STUDY #12 · 2026 · IN OBSERVATION

Kármán Vortex Street

A model-driven visual study of the alternating vortices shed in a wake.

MOVING IMAGE — DRIFTING STREET St 0.22 · a 0.70 · h/l ≈ 0.30 · satellite

WHAT IS THIS

In a steady flow past a blunt body, above a critical speed the wake sheds vortices alternately from its two sides, forming the staggered double row known as a Kármán vortex street — the pattern behind fluttering flags, aeolian tones and the ribbons of cloud trailing downwind of an island.

Rather than resolving a continuous flow, this study models the wake as a small set of point vortices that induce one another, with a cloud of passive tracers carried along to reveal the streaklines — the smoke, essentially. This study runs that point-vortex model in real time on the GPU.

a satellite cloud street — the wake as seen from above an island St 0.22 · a 0.70 · Γ 1.6 · palette satellite

Motif vortex shedding / staggered double row / streaklines / h:l ≈ 0.28

Method A small simulator was generated and modified with AI assistance, then ported to a real-time GPU (GLSL) renderer. The visual output was selected through parameter exploration.

Observation The street's geometry is governed by the shedding rhythm and where the rows are laid down; near a shoulder spacing a ≈ 0.70 the row-to-spacing ratio settles close to von Kármán's stable 0.28. The tracer streaklines, not the discrete cores, carry the motion — dye lit where the flow shears.

Reference Th. von Kármán, Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl., 509-517 (1911); Th. von Kármán & H. Rubach, Physikalische Zeitschrift, vol.13, 49-59 (1912).

Tools Python / NumPy / three.js / React / GLSL / ffmpeg / AI coding assistant

Year 2026

This is not a scientific simulation result, but a visual interpretation of the phenomenon.

PARAMETERS EXPLORED

param meaning effect on the image

St the Strouhal number — the shedding rhythm (dimensionless frequency) higher packs the vortices closer; h/l rises and passes the stable 0.28 near St ≈ 0.30

a shoulder spacing — where the rows are laid down directly controls the row separation h; a ≈ 0.70 lands h/l on von Kármán's 0.28

Γ circulation — each vortex's strength stronger circulation winds the dye tighter; too strong and the rows merge and break down downstream

δ core radius (regularisation) look only, not geometry: small gives tight cores, large gives soft merging swirls

Each image below records its exact parameter set.

SELECTED STILLS — 3

satellite — an island's cloud wake St 0.22 · a 0.70 · Γ 1.6 · satellite

dye tunnel — a laboratory pair of inks St 0.22 · a 0.70 · palette dye-tunnel

ember breakdown — pushed past stability Γ high · downstream merging · palette ember

PROCESS — PARAMETER SWEEPS

The geometry dial: sweeping the shoulder spacing a moves the row-to-spacing ratio h/l through von Kármán's stable value — the sweep lands on 0.28 near a ≈ 0.70.

the a sweep — h/l passing through 0.28 rows = a (shoulder spacing) · measured h/l per cell

SIGNATURE — ONE NUMBER IN THE TURBULENCE

Left to itself, the wake chooses 0.28.

Of all the ways two rows of vortices could stagger, von Kármán showed in 1911 that exactly one geometry is stable: a row-to-spacing ratio h/l ≈ 0.281. Flags, wires and island wakes all settle toward the same number.

The same happens inside this model: the Python engine measures h/l = 0.281 at a ≈ 0.70, and the GPU renderer drifts at ≈ 0.30 — order hiding just inside the turbulence.

the anatomy of the street — vorticity sign → two colours, and the stable ratio warm = counter-clockwise · cool = clockwise · h : l ≈ 0.28

COLOUR = VORTICITY

The colour encodes the sign of vorticity: warm for counter-clockwise vortices, cool for clockwise ones. Because a Kármán street is precisely an alternation of the two, this diverging map is an encoding of a physical quantity rather than a decorative choice.

The tracer streaklines stand in for smoke or dye — brightness reads as dye density, and the strands trace where the flow has stretched and rolled the sheet up around each core.

the two rotations as two inks, rolled up by each core warm ⇄ cool = vorticity sign · dye-tunnel

Palettes (satellite cloud street / dye-tunnel pair / hot-cold shear) are artistic approximations, not measurements.

REFERENCES

Th. von Kármán, "Über den Mechanismus des Widerstandes, den ein bewegter Körper in einer Flüssigkeit erfährt," Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Math.-Phys. Klasse, 509-517 (1911).
Th. von Kármán & H. Rubach, "Über den Mechanismus des Flüssigkeits- und Luftwiderstandes," Physikalische Zeitschrift, vol.13, 49-59 (1912).