Transforming Hilbert into an ocean wave

I have a new job.  I have advanced from the trivial consideration of a single bubble or even two bubbles at once (although that was only every other Thursday, when I’d been good) to a better place.   At my new level, which is physically in Rhode Island although mentally stranded out in an Atlantic storm,  cogitation and comprehension of millions of bubbles at once are required.     Cogitation is rather my thing, and I have been happily absorbing information on storms and bubbles and particulates and a mysterious thing called Langmuir circulation.   It’s amazing how quantitative you can make all this stuff, but it’s really only background for the main project, which is counting and sizing millions of bubbles at once by looking at their effect on the acoustic resonances between two circular plates.     You put radio hiss (a.k.a. white noise) into one plate, let it pass through the bubbles caused by the storm overhead and then watch with interest and popcorn while the other plate responds to all this fuss.  And then science is supposed to occur.

In learning the background for all of this, I have read a lot about turbulence.   The best thing to do with turbulence, according to the clever people who make a living out of this, is to measure eddies and make a Hilbert transform.    But what does Hilbert transform into?   And what is it of Eddy’s that is being measured anyway and does he know about it?   These are important questions for the tired mind.   Perhaps Hilbert is a small blue confused-looking animal with a skill for hiding in car glove compartments.   The day he transforms into something with sharp teeth and a taste for fingernails, you’d better watch out.    I don’t even want to think about Eddy and his potential measurements.

It is possible that although I’ve only been in Rhode Island for a week, I’ve already got cabin fever.  After a whole year I’ll probably be stalked by a small pack consisting of a Fourier (like a terrier but with more fur), two Laplaces (these are definitely blue, but only half of them exists) a few Hartleys (more sharp teeth, I’m afraid) and a small Identity (who has a monobrow and a permanently puzzled expression).    This sounds terrifying (or should that be Fourifying?).

If you happen to see my mind lurking about under the sofa, please post it back to me…

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