Reynolds Number

Re 150

Vortex street

Drag C_d—

Strouhal St—

sideways force on the obstacle — the wake’s heartbeat

Drag the dial. Drag the obstacle. Swipe through the fluid.

What am I looking at?

Inertia versus stickiness

Every fluid — air, water, honey, the rock of Earth’s mantle — is pulled between two things. Inertia: moving fluid wants to keep moving. Viscosity: fluid sticks to itself and smears every motion out. The Reynolds number is simply the ratio of the two.

Re = speed × sizeviscosity = inertiaviscous drag

Here is the strange part: only that ratio matters. A bacterium in water lives much as you would swimming in tar. A model plane in a wind tunnel tells you about the real one if the Re is the same. That is why one dial is enough to go from microbes to whales.

Build a world

Fluid Size Speed

Re = —

Things to try

Push the fluid at Re 1, then at Re 1,000. Swipe through it. In syrup your push dies the moment you stop; at high Re it keeps swirling long after.
Find where the wake starts to swing. Creep the dial up from 20. Somewhere near Re ≈ 47 the twin eddies break loose and begin to march.
Drag the obstacle. Haul it through still fluid and watch the vortices it sheds.
Draw your own shape with the pen, and see what kind of wake it leaves.
Un-stir a fluid. In Un-stirring, smear four drops of dye by turning the inner cylinder, then turn it back. In syrup the drops reassemble, every speck; in water they never do. G. I. Taylor showed this with corn syrup in 1967 — at low Re, the flow has no memory of its own.
Switch to Pressure to see the squeeze in front of the obstacle and the suction behind it — that difference is drag.

How this works

This is a real fluid solver, not an animation: a lattice-Boltzmann method (D2Q9) running on your GPU as WebGL shaders. Hundreds of thousands of cells, each updated about a thousand times per second, give the flow. The smoke is dye carried along by it. Above Re ≈ 2×10⁴ the grid can no longer resolve the smallest eddies; a Smagorinsky subgrid model stands in for them. Below Re ≈ 0.1 the picture stops changing at all — creeping flow looks the same all the way down to the bacteria. The flow is 2-D, so its turbulence is the flat kind; real wakes beyond Re ≈ 200 also twist in three dimensions.

In Un-stirring, water is the same solver with a turning wall. Syrup is Stokes flow, the limit Re → 0, where the flow follows the wall instantly and in proportion: the solver finds the flow for one wall speed, and every moment of the stroke is that, scaled. The dye is 65,536 particles, so nothing blurs, and what comes back is what the flow brought back.