Lecture Notes

 

Note 1: Here is a little guide/selection of required topics aimed at a better preparation of the oral exam, which applies to Geophysicists only (the requirements for Physicists are understandably stricter).

Note 2: Files marked with an asterisk * have been recently modified (during the a.y. 2024/25) to implement adjustments or corrections.

• Memories from thermodynamics

• A supposedly fun thing with tensors - Part 1

• A supposedly fun thing with tensors - Part 2*

• Folio 1 - General notions on continuous media

• Folio 2 - Material derivative of integrals; Integral and local laws

• Folio 3 - Stresses; Fluid statics: Isotropy and continuity of pressure

• Folio 4 - Euler's equation

• Folio 5 - Fluid statics: Mechanical equilibrium, equilibrium and stability of the atmosphere*

• Folio 6 - Hydrostatics of incompressible fluids

• Folio 7 - Dynamics of ideal fluids; Momentum and energy flux

• Folio 8 - Steady flow: Bernoulli's equation and applications*

• Folio 9 - Incompressibility; Kelvin's circulation theorem; Potential flow*

• Folio 10 - Gravity waves*

• Folio 11 - Energy transport in gravity waves; Appendices*

• Folio 12 - Real (viscous) fluids: Velocity gradient and stress tensors; Navier-Stokes equation

• Folio 13 - Notes about the Navier-Stokes equation in non-Cartesian coordinate systems

• Folio 14 - Symmetry of the stress tensor; Mechanical pressure and local equilibrium; Momentum flux and viscous dissipation

• Folio 15 - Examples of viscous flow: Poiseuille, Couette and gravity flows*

• Folio 16 - Similarity laws and dimensionless numbers*

• Folio 17 - Stokes flow: Motion of a sphere in a viscous fluid

• Folio 18 - Oscillatory motions in viscous fluids

• Folio 19 - Damping of gravity waves; Surface currents: Ekman layer

• Folio 20 - Stability/Instability; Instability of tangential discontinuities, Kelvin-Helmholtz instability

• Folio 21 - Heat exchange: Heat transfer equation as an energy/entropy balance equation; Fourier's law; Heat equation for incompressible flows

• Folio 22 - Heat exchange in the crust: Boundary conditions, steady-state and transient solutions

• Folio 23 - Green's function for the heat problem; Similarity laws for heat transfer; Solid-fluid heat exchange, Nusselt number

• Folio 24 - Natural convection, Grashof and Rayleigh numbers

• Folio 25 - Rayleigh-Bénard instability

• Folio 26 - Elastic solids: Phenomenological laws of linear elasticity; Stress and strain tensors, constitutive equation

• Folio 27 - Statics: Lithostatic stress tensor; Dynamics: Continuity and Navier equations

• Folio 28 - Elastic waves; Beyond linear elasticity: Basic viscoleastic models