Faster air or thinner air means a larger Reynolds number. For the Reynolds numbers of real things, from bacteria to hurricanes, see Reynolds Number of Everything.
Reynolds number
–How much the air’s push outweighs its stickiness. Below about 47 the wake behind a cylinder stays still; above it, it starts to sway.
- Drag coefficient
- –
- Lift coefficient
- –
- Strouhal number
- –
- Height of the shape
- –
- Time run
- 0
- Solver speed
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Drag: how hard the air pushes the shape downstream. Lift: how hard it pushes it up (positive) or down. Strouhal: how often eddies break away, compared with the time the air takes to pass the shape. All three are scaled by the shape’s height, so a larger shape does not score higher just for being large. Time is counted in solver steps.
IWhy the wake wobbles
Slowly moving air closes neatly behind a cylinder. A little faster, and two eddies sit in its lee, turning in opposite directions like a pair of gears. Up to a Reynolds number of about 47 they stay put.
Beyond that the pair cannot hold. One eddy grows, breaks away and drifts off; the other follows from the opposite side, and so on in turn. The wake becomes a double row of whirls known as a Kármán vortex street, after Theodore von Kármán, who explained it in 1911.
Each eddy that leaves tugs the body sideways, so the lift swings back and forth at the shedding frequency f. The Strouhal number St = f·D/U compares it with the time the air takes to pass the body. For a cylinder it settles near 0.2 over a wide range of speeds: the wake ticks like a clock. That is why telephone wires sing in the wind, and why tall chimneys carry spiral strakes to break the rhythm.
In this tunnel the walls are not far away, and the grid is coarse, so expect St between about 0.17 and 0.21 for the cylinder.
IIHow it is computed
The air is not treated as a smooth fluid but as a crowd of particles living on a grid. In every square sit nine groups of them: one group at rest, four heading to the neighbours beside, above and below, and four heading to the corners.
Each tick has two moves. Stream: every group hops one square in its direction. Collide: in each square the groups jostle, nudging their numbers towards the balance that matches the square’s density and velocity. How quickly they settle sets the viscosity. Where a group would hop into the obstacle, it bounces straight back; adding up those bounces gives the drag and the lift.
Out of these simple local rules, repeated thousands of times a second, come pressure, swirls and wakes that obey the Navier–Stokes equations. The method is called lattice Boltzmann, after Ludwig Boltzmann’s description of gases as colliding particles.
Here: a grid of 320 × 128 squares, speeds and lengths in grid units, a wind of at most 0.12 squares a step to keep the air nearly incompressible, a Smagorinsky eddy viscosity for steadiness at higher Reynolds numbers, and walls above and below that the air slides along freely. It is a two-dimensional sketch, not a design tool.