Vortex shedding · a live wind tunnel
Put almost anything in a steady wind and, above a certain speed, the air behind it starts to swing. A vortex peels off one side, then the other, and they line up in a staggered double row called a Kármán vortex street. It makes wires hum, chimneys shake and islands draw patterns in the clouds.
The tunnel below is a lattice-Boltzmann flow solver running on your graphics card, millions of times a second.
I · One number
Whether a wake is calm or swinging depends on one ratio. The Reynolds number, Re = UD/ν, compares the push of the air’s momentum with the drag of its own viscosity: speed U times size D, over kinematic viscosity ν. Scroll, and the tunnel steps up through the regimes.
At Re = 1 viscosity wins outright. That is a hair-thin fibre, a tenth of a millimetre across, in a draught of 15 cm/s. The smoke parts in front of the cylinder and closes up again behind it, in almost the same shape fore and aft. Nothing separates and nothing swings.
Speed up and the air can no longer follow the back of the cylinder. The thin boundary layer on its surface separates, and two eddies settle in the lee, turning in opposite directions. They stay put. Dye released from the surface collects inside them and circulates there, coral on top and blue below.
Above Re ≈ 47 the symmetric pair becomes unstable. A tiny sideways nudge grows exponentially, then levels off into a steady swing. On a log scale the growing lift force climbs in a straight line and then bends flat, the signature of what mathematicians call a Hopf bifurcation.
Now vortices peel off alternately and march downstream in two staggered rows, warm colours turning clockwise, cool ones counter-clockwise. In 1911 Theodore von Kármán showed that a street of ideal point vortices is only stable when the gap between the rows is about 0.28 of the spacing along a row. Henri Bénard had filmed the pattern three years earlier, and protested the name in 1930.
Real wakes turn three-dimensional above Re ≈ 190. This tunnel is a two-dimensional slice, so it keeps drawing a clean street.
II · The 0.2 rule
The Strouhal number St = fD/U compares the shedding frequency f with the time air takes to pass the body. For a circular cylinder it sits near 0.2 from Re of a few hundred up to about 200,000. At low Re it climbs toward that value. Move the slider and the live measurement settles onto the curve fitted to experiments by Williamson.
The live point runs a few percent high. The tunnel is only 12 diameters tall, and squeezing the flow raises its speed past the cylinder. Real wind tunnels correct for the same blockage effect.
III · Push and pull
Each departing vortex tugs the cylinder toward its own side, so the sideways force, the lift, swings once per shedding cycle. Drag gets a kick from every vortex, top or bottom alike, so it pulses twice per cycle. Plot one against the other and the trace draws a figure of eight.
IV · Sound
In 1878 Vincenc Strouhal whirled wires through the air and measured the tone they made. The pitch rose with speed and fell with thickness, because it is the shedding frequency, f = St·U/D. At these sizes the Reynolds number is in the thousands, where St ≈ 0.2.
The same forcing shakes tall steel chimneys when the shedding frequency matches the chimney’s own. The usual cure, helical strakes wound around the top, was found in 1957. Strakes work in three dimensions: vortices leave at different moments along the height, so their pushes cancel. A two-dimensional slice like this tunnel cannot show that.
The 1940 collapse of the Tacoma Narrows Bridge is often blamed on this effect. Engineers ruled it out: the shedding frequency did not match the deck’s motion. The bridge failed by flutter, a self-excited twisting that feeds on the wind.
V · Sky
Guadalupe Island, 260 km off Baja California, rises about 1.3 km into a sheet of low stratocumulus cloud. The wind sheds the same alternating eddies off it, and satellites see them as a vortex street hundreds of kilometres long, cut into the cloud deck. NASA’s MISR instrument photographed a famous example in June 2000.
The real Reynolds number is enormous. Turbulence in the lower atmosphere acts like a far thicker viscosity, and a temperature inversion caps the flow and keeps it nearly flat, which helps explain why the street looks so orderly.
VI · Wings
A wing at a small angle lets the air follow both surfaces and leave cleanly from its sharp trailing edge. Tilt it far enough and the flow tears away from the upper surface. The wing stalls, sheds vortices like any blunt body, and its lift starts to shake. This is a NACA 0012 section at Re = 1,000 based on chord.
VII · Free play
Every tool is open. Draw shapes into the flow, load a preset, and dial the Reynolds number. Drag and lift are measured on everything solid, with the obstacle’s frontal height as the reference length.
Who saw it first
Model notes
The air is modelled as packets of particle populations moving between neighbouring grid points in nine directions. Each step they stream to their neighbours and relax toward equilibrium; averaged, this reproduces the Navier–Stokes equations at low Mach number. The relaxation rate sets the viscosity, so the Reynolds slider changes τ.
The tunnel is 768 × 288 cells on a desktop (544 × 192 on phones), with the cylinder 24 cells across. Obstacles use half-way bounce-back; the walls are free-slip; air enters at the left at fixed speed (0.1 lattice units, Mach 0.17) and leaves through a hidden sponge layer that damps vortices before the exit. The regularized collision filters non-physical modes, and a Smagorinsky eddy viscosity (Cs = 0.1, rising to 0.15 at Re = 3,000) keeps fine eddies stable; at Re = 100 it changes the drag by less than 0.3%. Forces are summed over every solid link on the GPU and read back once per frame; the Strouhal number comes from zero crossings of the lift.
I checked the GPU solver against an independent CPU implementation of the same scheme (fields agree to 10−6) and against published results in the table.
| Cylinder | This tunnel | Open-flow reference |
|---|---|---|
| Drag Cd, Re 20 | 2.32 | 2.00 (Fornberg 1980) |
| Eddy length, Re 20 | 1.00 D | 0.93 D (Coutanceau & Bouard 1977) |
| Drag Cd, Re 40 | 1.74 | 1.50 (Fornberg 1980) |
| Eddy length, Re 40 | 2.33 D | 2.13 D (Coutanceau & Bouard 1977) |
| Onset of shedding | between Re 45 and 55 | Re ≈ 47 (Williamson 1996) |
| Strouhal, Re 55 | 0.141 | 0.130 (Williamson fit) |
| Strouhal, Re 100 | 0.173 | 0.164 (Williamson fit) |
| Mean Cd, Re 100 | 1.49 | ≈ 1.33 (2D simulations) |
| Cl amplitude, Re 100 | 0.40 | ≈ 0.33 (2D simulations) |
Measured on the desktop grid with the same solver, run to a settled state. The cylinder blocks 8% of the tunnel’s height, so drag, lift and frequency run high, as they do in real wind tunnels before blockage corrections.
Sources