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 of the Navier-Stokes equation in the physical world, paying attention to topics such as transitions of flow patterns, and including a selection of applications (such as turbulent flows, lift forces, flying, convection, weather, climate).

Outline Of Syllabus

Review of elementary fluid dynamics presented in Stage 2 (e.g. continuity equation, Euler equation, vorticity, stream function, complex potential for two-dimensional flows). More advanced complex complex potential methods to include singularities (sources, vortices), boundaries (method of images, microscopic and macroscopic description of viscosity, the Navier-Stokes equation, no-slip boundary conditions, analytic solutions of the Navier-Stokes equation (e.g. channel flows in Cartesian and cylindrical geometries, Couette flows, oscillating flows). Transitions to complex vortex flows (flows past cylinder, Taylor-Couette, and Reynolds problems). Dimensionless variables, Reynolds number, introduction to turbulence and energy cascade. Applications may include Milne-Thomson Theorem, Rayleigh-Benard thermal convection, drag, Magnus (lift) force, Hamiltonians, flows in rotating frames (Coriolis, centrifugal and Poincare forces), weather and climate.

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 ways 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.