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

Vortex street — where it appears

The double row of alternating vortices behind a bluff body, and the point-vortex model of it. The model settles the spacing exactly — a double row is neutrally stable only at a width-to-spacing ratio of ln(1 + √2)/π — and contains no viscosity, so it says nothing about when a street forms.

Named by 4 essays across 4 fields — each of them below, with the objects they name alongside it.

The street, as two rows of point vortices. The exact velocity field of a staggered double row of point vortices at the stable spacing ratio, with the row spacing and the circulation of one core printed from a line integral of the field rather than from the number that built it. This is a model of a wake. It contains no body, no viscosity and no mechanism that would shed anything, and the viscous stepper used here does not produce a street at any Reynolds number.

The street a steady calculation cannot draw

The alternating wake behind a cylinder is the most photographed structure in fluid mechanics, and a steady solution does not produce one. What can honestly be drawn instead is a model of it — and the model settles one thing exactly, which is the spacing.

turbulence · Wake The exposure lengths that give the true mean, and the ones that do not. How far a finite exposure of a shedding wake lands from the long-exposure mean, against how many shedding periods the shutter was open for. It is exactly zero at every whole number of periods — an average over a complete cycle is the mean, with no error at all — and between the zeros it falls as one over the exposure. Nothing about the picture tells the reader which of these they are looking at.

The shutter is part of the answer

Flow photographs are compared as though the exposure were a detail of the camera. It is a term in the measurement: an average over exactly one shedding period returns the true mean to fourteen figures, any other length carries a residue that falls only as one over the exposure, and a two-pulse velocity reading is short by exactly the sinc of the swept angle.

misconceptions · Visualisation Three bluff bodies, whose Strouhal numbers agree once the wake's width is used. The measured Strouhal number of each body, and Roshko's universal number formed with the wake's width and the speed on the free streamline that bounds it. The raw numbers span a factor of 1.462; the collapsed ones span 1.0011, with a mean of 0.16281. The shedding was never body-dependent — the length in the number was.

The frequency a wake chooses

Bluff bodies shed at Strouhal numbers from 0.145 to 0.212, and the spread is not a fact about shedding — it is a fact about which length went into the number. Change the length to the wake's own width and three bodies agree to a tenth of a per cent. Then let the body move, and the number stops deciding anything at all.

regimes · Strouhal Two eddies that stand still behind a cylinder in ideal flow. A uniform stream past a circular cylinder with a pair of opposite vortices standing 2 radii behind its centre and 0.859 either side of the axis, each of strength 10.31 in units of the stream speed times the radius — Föppl's equilibrium. The shading is the stream function: the fluid between the vortices and the cylinder circulates in two closed eddies and never leaves, while the stream divides round the whole assembly as if it were one longer body.

Two eddies can stand behind a cylinder, but not for long

Ideal flow, which has no viscosity and no wake, can still hold a pair of eddies standing behind a cylinder — at any distance behind it, with a strength fixed by the distance. They cost the cylinder nothing. And they cannot stay: nudged sideways by a thousandth of a radius, the pair grows its displacement exponentially and leaves, which is the first step of shedding a wake.

inviscid · Images

Named alongside it

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

Model limitPoint vortexWakeLinear stabilityMeasurementAveragingBase pressureBlasiusCirculationd'Alembert's paradoxDimensionless numberEquilibrium

All concepts