# MATH3261 Fluids, Oceans and Climate

MATH3261 is a Mathematics Level III course. See the course overview below.

Units of credit: 6

Prerequisites: 12 units of credit in Level II Mathematics courses, including MATH2011 (alternatively MATH2111) and or MATH2121 (alternativelyMATH2221), or (both MATH2019 (DN) and MATH2089), or (both MATH2069 (DN) and MATH2099)

Exclusion: MATH5285

Cycle of offering: Term 1

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 Overview

Weather, climate and oceanic currents play an enormous role in the Earth's environment, controlling cycles in the biosphere, regulating natural ecosystems, and impacting on human health. We depend on the ocean and atmosphere for resources and transport. Yet we also subject the system to pollution, including increased greenhouse gases, motor car emissions, oil spills and chlorofluorocarbons.

Understanding the dynamics of the atmosphere and oceans is one of the great challenges in science today. In this course you will learn how mathematical equations can be used to describe aspects of flow in both the ocean and atmosphere, and how solutions to these equations are obtained. We will cover circulation dynamics ranging in spatial scales from global down to molecular, spanning time-scales from fractions of a second up to decadal and beyond (e.g., climate change).

The course will include analysis of key concepts such as geostrophy, the conservation of potential vorticity, waves, tides, and buoyancy controlled flow. For example, the ocean-atmosphere system witnesses wave motions from millimetre scale capillary waves, to sea and swell, and beyond to planetary scales where the Earth's rotation affects dispersion. The study of these phenomena combines theory with mathematical techniques to shed insight into how flow in the ocean and atmosphere is forced and maintained.

Other topics include Rossby waves, shelf waves, turbulent boundary layers and stratification. The atmosphere-ocean system as a global heat engine for driving climate variablity and change. This is studied worldwide using models that are built upon the dynamics introduced in this course.