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

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.

Rayleigh-Taylor instability, Kelvin-Helmholtz instability, Rayleigh convection, convection in internally heated 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.

Readings/Bibliography

Lecture notes provided by the teacher at http://campus.unibo.it/ after completing the lectures of each chapter.

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, 2002.

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 tends to evaluate the fulfilment 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.

 

Office hours

See the website of Alberto Armigliato