We propose a model to describe lava tube formation, considering lava as a Newtonian fluid moving downslope in a rectangular channel. We obtain flow velocity using an analytical steady-state solution of the Navier-Stokes equation. Shear stress is also calculated from velocity for a Newtonian incompressible and isotropic fluid. A 2-D model with heat flux assigned at the upper surface is introduced to describe lava cooling by radiation into the atmosphere and to obtain the flow temperature. Lava crust is considered as a plastic body, and its rheology is described through the introduction of the yield strength as a function of temperature. It describes the capacity of crustal structure to prevent shear deformation for lower shear stress values. When lava temperature becomes lower than the solidus value T-s, a superficial thin solid layer develops in regions where shear stress sigma(xy) is smaller than yield strength tau. The model shows how the competition between these two functions (sigma(xy) and tau) controls the development of crust width and the possible transition from a mobile crust to a stationary roof. For typical parameter values of lava channels on Mount Etna, crust develops in the central part of the flow, laterally limited by two crust-free regions. We analyze the effects of some typical channel irregularities on surface shear stress and, as a consequence, on crust width growth. We consider a variation of channel width and ground slope, finding that crust widening is favored by channel widening or slope reduction. In both cases, the decrease in shear stress produces an increase in the fraction of channel width occupied by solid crust. Given a set of initial conditions defining eruptive parameters and channel features, the model provides critical values of channel width and ground slope that allow tube formation. The effect of different effusion rates on crust development is also studied, with the result that tube formation is favored by low flow rates, corresponding to lower values of sigma(xy).
Mechanism of formation of lava tubes
TALLARICO, Andrea;
2008-01-01
Abstract
We propose a model to describe lava tube formation, considering lava as a Newtonian fluid moving downslope in a rectangular channel. We obtain flow velocity using an analytical steady-state solution of the Navier-Stokes equation. Shear stress is also calculated from velocity for a Newtonian incompressible and isotropic fluid. A 2-D model with heat flux assigned at the upper surface is introduced to describe lava cooling by radiation into the atmosphere and to obtain the flow temperature. Lava crust is considered as a plastic body, and its rheology is described through the introduction of the yield strength as a function of temperature. It describes the capacity of crustal structure to prevent shear deformation for lower shear stress values. When lava temperature becomes lower than the solidus value T-s, a superficial thin solid layer develops in regions where shear stress sigma(xy) is smaller than yield strength tau. The model shows how the competition between these two functions (sigma(xy) and tau) controls the development of crust width and the possible transition from a mobile crust to a stationary roof. For typical parameter values of lava channels on Mount Etna, crust develops in the central part of the flow, laterally limited by two crust-free regions. We analyze the effects of some typical channel irregularities on surface shear stress and, as a consequence, on crust width growth. We consider a variation of channel width and ground slope, finding that crust widening is favored by channel widening or slope reduction. In both cases, the decrease in shear stress produces an increase in the fraction of channel width occupied by solid crust. Given a set of initial conditions defining eruptive parameters and channel features, the model provides critical values of channel width and ground slope that allow tube formation. The effect of different effusion rates on crust development is also studied, with the result that tube formation is favored by low flow rates, corresponding to lower values of sigma(xy).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
