31906 - Foundations of Geophysics 2

Learning outcomes

At the end of the course, the student will also possess basic knowledge of Newtonian fluid dynamics and its application to study gravity waves, thermal convection processes and turbulent flows. Moreover, the student will possess basic knowledge of fluid flow within confined and unconfined aquifers, including heat propagation across permeable media. Finally the student will learn the constitutive laws of poro-elastic materials, in which a fluid phase is present within a permeable elastic matrix, and of viscoelastic materials, endowed with behaviour intermediate between an elastic solid and a highly viscous fluid. In particular the student will be able to evaluate the conditions of gravitational instability in the mantle – to characterize the different regimes of propagation of gravity waves – to solve simple problems of fluid flow in confined and unconfined aquifers  – to describe quantitatively hydrothermal convection phenomena and rock-fluid interaction processes - to solve simple problems of quasi-static equilibrium in viscoelastic materials.

Course contents

Newtonian fluids, the Navier-Stokes equations, laminar flows and transition to turbulence, equations in a rotating planet: the vorticity equation. The Boussinesq approximation. 

Gravity waves at the free surface of a fluid layer, shallow water and deep water approximations, the role of surface tension; internal waves in stratified fluids.

Introduction to the theory of turbulence: cascade turbulence production, the Kolmogorov micro-scale, the Kolmogorov spectrum in the sub-inertial range. Eddy viscosity, geostrophic flow, Ekman spirals.

Rayleigh-Taylor instability,  Kelvin-Helmoltz instability, Rayleigh convection, convection in internally heated fluids.

Fluid fow in permeable media: the Darcy law, fluid flow in confined and unconfined aquifers, Dupuit approximation. Heat propagation across permeable media: hydrothermal convection.

Poro-elasticity, Biot's constants, the "effective stress" concept, drained and undrained conditions, the diffusion equation for the permeating fluid.

Visco-elasticity: spring-and-dashpot prototypes, tensorial generalization of constitutive relations. Differential and integral constitutive relations. Creep and relaxation functions. Quasi static equilibrium and the "Correspondence Principle" in the Laplace transform domain. Oscillatory motions, the complex modulus of rigidity and the internal friction.

Readings/Bibliography

Lecture notes of Prof. M. Bonafede

Teaching methods

Classroom lectures

Assessment methods

The learning assessment consists of an oral examination. The examination tends to evaluate the fulfilment of the Course learning outcomes:

-Knowledge of the dynamics of Newtonian and inviscid fluids.
-Knowledge of quantitative models on main phenomena, such as: gravity waves, convection, transition towards turbulence, fluid flows in porous media.
-Knowledge of constitutive equations of poro-elastic media.

The final score of the course of Foundations of Geophysics 2 is determined as the average of the scores obtained by answering three questions about the main Course subjects.

Office hours

See the website of Maria Elina Belardinelli

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