Post by telemeter on Apr 8, 2020 9:30:11 GMT
I took on Needham's encouragement here to verify his diagrams, so with the help of the excellent GeoGebra (free and you can save graphs if you register for an account - also free)) I had a go.
These are the results, where I have only been partially successful in suppressing flow lines inside the object
a) low strength vortex drive.google.com/file/d/1rQyEaFWrgpUxNzoOyxBbRQ8z6064Pr0U/view?usp=sharing
b) critical strength vortex drive.google.com/file/d/1GYkyfXWHHi1mYKY-kMBDB9uAeg18i1AM/view?usp=sharing
c) high strength vortex drive.google.com/file/d/1l7WozM_sKHniHfK35OHkoj7citDVTIIb/view?usp=sharing
Attached is a note confirming the critical strength by calculation. The difficulty for me was finding the correct function for the vortex, but was resolved by noting that to maintain the 'integrity' of the object in the plot, the stream function had to map the boundary of the unit circle to a constant eg the real axis (as is clearly stated on p528!). The note is therefore a spoiler. drive.google.com/file/d/1bpDRcvarmj57DGXXMSMBMSH0DUPukt_B/view?usp=sharing
telemeter
