C8415 - FOUNDATIONS OF GEOPHYSICS 2: FLUIDS

Learning outcomes

The student will acquire the fundamental theoretical concepts of fluid dynamics mainly for Newtonian rheologies, with some hints also on non-Newtonian rheologies, with a constant attention paid to problems of geophysical interest. In particular, the student will be able to: - characterize the different regimes of propagation of gravity waves in homogeneous as well as in stratified fluids; - quantify the conditions for the onset of instabilities due to differences in velocity, angular velocity, temperature; - understand the key concepts of turbulence.

Course contents

General introduction

• Fluids as continua
• Constitutive equations and Newtonian fluids
• Conservation laws, the Navier-Stokes equations, laws of thermodynamics for Newtonian fluids
• 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 in an inertial reference frame; shallow water and deep water approximations
• Surface tension and capillary waves
• Stationary waves
• Internal waves in stratified fluids.

Instability

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

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.
  

 

Prerequisites: fundamentals of continuum mechanics learnt in the the frame of the course Foundations of Geophysics 1: Solids

Readings/Bibliography

Lecture notes provided by the teacher in pptx and pdf formats at https://virtuale.unibo.it after each lecture.

The set of files provides a comprehensive presentation of the syllabus and can serve as a textbook for studying the subject.

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

• Pijush Kundu, Ira Cohen, David Dowling: Fluid Mechanics - , 6th Edition, Academic Press, 2016.
• 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 involving both writing on the blackboard and the use of digital material.

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 covered during the course, aims at evaluating the knowledge of the student and her/his independence in reasoning.

As an alternative to one of the three questions, students can choose to discuss orally the content of a scientific paper of their choice, coherent with the topics treated during the course. The choice of the paper must be communicated and possibly discussed with the teacher at least one week before the exam.

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

In the classroom: blackboard and projector.

In addition to the pptx and pdf files uploaded on Virtuale, the teacher will also provide a list of web links related to topics of interest to the course.

 

Students with Specific Learning Disorders (SLD) or with temporary or permanent disabilities are advised to contact the relevant University office in due time (https://site.unibo.it/studenti-con-disabilita-e-dsa/it): the office will propose possible adjustments to the students concerned, which must in any case be submitted, 15 days in advance, to the approval of the teacher, who will assess their suitability also in relation to the learning objectives of the course.

Office hours

See the website of Alberto Armigliato