We introduce a 3D model for near-vent channelized lava flows. We assume the lava to be an isothermal Newtonian liquid flowing in a rectangular channel down a constant slope. The flow velocity is calculated with an analytical steady-state solution of the Navier-Stokes equation. The surface velocity and the flow rate are calculated as functions of the flow thickness for different flow widths, and the results are compared with those of a 2D model. For typical Etna lava flow parameters, the influence of levees on the flow dynamics is significant when the flow width is less than 25 m. The model predicts the volume flow rate corresponding to the surface velocity, taking into account that both depend on flow thickness. The effusion rate is a critical parameter to evaluate lava flow hazard. We propose a model to calculate the effusion rate given the lava flow width, the topograhic slope, the lava density, the surface flow velocity, and either the lava viscosity or the flow thickness

S U M M A R YVolcanic rocks forming sills, dykes or lava flows may display a magnetic anisotropy derived from the viscous flow during their emplacement. We model a sill as a steadystate flow of a Bingham fluid, driven by a pressure gradient in a horizontal conduit. The magma velocity as a function of depth is calculated from the motion and constitutive equations. Vorticity and strain rate are determined for a reference system moving with the fluid. The angular velocity and the orientation of an ellipsoidal magnetic grain immersed in the fluid are calculated as functions of time or strain. Magnetic susceptibility is then calculated for a large number of grains with a uniform distribution of initial orientations. It is shown that the magnetic lineation oscillates in the vertical plane through the magma flow direction, and that the magnetic foliation plane changes periodically from horizontal to vertical. The results are compared with the magnetic fabric of Ferrar dolerite sills (Victoria Land, East Antarctica) derived from low-field susceptibility measurements.

The formation of lava tubes is a common phenomenon on some basaltic volcanoes, such as Etna. A model for tube formation by roofing of a channel is proposed and involves first describing lava as a Bingham liquid flowing down a slope. It is further assumed that lava flows in a channel with rectangular cross section: as a result of heat loss into the atmosphere, a crust is gradually formed on the upper surface of the flow and this crust eventually welds to the channel levees. We assume that a lava tube is formed when such a crust is sufficiently thick to resist the drag of the underlying flow and to sustain itself under its own weight. The minimum thickness of the crust satisfying such conditions depends on the tensile strength and shear strength of the crust itself. Assuming that the growth of the crust produces a downflow linear increase of the shear stress at the interface between flowing lava and the crust, the distance is evaluated between the eruption vent and the point where the tube is formed. The model predicts that if the flow rate is constant, the thickness of the flow increases as the crust fragments grow and weld to each other, and the velocity of the crust decreases to zero. Once the lava tube is formed, the initial flow rate can be achieved by a Row thickness smaller than the vertical size of the tube, with the same viscous dissipation: this may explain why under steady state conditions, the lava level inside a tube is frequently lower than the roof of the tube itself

[1] The availability of high-resolution thermal imagery of active lava flows has stimulated the use of radiance maps for the evaluation of lava effusion rates. This is made possible by simple formulae relating the lava flow rate to the energy radiated per unit time from the planimetric surface of the flow. Such formulae are based on a specific flow model and, consequently, their validity is subject to the model assumptions. An analysis of these assumptions reveals that the current use of the formulae is not consistent with the model. The reason why they provide reasonable, although very rough, values for effusion rates appears to be that the actual radiated energy is controlled by a feature (the nonuniform temperature of flow surface) which is not accounted for by the model and which counterbalances the effect of inconsistent use of the formulae. Citation: Dragoni, M., and A. Tallarico (2009), Assumptions in the evaluation of lava effusion rates from heat radiation, Geophys. Res. Lett., 36, L08302,

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[1] The shape of the front of a lava flow is controlled by the forces acting on the lava and, in turn, controls the flow dynamics. We present an analysis of the shape of the front of an advancing lava flow, considering both a Newtonian fluid and a Bingham fluid, which is the most commonly used non-Newtonian rheological model for lava. We assume than the flow front is moving at constant velocity on a sloping plane. The flow is considered as having an infinite extent perpendicularly to the flow direction, so that the problem is two-dimensional. The forces producing the flow advance are the gravity force and the pressure gradient due to the curvature of the flow surface. The differential equation for the shape of the front is solved analytically both in the case of a Newtonian fluid and in the case of the Bingham fluid. Since the fluid is considered as homogeneous and isothermal, the calculated shape applies to the fluid core of the flow front. The presence of a solid crust at the top of the flow, producing variable amounts of solid debris at the flow snout, alters the observable shape of the front and is taken into account in order to compare the model front shapes to those observed in the field.

Abstract. We propose a three-dimensional (3-D

[1] 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 s xy is smaller than yield strength t. The model shows how the competition between these two functions (s xy and t) 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 s xy .