Geophysical Fluid Dynamics

Academic year 2018/2019 Syllabus of previous years
Official course title Geophysical Fluid Dynamics
Course code PHD035 (AF:294874 AR:162392)
ECTS credits 6
Degree level Corso di Dottorato (D.M.45)
Educational sector code GEO/12
Period 2nd Semester
Course year 1
Contribution of the course to the overall degree programme goals
Aim of this course is to present results in Geophysical Fluid Dynamics regarding the instability of large scale flows in the ocean and atmosphere. The stability of fluid flows with respect to infinitesimal disturbances will be examined, using methodologies developed for linear stability analysis applied to homogenous and stratified fluids. The topics covered by this course are a necessary conceptual preface to a study of geostrophic turbulence in both ocean and atmosphere.
Lecture no. 1
Introduction: basic concepts of hydrodynamic instability
lecture no. 2
Stability Theory of homogeneous shear flows: Rayleigh Equation
lecture no. 3
Necessary conditions for instability P.1: Rayleigh Criterion
lecture no. 4
Necessary conditions for instability P.2 : Fjortoft criterion – Howard semi-circle theorem: P. 1(f-plane case)
lecture no. 5
Howard semi-circle theorem: P.2 (beta-plane case) – Piecewise linear flows – Jump conditions
lecture no. 6
Edge-waves – Interacting edge waves: dispersion relationship – Stratified shear flows. Part 1: Taylor-Goldstein Equation
lecture no. 7
Stratified shear flows. Part 2: Necessary condition for instability - Richardson number-based criterion
lecture no. 8
Kelvin-Helmholtz Instability. Baroclinic instability (introduction: a physical picture)
lecture no. 9
Setting the dynamical framework for baroclinic instability: linearized QG equations
lecture no. 10
Necessary conditions for baroclinic instability: the Charney-Stern-Pedlosky criterion
lecture no. 11
The Eady problem: P.1
lecture no. 12
The Eady problem: P.2
lecture no. 13
The two-layer model for baroclinic instability (Phillips problem)
lecture no. 14
The Charney problem: P.1
lecture no. 15
The Charney problem: P.2
Referral texts
Atmospheric and Oceanic Fluid Dynamics by G. Vallis, Cambridge Univ. Press, Nov 2006
Geophysical Fluid Dynamics 2nd edition, by J. Pedlosky, Springer, 1987
Course on Stability Theory by J. Pedlosky [ ]
An Introduction to Dynamic Meteorology, by J.R. Holton, Academic Press Inc., 2004
Introduction to Geophysical Fluid Dynamics by Benoit Cushman-Roisin, Prentice Hall.
Teaching language
Further information
The course may be enriched by the participation of some external lecturers (to be confirmed). Attendance is required. Daily preparation is also required. The assignments are set out in the course syllabus. Academic honesty is an important part of university training. While students may discuss assignments with their classmates and others, they are expected to make sure any written material they submit is their own work. Students are expected to know how to cite the work of others and present a bibliography of the research texts that were used.
Definitive programme.