Investigating lava flow rheology using video analysis and numerical flow models

Abstract

Lava rheology is a major control on lava flow behavior and a critical parameter in flow simulations, but is very difficult to measure at field conditions or correctly extrapolate from the lab scale. We present a new methodology for investigating lava rheology through a combination of controlled experiments, image analysis and numerical forward modeling. Our experimental setup, part of the Syracuse University Lava Project (http:// lavaproject.syr.edu) includes a large furnace capable of melting up to 450 kg of basalt, at temperatures well above the basalt liquidus. The lava is poured onto either a tilted bed of sand or a steel channel to produce meter-long flows. This experimental setup is probably the only facility that allows such large scale controlled lava flows made of natural basaltic material. We document the motion of the lava using a high-resolution video camera placed directly above the flows, and the temperature using infrared probes and cameras. After collecting the footage, we analyze the images for lava deformation and compare with numerical forward-models to constrain the rheological parameters and laws which best describe the flowing lava. For the video analysis, we employ the technique of Differential Optical Flow, which uses the time-variations of the spatial gradients of the image intensity to estimate velocity between consecutive frames. An important benefit for using optical flow, compared with other velocimetry methods, is that it outputs a spatially coherent flow field rather than point measurements. We demonstrate that the optical flow results agree with other measures of the flow velocity, and estimate the error due to noise and time-variability to be under 30% of the measured velocity. Our forward-models are calculated by solving the Stokes flow equations on an unstructured finite-element mesh defined using the geometry of the observed flow itself. We explore a range of rheological parameters, including the lava's apparent viscosity, the power-law exponent m and the thermal activation energy. Our measurements of apparent viscosity agree well with predictions of the composition-based Shaw (1972) and GRD model (Giordano, Russell and Dingwell, 2008). We find that for the high-temperature portion of the flow a weakly shear-thinning or Newtonian rheology (m > 0.7) with an effective activation energy of B = 5500 J gives the best fit to the data. Our methodology is the first time that high-resolution optical flow analysis of flowing lava is combined with numerical flow models to constrain rheology. The methodology we present here can be used in field conditions to obtain in-situ information on lava rheology, without physical interaction with the flow and without being limited to point-wise, low strain-rate, local measurements currently available through the use of rotational viscometers in the field.

Benchmarking computational fluid dynamics models of lava flow simulation for hazard assessment, forecasting, and risk management

“…Introducing cooling in theory and analogue fluids has captured the thermal signature of flows and the impacts of temperature-dependent rheology and a surface crust on flow emplacement (Griffiths and Fink, 1993;Griffiths et al, 2003;Kerr et al, 2006;Garel et al, 2012). Most recently, the use of molten basalt in experiments has extended this work, although still at the laboratory scale (Lev et al, 2012;Edwards et al, 2013;Dietterich et al, 2015).…”

“…However, if the temperature variation is limited to a very thin boundary layer compared with the lava flow thickness (e.g., Takagi and Huppert, 2010), the temperature variation between the hot central layer of the lava flow and the surface can be neglected, and the averaged flow flux is very close to the real lava flux. Natural lava flows usually have very large Peclet numbers (Lev et al, 2012), which corresponds to thin thermal boundary and very thick molten core where the temperature barely varies. In this case, the depth-averaged flow flux only deviates slightly from reality.…”

“…5). Solidification is approximated in the OpenFOAM and FLOW-3D models using a temperature-dependent rheology (Lev et al, 2012;Cordonnier et al, 2015). For comparison, we plot the results from isothermal VolcFlow and COMSOL simulations, which use the initial viscosity (corresponding to the eruption temperature) of the temperature-dependent flows.…”

“…While the scale of these experiments is small compared with natural flows, they share fundamental physics, such as low Reynolds numbers, large Bond numbers, and high Peclet numbers (Garel et al, 2012;Lev et al, 2012;Dietterich et al, 2015), which indicate laminar flow, negligible surface tension, and a very thin thermal boundary. However, natural lava flows contain much more complexity than is captured in these benchmarks, including multiphase rheology (bubbles, melt and crystals), growth and strength of a surface crust, and changing effusion rates (e.g., Cashman and Mangan, 2014).…”

“…Technological advances (including lidar, InSAR, and structure-from-motion photogrammetry) now permit accurate measurements of pre-eruptive topography, as well as repeat measurements of flow geometry that could provide near-real-time data on effusion rate, flow extent, and thickness during emplacement (e.g., Favalli et al, 2010;Poland, 2014;Slatcher et al, 2015). Ideally these measurements would be supplemented by corresponding measurements of thermorheological properties using a combination of field and remotely sensed measurements of temperature (thermocouples and thermal imaging; Lipman and Banks, 1987;Patrick et al, 2017) and rheology (samples and video analysis; Cashman et al, 1999;Lev et al, 2012;Soldati et al, 2016). We urge the community to come together to collect such data on future lava flows.…”