NUMERICAL INVESTIGATION AND DISCUSSION OF THE MAGNETOHYDRODYNAMICS OF BASALTIC LAVA FLOWS THROUGH TUBES BY FIRST ORDER APPROXIMATIONS OF THE MAGNETIC REYNOLDS NUMBER AND HARTMANN NUMBER

Magnetohydrodynamics (MHD) couples Navier-Stokes with Maxwell’s equations to describe the magnetic behaviors of electrically conducting fluids. Molten lava is electrically conductive and can move at high velocities particularly through tubes, which help insulate the flow to achieve rates of 10m/s. Thermal demagnetization in and around the lava tube, relating to the Currie isotherm, marks a negative magnetic anomaly due to loss of remnant magnetization. However, very small (nT) perturbations of the magnetic field around and within the lava tube may exist. The purpose of this study is to investigate the magnetohydrodynamics of a typical basaltic lava flow through a length section of tube. A range of values for electrical conductivity (σ), viscosity (ν), imposed magnetic field strength (B₀), velocity (u), and length scale (l) are used from the literature to provide first order approximations with upper and lower limits of the dimensionless numbers used in MHD. The magnetic Reynolds’s number (R_m) offers insight on the conducting fluid’s behavior. The two extremes cases are: R_m<<1 where diffusion dominates and advection is negligible, and R_m>>1 where magnetic field lines are advected with the flow and diffusion is negligible. Presented here is a first order approximation range of R_m= 0.06-0.8, which coincide with a diffusive dominated MHD flow. For MHD fluids at low R_m, the Hartmann number (Ha) represents the ratio between the Lorentz force and viscous force in fluid flow. The first order approximations for Ha of basaltic flows range between 0.02-0.7, implying a viscous dominated velocity profile. These low ranging numbers suggest that an imposed magnetic field on a lava flow will only induce small perturbations in the magnetic field lines. However at larger length scales, such as those found on the planetary scale, the R_m and Ha numbers are larger than 1 and solutions to the MHD equations become much more complex and warrant further investigation.