Topics in fluid mechanics: preamble

The course develops various topics in fluid mechanics which lie beyond the remit of the introductory fluid mechanics courses, which deal variously with wave motion in inviscid flows, viscous boundary layers at high Reynolds number, inertia-free  flows such as Stokes flow or those of lubrication theory. As such it will assume a fluency with these subjects, and the problem sheet 0 (online) provides some exercises on them. Having said that, all that is really required as a prerequisite is a knowledge of the form and origin of the Navier-Stokes equations, and the topics to be studied can be thought of as variations on an underlying theme. Four topics will be dealt with: these are thin films/groundwater flow, convection, rotating flows and two-phase flows. 

Lecture delivery 

Lectures are face to face on Mondays and Tuesdays; apparently these will also be live-streamed and also recorded. They will follow the format of the online 2020 recorded lectures, that is, delivered at the lectern with handwritten lecture notes on the screen. There will thus be much less writing on the board. The written lecture notes define the course. There are also printed lecture notes, which by this stage have been elaborated almost to book form. Various other resources will be provided, as described below. The 2020 lectures as recorded were the following, with duration in minutes:

1. Lubrication theory and thin films: 				46
2. Droplet dynamics:							57
3. Elongational flows							46
4. Groundwater flow							60
5. Convection								42
6.Convection at high Ra						41
7. Double-diffusive convection					41
8. Plumes									47
9. Rotating flows								35
10. Stratified flow								49
11. Geostrophic and quasi-geostrophic approximation	46
12. Baroclinic instability						46
13. Two-phase flow							51
14. Averaging								47
15. Scaling two-phase flow models					52
16. Density wave oscillations						47

The lecture material will be identical to this, but depending on circumstances, the division of the live lectures may be slightly altered. For example, it looks like lecture 4 will run into lecture 5. With luck, everything will get done, but if not, I may refer you to the 2020 recorded lectures for live gaps. In any case, these may be of independent usefulness.

Web resources

Announcements

The announcements section in moodle will be used to alert you to resource posting. For example, the printed lecture notes will likely be upgraded during the term, and when this is done, an announcement will be made.

Discussion

There is also a discussion forum. I will probably try and open this up. How it is used is unpredictable. It may be questions for lecturer or tutor, or it may just be for intra-student discussion.

Problem sheets

There are four problem sheets in the assignments section. These have already (1/10/21) been posted. They contain questions labelled A,B,C. Only B questions should be handed in for marking, and only these will be gone through in detail in the classes. The A questions should be relatively straightforward, while the C questions provide further opportunities for practice. With luck, there may be time for questions in class on the C questions (and after that, the A questions). My feeling is that you will want to have a go at some of the A or C questions as well as the B ones. Answers to everything will be posted after work is submitted.

Other resources

Also in the course material section, you will find
1. This file.
2. A folder: written_notes. This folder contains the written notes of the lectures as a pdf. These will be shown on screen during the live lectures.
3. A folder: printed_notes. This contains the printed lecture notes. As already mentioned, updates to these may be provided during term (and even after).
4. A folder: answers. The problem sheet answers will be posted here after work is submitted and presumably before the classes (though that depends on their timing).
5. A folder: fhs_answers. During online revision in TT2020 and TT2021, I wrote out answers to a lot of old fhs questions, and these will be posted here. They come with a health warning, as they are just my version of the answers to questions which I mostly (except the last three years) did not set. They will be of use next Trinity Term.

There should also be the Panopto lectures recorded in 2020, but these are being uploaded by the administrative staff, hopefully soon.

Andrew Fowler
1/10/2020