Viscous Flow

This is the home page for the 3rd/4th year Mathematics course on viscous fluid mechanics. It complements the course `Inviscid Fluid Mechanics.' Neither of these courses is a prerequisite for the other, although they should provide mutual reinforcement, and you are encouraged to attend both. Some familiarity with the core methods course M2M1 should be considered essential for each.

Fluid dynamics is a fascinating and important subject, of which examples occur all around us every day. The picture on the right, showing three consecutive images of a falling milkdrop, was taken by Harold Edgerton in 1957 using strobe lighting. The photo on the left was taken by John Bush of MIT - it shows a highly complex but stable "fishbone" structure formed when two jets collide.

This page is under development and will change as the course progresses. Here is the syllabus.

Click on the topics below to view or print files of the course material. If you are unable to access any of the files mail me.

Handouts

• Revision of M2M1, Some useful vector identities
• Kinematics and mass conservation
• Dynamics: Stress and strain for a Newtonian fluid.
• Boundary conditions and energy balance.
• Low Reynolds number: Stokes flows.
• Lubrication theory: flow in thin layers.
• High Reynolds number: Boundary layer theory.

Problem sheets

• Sheet 1: Stress, strain and the Navier-Stokes equations
• Sheet 2: Exact solutions to the Navier-Stokes equations
• Sheet 3: Low Reynolds number flows
• Sheet 4: Thin layer flows: Lubrication theory and boundary layer flows

Exams:

The exam will have the usual 5 question format. Here are the last three years' papers:
• 2003 Exam
• 2004 Exam
• 2005 Exam

Coursework:

Those taking the course may vote as to whether coursework will take place. If so, three or four pieces of work will be set throughout the course. This is in addition to the `enhanced study' for the M4A10 version.

Click here to return to Jonathan Mestel's home page or send e-mail to j.mestel@ic.ac.uk