Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Series

Taylor — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The marginal Taylor number against the axial wavenumber. The smallest Taylor number at which a disturbance of a given axial wavenumber is neutral. Its minimum is 1707.757 at a wavenumber of 3.1158, which are the critical Rayleigh number and critical wavenumber of a layer of fluid heated between two rigid walls — the same numbers, because in the narrow-gap limit the two problems are the same sixth-order eigenvalue problem. This curve is computed by that essay's own solver.

    A transition that needs a second number

    Fluid between rotating cylinders goes unstable at a Taylor number of 1707.762 — which is the same number, to every digit, as a layer of fluid heated between two rigid walls. It is not an analogy. And two things the number cannot carry decide whether the transition happens at all and what it looks like when it does.

    part 1 · regimes
  2. The curve that lets in more than one answer. The neutral stability curve: the driving needed to sustain a disturbance of a given wavelength. It has a minimum, so at any driving above the minimum there is a whole band of wavelengths that can grow — and the system has to pick one.

    The state a machine was started into

    Above the critical driving there is not one flow but a band of them, and a container of a given size can hold several. Which one appears is decided by how the apparatus was brought up to speed, and at twice critical there are eight to choose from.

    part 2 · regimes

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