Kármán Vortex Street Wind TunnelBeta
Make wires sing with wind vortices and calm a swaying chimney
This tool is a beta version still being stabilized. Please let us know if a result looks off.
Ever heard power lines hum on a windy day? Each time a vortex breaks off behind the wire, the wire shakes and makes a sound. Change the wind speed to make the wire sing the target note.
Goal Hold the target note within ±5% for 2 seconds
Each time a vortex breaks off one side, the body is pushed toward the other.
Why does the wind wiggle behind a post?
As wind slides past a cylinder, the air right at the surface is slowed by friction. That slow layer can't follow the back of the cylinder all the way round, so it peels off and rolls up into a vortex.
In a gentle wind, a pair of vortices just sits behind the cylinder. Above a certain speed the symmetry breaks and they detach alternately — top, bottom, top… — forming the zigzag row known as a Kármán vortex street.
Every time a vortex leaves one side, the cylinder is nudged toward the other, so it rocks back and forth at f ≈ 0.2 × wind speed ÷ diameter. That's the hum of power lines in the wind (the Aeolian tone), the sway of chimneys and bridges, and the swirl trains seen behind islands in satellite photos of clouds.
A tail plate behind the cylinder stops the top and bottom vortices from talking to each other, so the alternating rhythm falls apart. Real chimneys wrap helical strakes around themselves to make vortices break off at different times at different heights — same idea.
The air in this tunnel is far more viscous than real air so the vortices stay crisp (Reynolds numbers of tens to hundreds). In that range the Strouhal number is below a real wire's 0.2 (about 0.15–0.16 for the thin wire, about 0.2 for the thick one), so hitting a note takes more wind than the formula says. The rules are the same: more wind, higher note; thicker wire, lower note.
Working…
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It hasn't frozen — the result will appear when the calculation finishes.
About Kármán Vortex Street Wind Tunnel
This wind tunnel computes the airflow with a two-dimensional lattice Boltzmann method (D2Q9 lattice, BGK collision). Uniform wind enters from the left of a 300 × 120 cell grid, and the last 30 columns on the right form a sponge layer that soaks up vortices before they can bounce back. The body surface is a bounce-back wall: particle populations that hit it are sent straight back, and the momentum exchanged there is summed every step to give the drag and the sideways force on the body. The smoke streaks are passive tracer particles carried by the velocity field; they do not push on the flow.
The air on screen is far more viscous than real air. The lattice viscosity is fixed at 0.012, which keeps the Reynolds number in the tens to low hundreds, while a real power line in a breeze sits in the thousands. The tool is therefore built to show why vortices shed and at what rhythm. It is not a way to predict how loud a real wire hums or how much stress a real chimney sees.
Why the vortices take turns
Flow that splits at the front of a cylinder follows the surface and separates near the sides. The two separated shear layers roll up behind the body, and a perfectly symmetric pair turns out to be unstable. If the upper vortex grows slightly, it draws the lower shear layer across the wake and cuts off its supply; then the lower side does the same in return. Vortices peel off top, bottom, top, bottom, and the staggered double row they form downstream is the Kármán vortex street.
Each time a vortex leaves, the circulation around the cylinder changes sign, and the body is pushed sideways. That is why the side-force graph looks like a sine wave, with one full swing per pair of vortices. Williamson's 1996 review puts the onset of periodic shedding behind a circular cylinder at Re ≈ 49. Turn the wind right down in the free tunnel and the oscillation stops: two attached twin vortices sit behind the body and nothing is shed.
How far the 0.2 Strouhal rule holds
The Strouhal number St = fD/U, built from shedding frequency f, diameter D and wind speed U, stays near 0.2 for a circular cylinder from roughly Re 300 to about 10⁵. That gives a quick pitch estimate for a singing wire, f ≈ 0.2·U/D. A 1 cm wire in an 11 m/s wind gives 0.2 × 11 / 0.01 = 220 Hz, the A below middle C.
In this simulation the Reynolds number is around 100, and there St is noticeably lower. Williamson's measurements give about 0.16 at Re 100 and about 0.19 at Re 160. The thin wire (10 cells) at 11 m/s is at a lattice Re of about 73, where St is closer to 0.15, so the tone the tool measures is below 220 Hz and you need more wind than the formula says. Measured in the tool, the thin wire reaches A3 (220 Hz) at about 13.4 m/s (St about 0.16) and E3 (165 Hz) at about 10.8 m/s (St about 0.15), while the thick wire reaches A2 (110 Hz) at about 10.9 m/s (St about 0.20). When you hit a target note, the tool shows that wind speed next to the St 0.2 formula value. A 20-cell cylinder in a 120-cell-wide tunnel also blocks about 17% of the channel, and that confinement nudges St back up a little. Under the measured St the tool also shows a blockage-corrected St, which uses the Allen–Vincenti formula to replace the wind speed with the speed the body actually feels, U·(1 + π²β²/12 + C_D·β/4), where β is the blockage ratio and C_D the measured drag coefficient. For a 20-cell cylinder at 10 m/s (Re about 133) the tool measures St 0.200 and C_D about 1.67; the corrected St is 0.183, close to the open-flow value of 0.179 from Williamson's fit.
Why engineers worry about it
If the shedding frequency matches a structure's natural frequency, a small sideways push adds up cycle after cycle. Worse, once the structure moves, the shedding tends to synchronise with the motion, a behaviour called lock-in, so it keeps pumping energy in over a band of wind speeds rather than at a single one. Tall steel stacks are often wrapped with helical strakes so that vortices do not leave along the whole height at once.
The chimney challenge is two-dimensional, so a helix is not available. What works in 2D is keeping the two shear layers apart. A flat plate behind the body, the splitter plate, does exactly that, and it is the tail-plate shape in the free tunnel. A plate about one diameter long cuts the side-force amplitude clearly.
What to look for with each shape
- Circle: the separation point slides along the curved surface, so the swing is smooth.
- Square post and flat plate: flow always separates at the sharp corners. The wake is wider, mean drag is higher than for the circle, and the period is longer.
- Wing at 8° angle of attack: shedding is weak and the side force has a non-zero average. Instead of rocking back and forth, the body feels a steady push to one side, which is lift.
Worked examples
Singing wire: A3 on the thin wire
- Input
1 cm diameter, target 220 Hz, assume St = 0.2- Output
Wind needed U = fD/St = 220 × 0.01 / 0.2 = 11 m/s
In real air Re = 11 × 0.01 / 1.5×10⁻⁵ ≈ 7,300, where St ≈ 0.2 holds well. On screen Re is about 73, so 11 m/s gives only about 170 Hz (St about 0.15); 220 Hz comes at about 13.4 m/s.
An octave lower with the thick wire
- Input
2 cm diameter, target 110 Hz- Output
With St = 0.2, half the frequency at the same 11 m/s
Because f = St·U/D, doubling the diameter drops the pitch by an octave. The thick wire also doubles the lattice Re (to about 147), which lifts St to about 0.20, so inside the grid 11 m/s gives about 170 Hz on the thin wire and about 111 Hz on the thick one, less than an octave apart.
Chimney challenge conditions
- Input
20-cell diameter, 12 m/s (lattice speed 0.096), ν = 0.012- Output
Lattice Re = 0.096 × 20 / 0.012 = 160
Shedding is very regular here, which makes it a clean baseline for checking whether your walls bring the sway below 35% of the original.
How to use it
- In Singing Wire, raise the wind slowly and watch for the moment the side-force graph starts to oscillate.
- Use the Strouhal and Reynolds readouts to home in on the target note.
- In Swaying Chimney, draw walls behind or beside the post and compare the sway ratio.
- In the free tunnel, change shapes and switch to the swirl view to see which way each vortex spins.
Frequently asked questions
Is the hum of a power line the wire vibrating?
Mostly it is the pressure fluctuation from vortices shedding alternately behind the wire, the Aeolian tone. You can hear it even when the wire barely moves. If the shedding frequency meets one of the wire's natural frequencies, the wire itself can start to vibrate strongly.
Why does the pitch rise with wind speed?
Because St = fD/U is nearly constant over a wide range. For a fixed diameter f is proportional to U; for a fixed wind it is inversely proportional to D.
Why is the on-screen Reynolds number so low?
With a limited number of cells, making the fluid as thin as real air makes the scheme unstable, so viscosity is set high and Re stays in the tens to hundreds. The shape and rhythm of the vortices come out similar, but a real high-Re wake is turbulent and much messier.
What changes in three dimensions?
Behind a real cylinder the wake develops spanwise waviness from about Re 190 (Williamson 1996). This tool is 2D, so it keeps a clean street beyond that point.
Notes
Forces are shown in lattice units, not newtons. Compare them only as ratios under the same conditions.
Related guides
Sources
- C. H. K. Williamson, Vortex dynamics in the cylinder wake, Annu. Rev. Fluid Mech. 28, 477–539 (1996)
- O. Reynolds, An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous…, Phil. Trans. R. Soc. 174, 935–982 (1883)
- NASA Glenn Research Center — Beginner's Guide to Aeronautics: Reynolds Number
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