31906 - Foundations of Geophysics 2

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

• Brief recap on continuum mechanics: the fundamental tensors used in fluid dynamics and the constitutive relations
• Newtonian fluids
• Conservation laws, the Navier-Stokes equations, laws of thermodynamics
• Laminar flows and transition to turbulence: the Reynolds number
• Hints on non-Newtonian fluids
• 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.

Instability

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

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 (possible).
  

 

Readings/Bibliography

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.

Some papers on specific topics will be made available in Virtuale: the students may optionally read them to get a bit more into the details of those topics.

Teaching methods

Classroom lectures.

Attending the lessons is not compulsory, but it is warmly recommended for the learning process.

Assessment methods

The learning assessment consists of an oral examination based on which a mark will be proposed..

The examination, which usually foresees three questions on different topics, aims at evaluating the knowledge of the student and her/his independence in reasoning on:

• the dynamics of Newtonian and inviscid fluids;
• the quantitative models of the main phenomena illustrated during the lessons, such as: gravity waves, convection, transition towards turbulence.

The exam does NOT foresee any written report to be delivered by the student before the exam.

The exam duration is one hour on average.

 

Teaching tools

The teacher will upload on the "Virtuale" platform few simple codes allowing the students to become acquainted through a "hands on" approach with some of the theoretical concepts illustrated during the lessons.

 

Office hours

See the website of Alberto Armigliato