Cooling of a channeled lava flow with non-Newtonian rheology: crust formation and surface radiance

We present here the results from dynamical and thermal models that
describe a channeled lava flow as it cools by radiation. In particular, the
effects of power-law rheology and of the presence of bends in the flow are
considered, as well as the formation of surface crust and lava tubes. On
the basis of the thermal models, we analyze the assumptions implicit in
the currently used formulae for evaluation of lava flow rates from satellite
thermal imagery. Assuming a steady flow down an inclined rectangular
channel, we solve numerically the equation of motion by the finite-volume
method and a classical iterative solution. Our results show that the use of
power-law rheology results in relevant differences in the average velocity
and volume flow rate with respect to Newtonian rheology. Crust formation
is strongly influenced by power-law rheology; in particular, the growth
rate and the velocity profile inside the channel are strongly modified. In
addition, channel curvature affects the flow dynamics and surface
morphology. The size and shape of surface solid plates are controlled by
competition between the shear stress and the crust yield strength: the
degree of crust cover of the channel is studied as a function of the
curvature. Simple formulae are currently used to relate the lava flow rate
to the energy radiated by the lava flow as inferred from satellite thermal
imagery. Such formulae are based on a specific model, and consequently,
their validity is subject to the model assumptions. An analysis of these
assumptions reveals that the current use of such formulae is not consistent
with the model.