Lava Tube Stability
Center for Atmosphere ocean Science, Courant Institute
Lava tubes of great length exist in many settings. We investigate the nature and stability of an idealized model and ask ?how far can the fluid flow and remain liquid?? We first present laboratory experiments which show that the pressure difference across a tubular drainage channel reaches a maximum just before the tube becomes unstable, a result which is not in accord with previous theoretical studies. Next, we construct a theoretical model of a drainage tube, similar to that used in injection molding studies but with a novel pressure-flux upstream boundary condition. A stability analysis shows that by varying a parameter in this boundary condition, the maximum possible length of a stable steady-state tube, as well as the pressure difference across a marginally stable tube, can vary from a fixed finite value to inifity. This is one possible explanation for our experimental results. We conclude that the distance traveled by melt in a lava tube is very sensitive to the conditions that govern pressure and flow rate at the upstream end.