46350 - Physics of Volcanism

Learning outcomes

Basic knowledge about the physical causes of volcanism and modelling of volcanic eruptions.

Course contents

Introduction: formation of terrestrial planets and causes of volcanism, volcanism in the Solar System, volcanic activity of the Earth.

Phenomenology: geographical distribution of volcanoes, eruptive styles, explosive and effusive activities and associated phenomena, composition and physical properties of magmas, energy released by an eruption, volcanic hazard, explosivity index, supervolcanoes, large basaltic floods, climatic effects of eruptions, active volcanoes in Italy, volcanic risk.

Systems of curvilinear coordinates: differentiation of vectors in orthogonal coordinates, the strain tensor in orthogonal coordinates, vector operators in cylindrical and spherical coordinates, tensor components in curvilinear coordinates.

Viscous fluids: equations of motion and continuity, constitutive equation, isotropic and incompressible Newtonian fluids, dissipation function, Navier-Stokes equation, vorticity, Helmholtz equation, Reynolds number, non-Newtonian fluids.

Flow in pipes: steady-state flow between plane and parallel walls, flow rate, cylindrical pipes with circular and elliptical cross sections, mechanical erosion of the walls, application to volcanic conduits and lava tubes.

Thermal processes in solids: internal heat of the Earth, surface heat flow and comparison with the solar flow, thermal conduction, Fourier law, heat equation, geotherms, Dirichlet problems, conformal mapping, temperatures around a lava flow and a lava tube, point-like heat sources, time-dependent problems, the Laplace solution, propagation of heat in one direction, cooling of a lava body.

Thermal processes in fluids: thermal conduction, heat equation, advection and viscous dissipation, Prandtl and Péclet numbers, flow in a cylindrical pipe with viscous dissipation, convection.

Fluids in the gravity field: conditions for the mechanical equilibrium, buoyancy force, Boussinesq approximation, Rayleigh-Taylor instability, diapyrism, stream function, thermal convection, Grashof and Rayleigh numbers, compressible fluid in the gravity field, adiabatic temperature gradient, gravity field in the Earth's interior.

Genesis of magma: temperature and pressure in the Earth, thermal properties of rocks, the Clausius-Clapeyron equation, liquidus e solidus temperatures, depth of magma genesis, mechanisms of magma ascent, plutons and magma chambers.

Porous media: porosity of rocks, permeability, pore pressure, Darcy law, mass and heat transport, model for an isotropic porous medium, magma migration through the Earth's mantle, thermal convection in a porous layer, flow above a magma body, hydrothermal systems, hot springs, geysers, porous elastic media.

Rheology: brittle and ductile behaviours, rheological models, linear viscoelastic bodies, the Maxwell and Kelvin bodies, deformation under constant load, correspondence principle, plastic, elastoplastic and viscoplastic bodies, the Bingham body, rheology of lavas, Arrhenius law.

Magma chambers: evolution of pressure and mechanisms of eruptions, pressurized spherical cavity in an elastic and in a viscoelastic medium, the Mogi model, phase transitions and magma differentiation, cooling of a spherical magma chamber, volatile components, saturation and solubility, the Henry law, magma vesciculation, solidification of the magma chamber.

Lava flows: relationships among temperature, rheology and dynamics, Newtonian flow model, thickness and flow rate, shape of the flow front, Bingham flow model, thermal processes, cooling by radiation, formation of lava tubes.

Readings/Bibliography

A. Biancotti e altri, Atlante della Terra, UTET, 1999.
E. Boschi, M. Dragoni, Sismologia, UTET, 2000.
D.L. Turcotte, G. Schubert, Geodynamics, John Wiley, 1982.

Teaching methods

Lectures and exercises in the classroom.

Assessment methods

Oral examination.

Teaching tools

Lectures with overhead projector.

Office hours

See the website of Michele Dragoni