These lecture notes (acrobat file, 3.4 Mbyte) formed the basis for a graduate course that I often gave during my teaching years in the Department of Applied Mathematics and Theoretical Physics, in Part III of the Mathematical Tripos.

Some parts of the notes are in quite good shape but others may not be, especially those parts that weren't used in the more recent versions of the lecture course, namely sections 3.5, 4.2, 4.5 and 4.6. I fear it may be some time before I can get around to tidying it all up properly. So for now I'm making the notes available on an `as is' or `caveat emptor' basis -- not guaranteed to be error-free!

Here are the four examples sheets for the course as most recently taught: sheet 1, sheet 2, sheet 3, sheet 4.

The last question on sheet 4 invites the student to derive an important result not covered in the notes, sometimes called the Taylor-Bretherton identity, after G. I. Taylor and F. P. Bretherton -- though it might be historically more just to call it the Taylor-Charney-Stern-Bretherton-Eady-Green identity -- so we'll probably end up with Taylor identity for brevity. It is key to understanding the fundamentally anti-frictional properties of stratified, layerwise-two-dimensional turbulence, such as the self-sharpening of jet streams. A powerful generalization has recently been discovered by W. R. Young.