Lava Delta Formation: Mathematical Modeling and Laboratory Experiments

We analyze the dynamics of evolving lava-fed deltas through the use of shallow-layer mathematical models and analog laboratory experiments. Numerical and asymptotic solutions are calculated for the cases of planar and three-dimensional flows fed by a point source upstream of the shoreline. We consider several modes of delta formation: a reduction in the driving buoyancy force; an enhanced viscosity of the submerged material; and the production of a granular subaqueous platform, over which a subaerial current can propagate. These modes of delta formation result in different behaviors. Under a steady supply of fluid upstream, the buoyancy-driven case develops a solution with a steady subaerial delta and a subaqueous current which propagates at a constant speed, while the granular platform model extends the delta indefinitely. We determine a late-time power-law relation for the shoreline extent with time in this case. When the viscosity contrast is large, the model with an enhanced subaqueous viscosity is shown to mimic the initial dynamics of the granular platform model, but ultimately reaches a steady shoreline extent at sufficiently late times, as for the buoyancy-driven model. The distinct behaviors of these models are further illustrated through laboratory experiments, utilizing the gelling reaction of sodium alginate solution in the presence of calcium ions as a novel analog for the abrupt rheological changes that occur when lava makes contact with water. These experiments provide quantitative verification of the buoyancy-driven model in the absence of the reaction, and demonstrate the effects of a subaqueous platform qualitatively in its presence.