First derivation is very cool. Energy minimization leads to the fluid cylinder instability. Makes sense, and the derivation is simple enough.
Very cool to see Bessel functions popping up, though given the type of equations and the space on which we're solving them, this doesn't seem particularly surprising, comparing to experience with Math 180.
Overall, it all makes sense to me. It's very interesting to see that what is fundamentally a stability analysis can be performed by linearizing and solving the system and then looking at solutions for which the waves grow. I'm a little unclear as to where the "asymmetric modes" part of the final paragraph comes from, but the fact that wavelengths greater than a threshold value grow to infinity actually makes sense to me.
NB: Sorry I've missed so many blog entries. If I can find time, I'm going to go back and write them, but these past two weeks have been absolutely vicious.
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