MATH3261 is a Mathematics Level III course.

Units of credit: 6

Prerequisites: 12 units of credit in Level 2 Math courses including (MATH2011 or MATH2111) or MATH2121 or MATH2221), or (both MATH2019 (DN) and MATH2089), or (both MATH2069 (DN) and MATH2099).

Exclusion: MATH5285 (jointly taught)

Cycle of offering: Term 3 2021

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information: This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains up-to-date timetabling information.

If you are currently enrolled in MATH3261, you can log into UNSW Moodle for this course.

Course aims

The course aims to provide a solid foundation for the analysis of geophysical flows that arise in the study of the ocean and atmosphere, and their interactions in the climate system. The course introduces the equations of motion and conservation laws that govern the fluid dynamics of the atmosphere and the ocean. These equations are then systematically simplified and solved to quantitatively model key phenomena selected from the enormously rich variety of atmospheric and oceanic flows. Emphasis is on large-scale phenomena important in the global climate system and on physically relevant approximations.

Course description

In this course, students learn about the mathematical modelling and theory of problems arising in the flow of fluids, oceans and global climate. We will cover Cartesian tensors, kinematics, mass conservation, vorticity, Navier-Stokes equations, topics from inviscid and viscous fluid flow, gas dynamics, sound waves and water waves. The dynamics underlying the circulation of the atmosphere and oceans are detailed using key concepts such as geostrophy, the deformation radius and the conservation of potential vorticity. The role of Rossby waves, shelf waves, turbulent boundary layers and stratification is discussed. The atmosphere-ocean system as a global heat engine for climate variability is examined using models for buoyant forcing, quasi-geostrophy and baroclinic instability.