Linking Rheology to Morphology in Lava Flows: A Theoretical Framework for Power-Law and Prefractal Scaling

Abstract

Volcanism is a fundamental planetary process, and understanding the dynamics of lava flows is critical for both hazard mitigation and geological studies. The final length and morphology of a lava flow are governed by a complex interplay between effusion rate, total volume, topography, and the lava's evolving thermo-rheological properties. While empirical power laws relating flow length to effusion rate or volume have proven useful, they do not fully capture the physical processes driving flow behavior, particularly the effects of crust formation and fragmentation. This paper presents an integrated theoretical framework that links macroscopic flow dynamics with the microscale processes of fragmentation. We begin by deriving scaling laws for flow length and width based on a Herschel-Bulkley fluid model. We then introduce a novel component to this framework by postulating that key rheological parameters evolve as a function of the flow's developing prefractal dimension, which quantifies its fragmentation and complexity. Finally, we propose a modified power law for the final flow length that accounts for energy dissipation due to both viscous shearing and the creation of new prefractal surfaces. By analyzing observational data from various basaltic to rhyolitic lava flows, we calibrate and discuss the model's empirical coefficients. The results demonstrate that highly fragmented lava flows like 'a'ā have their runout distance significantly reduced by the energetic cost of their increasing complexity, consistent with field observations. This framework provides a more physically robust foundation for forecasting lava flow behavior and interpreting their final morphologies.