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

Free shear — where it appears

A flow with velocity differences and no wall — a jet, a wake or a mixing layer. Such flows spread by entraining their surroundings, have intermittent edges, and are described by similarity solutions whose spreading rate is measured rather than derived.

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

The jet has to be fed from the sides. The velocity field of the plane jet with streamlines integrated through it. The seven central streamlines run down the jet and spread; the ten started at the top and bottom edges bend inwards and join it, which is entrainment and is a consequence of the solution rather than an addition to it. The dashed lines are the half-speed edges, widening as x^{2/3}. The transverse velocity far from the axis is 5.70e-3 m/s at this station, inward on both sides — a jet is a sink as seen from a distance, which is why two parallel jets pull together.

What a jet keeps, and what it collects

A jet leaving a nozzle into still fluid has no boundary anywhere and one conserved quantity. Its momentum flux is exactly the same at every station downstream; its mass flux is not conserved at all and grows without limit, because a jet is a machine for acquiring fluid it did not start with.

viscous · Free shear Most of the fluctuation is the switching. What a hot wire at the edge of a shear layer records, taken apart. The conditional intensity — the fluctuation inside the turbulent fluid — is flat at 0.16 by construction. The measured intensity peaks 20 per cent above it, and the excess is the third curve: the variance of a signal that keeps switching between two mean velocities, which peaks where the switching is most even and is not turbulence at all. A model calibrated against the measured curve is being fitted to an artefact of averaging.

Turbulent some of the time

At the edge of a jet or a wake a probe is inside turbulent fluid for part of the time and in perfectly smooth flow for the rest, and an ordinary time average mixes the two. Most of the fluctuation it records there is not turbulence at all — it is the switching between two states, and it peaks where the switching is most even rather than where the turbulence is strongest.

turbulence · Intermittency

Named alongside it

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

Boundary layerClosureConditional averageConservationEddy viscosityEntrainmentIntermittencyJetLinear stabilityMeasurementMixingModel limit

All concepts