31906 - Foundations of Geophysics 2

Academic Year 2021/2022

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Physics of the Earth System (cod. 8626)

Learning outcomes

By the end of the course, the student will acquire basic knowledge of Newtonian fluid dynamics and its application to the study of gravity waves, thermal convection processes and turbulent flows. 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 related to instability and to the transition towards turbulence.

Course contents

General introduction

  • Newtonian fluids
  • Conservation laws, the Navier-Stokes equations, laws of thermodynamics
  • Laminar flows and transition to turbulence: the Reynolds number
  • Equations in a rotating planet: the vorticity equation
  • The Boussinesq approximation. 

Waves in fluids

  • Gravity waves at the free surface of a fluid layer, shallow water and deep water approximations
  • Surface tension and capillary waves
  • Internal waves in stratified fluids.


  • Kelvin-Helmholtz instability
  • Rayleigh convection, convection in internally heated fluids
  • Rayleigh-Taylor instability

Introduction to the theory of turbulence

  • Reynolds decomposition
  • Equations governing turbulent flows
  • Energy for the average flow and for the turbulent flow
  • Cascade turbulence production, the Kolmogorov micro-scale, the Kolmogorov spectrum in the sub-inertial range
  • Eddy viscosity, geostrophic flows, Ekman spirals.


Lecture notes provided by the teacher at https://virtuale.unibo.it after each lecture.

Most of the topics presented in the course can be found in:

  • Pijush Kundu, Ira Cohen, David Dowling: Fluid Mechanics - Academic Press. The most recent edition is the sixth, published in 2015.
  • Donald Turcotte, Gerald Schubert: Geodynamics - Cambridge University Press, 3rd Edition, 2014.
  • Etienne Guyon, Jean-Pierre Hulin, Luc Petit, Catalin D. Mitescu: Physical Hydrodynamics (2nd Ed.) - Oxford University Press, 2015.

Teaching methods

Classroom lectures

Assessment methods

The learning assessment consists of an oral examination.

The examination, which usually foresees three questions on different topics, aims at evaluating the fulfillment of the Course learning outcomes:

-knowledge of the dynamics of Newtonian and inviscid fluids.
-knowledge of quantitative models of main phenomena, such as: gravity waves, convection, transition towards turbulence.

The exam duration is one hour on average.


Office hours

See the website of Alberto Armigliato


Sustainable cities Climate Action

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.