Geophysical Fluid Dynamics

Duration
 Two Weeks, Period 1

Lecturer
 Marcel Oliver (International University Bremen, Germany)

Consultation Hours
 Thursdays 1112h Carslaw Room 635 (Weeks 1 & 2 only).

Assessment
 5 short assignments.

Assumed Knowledge
 A first course on PDEs or equivalent exposure, a rigorous course in Analysis
as well as vector calculus. The following will help, but are not essential prerequisites: functional
analysis and some exposure to fluid mechanics.

Course Outline
 This course is an introduction to mathematical problems in geophysical fluid dynamics.
The course is structured in three parts:
Part I: The equations of geophysical fluid dynamics
 The rotating Euler equations, the Boussinesq approximation, hydrostatic balance
 Energy and vorticity; vorticitystreamfunction formulation in twodimensional flows
 Special solutions; linear and nonlinear stability
 Shallow water and nearlygeostrophic limit equations
Part II: The quasigeostrophic equations as a singular partial differential equations limit.
 Review of function spaces and basic facts from Functional Analysis
 Wellposedness of shallow water and quasigeostrophic equations
 Convergence theory for balanced initial data
 Unbalanced data: EmbidMajda theory
 Unbalanced data: BabinMahalovNikolaenko theory
Part III: Further topics (if sufficient time and interest)
 Nonlinear dispersive waves
 Semigeostrophic limits
 Variational methods

References
 The lectures are loosely based on the book by A. Majda, Introduction to PDEs and waves for the
atmosphere and ocean, American Mathematical Society, 2003, supplemented by additional reading and
original research papers.
