Two-dimensional Model of Pāhoehoe Lava Flow at the Single-to-multi-lobe-scale

Lava flows form when molten rock effusively erupts onto the surface of planets and spreads. While the first-order dynamics of lava spreading can be described using gravity-current type equations or gradient-based algorithms, complex lobe-scale (decimeter to meter) behaviors such as crust inflation and flow breakout remains challenging to model in existing frameworks. Capturing such lobe-scale dynamics could significantly advance our capability to forecast the paths taken by surface flows and interpret depositional history.

Here, we develop a 2D (birds-eye view) model of lava spreading at the single-to-multi-lobe scale. We focus on understanding the dynamics of pāhoehoe flow, where a smooth layer of quenched lava encrusts the spreading of the molten liquid. Considering that lava flows within the laterally-extensive and vertically-thin space between the top crust and the ground, we use lubrication theory to describe its spreading dynamics. We use phase-field type equations for two-phase Hele-Shaw flow where the flow aperture is defined as the distance between the solidified crust at the top and the ground (determined by topography). The aperture decreases as the top and bottom crusts grow, and we inform this relationship with analytical solutions of the Stefan problem. The aperture increases as the top crust inflates due to local over-pressure, and we describe such inflation with nonlinear plate theory. In an effort to incorporate dynamics of flow arrest and breakouts, we introduce a phenomenological lava-air surface tension that increases as the interface solidifies. We use the model to investigate the coupled interactions amongst crust growth, crust/lobe inflation and fluid flow, and we explore the pattern formation of pāhoehoe lava flow under different discharge dynamics.