MAS6420 Topics in Advanced Fluid Mechanics

Semester 1, 2017/18 20 Credits
Lecturer: Prof Koji Ohkitani
Aims Assessment Full Syllabus

This module aims to describe advanced mathematical handling of fluid equations in an easily accessible fashion. A number of topics are treated in connection with the mathematical modelling of formation of the (near-)singular structures with concentrated vorticity in inviscid flows. After discussing prototype problems in one and two dimensions, we describe the three-dimensional flows in terms of vortex dynamics. Minimally required mathematical tools are explained during the course in a self-contained manner. Candidates are directed to read key original papers on some topics to deepen their understanding.

There are no prerequisites for this module.
No other modules have this module as a prerequisite.


Outline syllabus

  • Fluid dynamical equations revisited
  • 1D model equations
  • Vortex sheet problem
  • Vortex patch problem
  • 3D Euler equations
  • 3D Navier-Stokes equations
  • 2D incompressible fluid equations (if time permits)



Aims

This unit aims to familiarise candidates with advanced mathematical techniques used in fluid mechanics, in particular in vortex dynamics, by working out prototype problems.

20 lectures, no tutorials

Assessment

One formal 2-hour written examination [80%]. Format: 3 questions from 4. Students will also be required to complete derivations from approx. 5 papers on a reading list [20%].

Full syllabus

  • Fluid dynamical equations revisited
  • 1D model equations
  • Vortex sheet problem
  • Vortex patch problem
  • 3D Euler equations
  • 3D Navier-Stokes equations
  • 2D incompressible fluid equations (if time permits)