24 March 2009

Nearly sufficently advanced technology

Stephen Pope's Turbulent Flows is one of the go-to books for graduate courses in turbulence. It flows well, re-reading sections rewards the reader with new material, and the book attempts to develop results instead of just arriving with them from on high. All goodness. Still, every so often, Pope casually drops a bomb to check if you're paying attention. Most of the time I'm not, but tonight I saw one:

Oh, I thought, he's just using a Taylor expansion. No big deal. I kept on reading.

Pope then quietly announces that it was a stochastic Taylor expansion. At least that's my guess at what that object would be called.

I've never seen a “stochastic Taylor expansion” developed, nor do I know the technical constraints that say whether an expansion does or does not exist for random fields like u, v, and w. Any mathematical concept lacking a Wikipedia entry (as of today, anyhow) probably requires a bit more fanfare. A footnote? A reference? A statement declaring ├╝berformality? Not Pope's style it seems...

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