# EOSC 512 · Advanced Geophysical Fluid Dynamics

#### Course Description:

The purpose of this course is to a) 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 b) to develop the skills required to manipulate and use these principles to solve problems.

#### Prerequisites:

Formally none. However, this course is mathematical and assumes a working knowledge of vector calculus (*e.g.* div, grad, curl), partial differential equations (*i.e.* you can solve at least some of them), and some exposure to complex analysis (*e.g.* you know that if* z=x+iy*, then *ez = excos(y)+iexsin(y*)*)*. A background in fluid dynamics, geophysics, atmospheric sciences, and/or oceanography is not required (although undoubtedly will be helpful).

#### Instructor:

Rich Pawlowicz

office: ESB 3019

email:

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Meeting Times:

EOSC 512 will be held at a time that can accommodate the majority of students (ideally 3x1 hour blocks each week). Please contact the instructor to register your interest and indicate your timetable availability; a scheduling meeting will be held on the first Thursday of classes at 9am.

**Note added Sep 4 2020: Current proposed schedule: Tuesday 4-5pm, Wed 9-10am, Thursday 4-5pm**

#### Course Learning Goals:

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, complex exponentials in wave and instability problems, and appropriate matching conditions and interfaces and transitions.
- 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, trapped and free wave problems in non-rotating and rotating systems, and instability problems.