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

Far field — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Three contours, one force, three different accounts of it. The same vortex, and the same total force on it, computed by a momentum balance over three contours of the same area. All three give ρUΓ to eight figures. What differs is the bookkeeping: the tall box gets 16 per cent of it from pressure and the rest from momentum flux, the wide box gets 84 per cent from pressure, and the circle gets exactly half. Neither part converges on its own as the contour is enlarged — each falls off like 1/r while the contour grows like r — so the split is a property of the shape of the limit rather than of the flow.

    Where the reaction to a wing's lift is

    The force on a body can be computed on any contour drawn round it, and the answer is the same every time. How much of that answer is pressure and how much is momentum flux is not — it runs from three per cent to ninety-seven, and the difference is the shape of the contour.

    part 1 · inviscid
  2. The two bodies the far field cannot tell apart. A circular cylinder and the Rankine oval that has the same doublet strength: 1.17 radii long against the circle's one, and 0.94 tall against its one, with a source and a sink 1.2 apart inside it. On the pale ring, one and a half radii out, the two flows differ by 19 per cent of the disturbance; at six radii by one per cent; at infinity not at all. What a far field records of a body is three numbers — its circulation, its net outflow and its doublet — and nothing else survives the journey.

    What the far field remembers

    Three numbers survive the journey to infinity — a circulation, a net outflow and a dipole — and nothing else about a body does. Two shapes with nothing in common can therefore make the same flow a few radii away, and the difference between them dies two orders faster than the disturbance either one makes.

    part 2 · inviscid

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