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

Frozen turbulence — where it appears

Taylor's hypothesis that turbulence is carried past a fixed point faster than it changes, so a time record there reads as a spatial record along the mean flow. It turns a probe's frequency into a wavenumber and fails where the eddies evolve as fast as they are swept.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Small scales forget fast and large ones slowly, and the window only sees the large. Each scale's memory over a single probe's integral time against wavenumber in inverse samples, for one memory at every scale and for memories falling as the wavenumber to the minus two-thirds and minus one above the field's own wavenumber, 1/λ, and held there below it. All three give the same probe integral time; the window of 64 samples passes wavenumbers below about 2π/64 = 0.098, where the sweeping law's memory is 1.26 probe times and the single law's 1.

The camera needs the window's memory, not the probe's

A run of particle-image frames stops gaining independent values for its mean once frames are closer than the flow's memory — but the memory that counts is the window mean's, and when large eddies live longer than small ones it is longer than the integral time a single probe measures. Give each scale its own memory and the frame rate that stops buying moves by up to a quarter where the flow forgets before it is swept, by nothing where the sweep sets it, and by however much longer the largest eddies live. Fed the window's own memory, the single-memory rule gives it back to two per cent.

turbulence · Spectrum Sweep slows every load's crossings by about a tenth at 35°, and leaves one root's excess over the lift standing. Against the sweep, for an elliptic wing of aspect ratio nine whose span is eight hundredths of the turbulence's integral scale: left, the lift's and one root's crossing rates as fractions of the straight wing's; right, one root's rate over the lift's. At 35° the lift crosses its mean 0.899 times as often as on the straight wing and the root 0.887; the root's excess over the lift goes from 1.19 to 1.17, and at 45° to 1.16.

Sweep slows a wing root's gust cycles and leaves their excess over the lift

On a straight wing every station meets a gust at the same instant, and one wing root's bending moment crosses its mean nearly a fifth more often than the lift, because it reads the rolling half of the gust. Sweep the wing back and the outer stations meet the gust later, by their distance aft. That delay averages the gust along the flight path as a second, softer chord would: at 35° every load crosses its mean about a tenth less often, the root slightly more than the lift since its weight sits further out, and the variance hardly changes at all. The rolling excess survives almost whole.

circulation · Gust

Named alongside it

The objects these essays reach for when they reach for this one.

Model limitSpectrumAveragingBending momentFatigueFrequency responseGustIntegral scaleMeasurementMemory kernelParticle-image velocimetryReciprocity

All concepts