I wish I'd had more time to blog recently, but life has been a little too crazy.
At any rate, this is cool stuff. It's nice to see how the free-surface boundary conditions play out in the mathematical PDEs framework, and it's even cooler to see a fairly rigorous proof of Bernoulli's theorem. Obviously the same concepts are there, but, well I'm a mathematician, so it's better now.
Definitely cool to see the Fourier transform appear in the end, too. I'd be curious to hear about the general applicability of the FT in fluids - it's certainly a big hammer and great for making this smooth. (No pun intended.)
The series expansion strangely reminded by of perturbation theory from big quantum; I'm guessing this is a fairly standard approach, I think it's more the notation. That said, I wonder how applicable the linearized equations are and/or what are their drawbacks?
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