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

Coherent structures — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Q and the vorticity along a radius of one vortex. Two candidate measures of where the vortex is, along a radius of a Lamb–Oseen vortex. The vorticity is a Gaussian: positive at every radius, so a threshold on it puts the edge wherever the threshold is put. Q — the excess of rotation over strain — changes sign exactly once, at 1.121 core radii, and that radius is a property of the flow rather than of the person drawing it. Inside it, 71.5 per cent of the circulation.

    Where a vortex stops

    Four criteria decide where a vortex ends, and in two dimensions three of them are the same criterion. The fourth is a knob. And the one that is not a knob is not objective: a co-rotating pair of vortices occupies two per cent of a window to one observer and twenty-five to another.

    part 1 · kinematics
  2. The stretching a window of history did, drawn as a field. The largest finite-time Lyapunov exponent over eight units of time in the double gyre, darkest where two neighbouring parcels were pulled furthest apart. The bright crest is a curve across the domain, and it is a property of the eight units rather than of any instant inside them.

    A boundary that only exists over a window

    The curve that separates fluid going one way from fluid going another is not in any snapshot of the flow. It is the crest of a field built from a stretch of history, it moves when the stretch is changed, and reversing the direction of time gives a different curve entirely — both of them real.

    part 2 · kinematics

All series