MTH3360 · Fluid dynamics

Overview

Fluid flows are all around us, from waves on the beach to microorganisms navigating their environment, and mathematics allows us to make precise and useful predictions about how they behave. In this unit you will develop mathematical tools for describing, simplifying and solving problems in fluid motion. You will derive the governing Navier-Stokes equations, find exact solutions in tractable cases, and learn systematic methods for reducing them when the geometry or physical parameters of a problem allow. You will see familiar tools from your mathematical training reappear in a physical setting, encounter new ones as the problems demand them, and learn to reason about what solutions should look like and why.

Areas of study: Applied mathematics Mathematical statistics Mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

Learning outcomes

1. Describe fluid motion mathematically using the continuum framework;
2. Summarise the derivation of the governing Navier-Stokes equations;
3. Use dimensional analysis and scaling to identify the dominant physical balance in a flow;
4. Derive simplified governing equations for specific flow regimes and assess the validity of those reductions;
5. Obtain solutions to the governing and reduced equations in tractable cases;
6. Interpret solutions physically and critically assess their accuracy, limitations, and range of validity.

Workload

• 2 hours of pre-recorded lectures; • One 3-hour applied class and • 7 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.