the first model fissure.…”

“…In particular, near the margins where the flow is first interacting with the terrain and flow routing is first being established, Reynolds numbers are characteristically small. Standing waves and other features of critical flow in open channels are similarly rare in lava flows and do not typically develop during a flow's initial emplacement nor close to the advancing front (e.g., Dietterich et al., 2022; Le Moigne et al., 2020). Consequently, the dynamically important sections of advancing lava flows can be assumed to exhibit very small Froude and Reynolds numbers.…”