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

Taylor microscale — where it appears

A length obtained by fitting a parabola to the two-point velocity correlation at the origin. It is the size of no eddy at all, sitting between the energy-containing scale and the dissipation scale, and it earns its place because the dissipation can be written in terms of it exactly.

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

Model spectra at four Reynolds numbers, compensated. The spectrum multiplied by k^(5/3) and divided by eps^(2/3), so that a true inertial range is a horizontal line at the Kolmogorov constant. What a finite Reynolds number has instead is a single maximum: it reaches 1.4996 at the highest and 1.49 at the lowest, and the band over which it is flat to one per cent goes from a third of a decade to two.

The range a real Reynolds number does not have

Kolmogorov's minus five thirds is a statement about a band of scales that has forgotten the forcing and does not feel the viscosity. Both conditions are about separation, and separation is exactly what a finite Reynolds number does not have much of.

turbulence · Spectrum The coefficient that was a constant, against the number it is said not to depend on. The dissipation coefficient Cε = eps·l/u³ along two decays, plotted against the Taylor-scale Reynolds number they pass through. One is flat because it was put in flat; the other falls as the reciprocal of the Reynolds number, which is what is measured in the near field of a grid. Neither line is a derivation. What is exact is the relation between them, Cε = 15(ℓ/λ)/Reλ, which is a rearrangement of two definitions and holds along both curves to 5·10⁻¹⁶.

The constant that travels

Every decay law in the subject rests on the dissipation being some constant times u³ over a length. The constant is not one. Letting it move the way grid measurements say it moves changes the decay exponent by a quarter — and lands one of the answers five per cent from another that is entirely different physics.

turbulence · Decay

Named alongside it

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

DissipationMeasurementModel limitPower lawReynolds numberAsymptoticsClosureCompensated spectrumDecayInertial rangeIntegral scaleInvariant

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