Module Catalogue 2025/26

Pre Requisite Comment

PHY2033 is acceptable in place of MAS283

Co Requisite Comment

N/A

Aims

To present advanced topics of fluid dynamics building on the introductory concepts developed at Stage 2.

Module Summary
To introduce the mathematical tools to model two-dimensional inviscid flows more advanced than seen at Stage 2 and to predict the motion of realistic viscous flows using the Navier-Stokes equation.

To illustrate the variety of solutions to the Navier-Stokes equation to a physical world, including a selection of applications (such as weather phenomena, viscosity measurement and biological fluids).

Outline Of Syllabus

Review of elementary fluid dynamics presented in Stage 2 (e.g. continuity equation, Euler equation, vorticity, velocity potential). More advanced complex potential methods to study two-dimensional inviscid flows to include singularities (sources, vortices), boundaries (method of images) will be introduced.

Viscour flows: microscopic and macroscopic description of viscosity, the Navier-Stokes equation, no-slip boundary conditions, analytic solutions of the Navier-Stokes equation (e.g., pipe flows in cylindrical geometries, Couette flows, flow down an incline.

Dimensionless variables, Reynolds number, dynamical similarity.

A brief overview of fluid instabilities: transitions to complex vortex flows (flows past cylinder, Taylor-Couette and Reynolds problems).

Introduction to turbulence and energy cascade.

Applications may include drag, Magnus (lift) force, weather and biological fluids.

Intended Knowledge Outcomes

Students will become familiar with:
- The mathematical methods to model two-dimensional, inviscid, imcompressile flows including vortex configurations in the presence of boundaries.

- The concept of viscous dissipation.

- The Navier-Stokes equation, from its simple analytic solutions to the non-uniqueness and complexity of its solutions at increasing driving parameters.

- The basic physical mechanisms which determine the features of fluid phenomena at small (e.g., swimming microbes) and large (e.g., flying planes) scales.

Intended Skill Outcomes

Students will be able to:

- Set up idealized inviscid models of two-dimensional flows including singularities (e.g., vortices or sources and sinks) and solve these models using complex variables.

- Set up well-defined models of realistic viscous flows to be solved using analytical or numerical methods.

- Appreciate the nature of flows visible in real life, from the kitchen to airplanes to the atmosphere.

- Reflect on the employability value of the skills learnt, and how they apply to academic and industrial settings.

Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate and create.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work.

Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one way for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

General Notes

N/A