Advanced Fluid Dynamics module (MA52005)

About the module

This module covers advanced topics in Fluid Dynamics for the Level 5 student who has already undertaken an introductory course. This module may optionally be taken by students on Mathematics or Physics MSc programmes as well as MMath in Mathematics, MSci in Mathematical Biology or MSci Mathematics and Physics.

The course focuses on vortex dynamics and uses this as basis to understand and describe turbulence, one of the most intriguing phenomena of fluid dynamics. It also provides an introduction to non-Newtonian fluids and their fascinating properties. It takes the viewpoint of an applied mathematician/theoretical physicist and derives fundamental properties from the underlying system of equations.

If you have questions about this module or the possible combinations, please contact your Advisor of Studies.

Prerequisites

Students taking this module must usually have achieved a pass mark in the module MA42007 (Mathematics of Fluids I), or a similar course.

Indicative Content

• Introduction (recap of basic fluid dynamics)

  Navier-Stokes equations and their approximations and modifications

• Boundary Layers

  Nondimensionalisation, Blasius boundary layer

• Vortex Dynamics

  2D dynamics, point vortices, vortex sheets, dynamics of vortex filaments, effects of viscosity, energy and enstrophy dissipation

• Turbulence

  Instabilities, scales, description in Fourier space, Kolmogorov′s theory, 3D vs. 2D turbulence

• Non-Newtonian Fluids

  Types of non-Newtonian fluids, Ostwald - de Waele model, Bingham plastic

Delivery and Assessment

The module is delivered in the form of lectures and workshops/tutorials and assessed via an exam (80%) and coursework (20%) consisting of homeworks.

Credit Rating

This module is a Scottish Higher Education Level 5 or SCQF level 11 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.