Welcome to EOSC 512: Advanced Geophysical Fluid Dynamics!  The purpose of this course is to 1) introduce the student to the dynamical principles governing the large-scale, low-frequency motions in strongly rotating fluid systems (like the ocean, atmosphere, and liquid planetary core) and their consequences; and 2) to develop the skills required to manipulate and use these principles to solve problems. 

At the end of this course, students should be able to:
  • write down the `standard equations' of geophysical fluid dynamics (GFD), identify the different terms, evaluate their relative importance based on scaling arguments, and explain how different dynamical features depend on these terms. Examples include the geostrophic and quasi-geostrophic equations, boundary layer equations, and thermodynamic relationships;
  • define standard terms and concepts used in GFD (the ``language'' of GFD), and identify them when they arise in the context of dynamical interpretations.  Examples include Eulerian, Lagrangian, hydrostatic, Boussinesq, the Coriolis acceleration/force, Ekman layers, vorticity, geostrophic, barotropic, and baroclinic;
  • use standard mathematical techniques to simplify complex equation sets relevant to GFD.  Examples include linearization, scaling arguments, normal mode techniques, and complex exponentials in wave and instability problems;
  • use the appropriate approximations and mathematical techniques to simplify and solve particular ``canonical'' GFD problems.  Examples include a description of Taylor columns, a description of Ekman layers, spin-down problems, Rossby adjustment problems, wave problems in non-rotating and rotating systems, and instability problems.

This course is closely modelled after the first-year graduate course "12.800 Fluid Dynamics of the Atmosphere and Ocean" taught by Joe Pedlosky in the MIT-Woods Hole Joint Program.  I will be forever grateful to have had the privledge of learning GFD from such an inspirational teacher.

Syllabus:

Information about this year's offering of EOSC 512 is contained in the course syllabus.  The most up-to-date version will be posted here.

Lecture Notes:

  1. ​Some Basics​​ (definition of a fluid; the continuum hypothesis; the fluid element; kinematics; rates of change)
  2. The Continuum Equations (the mass equation; the momentum equation; the stress tensor; the momentum equation in differential form)
  3. The Stress Tensor & The Navier-Stokes Equations (symmetry of the stress tensor; putting the stress tensor in diagonal form; the static pressure; analysis of fluid motion at a point; vorticity; rate of strain; principal strain axes & the decomposition of the motion; the relation between stress & rate of stain; viscosity; the Navier-Stokes Equations)
  4. Rotating Coordinate Systems & The Rotating Equations of Motion (rates of change in a rotating frame; the Coriolis acceleration/force; the Navier-Stokes equations in a rotating frame)
  5. Boundary Conditions & Frictional Boundary Layers (boundary conditions at a solid surface; boundary conditions at a fluid surface; Ekman layers over a solid surface; Ekman layers below a free surface; exaple applications: coastal upwelling and the ocean gyre circulation; the Ekman spin-down time)
  6. Circulation and Vorticity (Kelvin's circulation theorem, example applications: the Rossby wave, ocean gyre circulation and the bathtub vortex; vortex tube stretching; the vorticity equation; example applications: thermal wind and the Taylor-Proudman theorem; Ertel's theorem; potential vorticity)
  7. Dynamical Balances (geostrophy scaling and geostrophic balance; consequences of geostrophy; the quasi-geostrophic potential vorticity equation; example application: baroclinic Rossby waves)
  8. Other Topics (recommendations for resources for topics we don't have time to cover i.e. thermodynamics; wave motions; general circulation theory; instabilities and turbulence)

Problem Sets:

Useful Texts:

​The class does not follow any specific text, but the texts listed below can be helpful for additional reading.  Physical copies of these texts will be made available for a shortened, in-library loan period via Course Reserves at the Woodward Library.  Items marked with an * are also available online as e-books through the UBC Library website. 
  • *Kundu, P.K. Fluid Mechanics. Academic Press. (Any edition 1990 or later) = a popular text for students of all flavours of fluid dynamics​
  • Batchelor, G.K. An Introduction to Fluid Dynamics. Cambridge Univ. Press. (Any edition 1967 or later.) = the(?) classic text on fluid dynamics; less "warm and fuzzy" than Kundu
  • *Aris, R. Vectors, Tensors and the Basic Equations of Fluid Mechanics. Prentice Hall. (Any edition 1962 or later.) = a nice little text that demonstrates the mathematics of tensors applied to the theory of fluid mechanics
  • Cushman-Roisin, B. Introduction to Geophysical Fluid Dynamics. Prentice-Hall. (Any edition 1994 or later.) = my personal fvaourite introductory-level text; a description of the basic concepts of GFD emphasizing the physical interpretation and keeping the mathematics "light"
  • *Pedlosky, J. Geophysical Fluid Dynamics. Springer Verlag. (Any edition 1979 or later.) = a comprehensive and complete mathematical discussion of dynamical oceanography; dense and relies a lot on nondimensionalization (which isn't for everyone)
  • Gill, A.E., Atmospheric-Ocean Dynamics. Academic Press. 1982 = similar content as Pedlosky but with a less formal approach and with reference to real-world observations
  • *Marshall, J. and R.A. Plumb.  Atmosphere, Ocean and Climate Dynamics: An Introductory Text. Academic Press. 2008 = an introductory text designed for a senior-level undergraduate course
  • *Vallis, G.K.  Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge Univ. Press. (Any edition 2006 or later.) = a graduate-level text suitable for advanced courses in GFD (I wished this text existed when I was a first-year graduate student!)

Regrettably, I have yet to go fast enough through the above material to have time to cover wave theory relevant to the interests of oceanographers and meteorologists (there is enough material here for its own class!)  Some resources on this topic that I recommend are: 
  • Pedlosky, J. Waves in the Ocean and Atmosphere: Introduction to Wave Dynamics. Springer. 2003 = a reworking of Joe Pedlosky's lecture notes for a core course on wave theory for physical oceanography and meteorology students.
  • LeBlond, P.H. and L. Mysak, Waves in the Ocean. Elsevier. 1978 = a very good reference for wave and wave motions (unfortunately now out-of-print).

Finally, some other texts that are more ocean- or atmosphere-centric (of potential interest depending on whether you self-identify as an atmospheric scientist or a physical oceanographer) and that focus more on observations or models are:
  • Talley, L.D., G. L. Pickard, W. J. Emery and J. H. Swift, Descriptive Physical Oceanography: An Introduction. Elsevier Ltd. 2011 = an introduction to the field of physical oceanography with an emphasis on large-scale oceanography based mainly on observations.
  • Wunsch, C.W.  Modern Observational Physical Oceanography: Understanding the Global Ocean. Princeton University Press. 2015 = an interesting text that addresses the link between GFD and ocean observations. 
  • Pond, S. and G. L. Pickard.  Introductory Dynamic Oceanography. Pergamon. 1983 = practical advice for observationalists (e.g. how to actually compute a geostrophic velocity from real data).
  • Holton, J. R. An Introduction to Dynamic Meteorology, Second Edition. Academic Press. 1979 = the classic text for upper-year undergraduate/first-year graduate students majoring in atmospheric sciences.
  • Griffies, S. M.  Fundamentals of Ocean Climate Models. Princeton University Press. 2004 = a treatment of the physical, mathematical, and numerical foundations of ocean circulation models used in modern climate models.

Other Helpful and/or Cool Things:

Last updated December 2024