A Numerical Simulation of Basaltic Lava Flows and its Application to the 1983 Lava Flows at Miyakejima

Abstract

A method of the numerical simulation for low viscous lava flows is presented. The lava flows over the digital topographic maps are formulated, expanding the simple solution of Navier-Stokes’ equation concerning the liquid of a constant thickness which flows downward by gravity on an inclined plane. The progress of the fronts of lava flows is, however, nonstationary process. Therefore, the concepts of the minimum thickness of lava flows are introduced to compensate the simplicity of our formulation. The minimun thickness is defined so as to depend on the inclination of the ground, the physical properties of lava and the minimum velocity of lava flows. The method of the numerical calculation was applied to the reproduction of the 1983 lava flows at Miyakejima, assuming the condition of the extrusion of the lava and their physical properties. The topographic map of Miyakejima was digitized with the sampling square of 25 m×25 m. The simulated lava flows fairly coincided with the actual ones in their path and width, when the viscosity of the lave was assumed to be 2×10⁵ poises. The extension of the reproduced lava flows with time agreed with the observation when the successive increase of the viscosity from 5×10⁴ poises to 1×10⁷ poises was assumed. This result suggests that the macroscopic viscosity of the lava flows increased by about one hundred times in their progress. The proposed method of the numerical simulation for lava flows may be available for predicting the paths and the extension of the forthcoming lava flows.