## MAS6420 Topics in Advanced Fluid Mechanics

 Semester 1, 2019/20 20 Credits Lecturer: Prof Koji Ohkitani Timetable Aims Outcomes 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.

## Learning outcomes

At the end of the course the student should: - be able to understand the concept of the Hamiltonian and the Lagrange-function - be able to solve dynamical problems in the formulations of Lagrange and Hamilton - have understood the concept of a canonical transformation - be able to understand the concept of a field and do calculations in classical field theory - appreciate Noether #39;s theorem and its applications - be able to undertake independent study and research

20 lectures, no tutorials

## Assessment

One formal 2.5-hour written examination [80%]. Format: 4 questions from 5. 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)

## Timetable

 Thu 09:00 - 09:50 lecture Hicks Seminar Room F20 Fri 09:00 - 09:50 lecture Hicks Seminar Room F41