Lava flows: Theory, lab experiments and field data by Herbert Huppert

23/01/2020

Lava flows: Theory, lab experiments and field data by Herbert Huppert

 During lava flows, many material loss is experienced by inhabitants. But how does objects and topography alter the path of the lava flow? Are wall a valid option to protect to a certain extend important infrastructure like hospitals? Would there be any "dry spots" behind buildings allowing for the the safekeeping of valuable resources? All these are questions Herbert Huppert tries to answer with his modelling of lava flow behaviour.

Herbert Huppert is an australian researcher, now stationed at the University of Cambridge. His background is in geophysics and applied maths, which makes him proefficient in making mathematical and numerical models to apply to Earth science processes. Now his focus is in fluid dynamics, phase change in rocks and other Earth processes at Cambridge.

Dry spot depending on house orientation

The first experiment aims to visually look at the general behaviour of a lava-like fluid with general obstacles. In order to do so, a viscous fluid (in this case thickened golden syrup) is dumped in one go from the top of an inclined plane bounded by tall walls. Small model houses and wall are put on the path to try and see the effect it has on the flow path of the syrup. In the case of the small houses, the syrup first left a "dry spot" (area downhill of the house with no lava), but was quickly surrounded. Immediately downhill of it, the thickness of the syrup flow is smaller. The larger houses,
like churches and such did leave a dry spot downhill of them. Small walls seemed only mildly effective as they got quickly overrun by the syrup flow, only diviating the flow when it first hit the wall. The "infinitely" (too large to be overrun in this model) tall walls though proved very efficient in deviating the flow and providing a dry spot, possibly protecting a house from most the the damage. This experiment has obvious flaws such as the side walls concentrating the flow, the initial dump of syrup and the assumed viscosity and sise of the buildings. It still allowed for a conceptual model to base numerical models of, knowing that topography need to be accounted for on top of it.

Multiple mathematical models got derived to try and find the best geometries for deviating lava flows. The first is looking in 2D as a cross-section, along the path of the lava flow, with varying topography. When it is at a shallow angle, the flow can overcome the topographic high without a major change in thickness. With a steeper slope stopping the path, the lava will form a pond before overcoming the obstacle aas a thinner flow. This is does not represent all of reality as in 3D it would go around the obstacle if possible. This is why churches, often build at the top of a hill in a village, are less affected by lava flows.

2D model of topography inducing ponding within the lava flow

 The second mathematical model looks at how a viscous newtonian fluid flows around a "tall cylinder" (assumed infinite hight, cannot be overtopped). Even with lava being a non-newtonian fluid, the results from the mathematical model closely link field examples, thus making the assumption possible. This helped calibrating the viscosity of the lava in the model to fing realistic results.

The third mathematical model is, using the derived viscosity for lava, looking at the spread of the lava after a wedge. Here it is visible that the lava flow follows the object, but after a certain opening angle, the flow  behaves similarly in all cases. The tighter the angle in the opstructor, the bigger the dry spot.

behaviour of the lava after an angle in an obstructing object

 Herbert insisted that these experiments and mathematical models were nice but that the main thing that was lacking is field data from actual field geologists to check and refine the models. Some place have already placed dows a few walls in a preventive attempt to protect high risc buildings. My opinion is that, even though the prediction of dry spots is nice in order to limit damage to some valuable equipment, lava flows are far from being the most dangerous or damaging results of volcanic eruptions. Lava flows are, exept a few isolated cases, very slow and cover only a small area. Pyroclastic flows and ash related mud floods are way more dangerous and would need a bigger focus on prediction a remediations. They both are extremely fast and widespread results of explosive volcanism. Otherwise, nontherless a good example in modelling Earth preocesse with mathematical models.