Fluid dynamics · unsteady wakes

Kármán Vortex Street

Why does the wake behind a fixed cylinder shed vortices from alternate sides? Above a critical Reynolds number the symmetric wake is unstable. The tiniest disturbance grows, so vorticity gathers and breaks away from one side, then the other. Each release flips the sideways force on the cylinder, and the flipping repeats at a frequency set by the Strouhal number.

Watch the shear layers behind a cylinder become unstable in a transparent wind tunnel. Change the inflow speed, diameter and viscosity to push the Reynolds number past the shedding threshold. The lift then reverses periodically, and the wake settles on a Strouhal frequency.

Reynolds

\mathrm{Re}_D

$120$

Strouhal

\mathrm{St}

$0.166$

Shedding frequency $1.66\,\mathrm{Hz}$

Lift coefficient

C_L

$0.00$

Drag coefficient

C_D

$1.20$

Wake regimeLaminar shedding

This reduced-order two-dimensional wake model uses $\mathrm{St}=fD/U_\infty$ to set how often vortices are released. It does not resolve three-dimensional transition, the turbulent cascade, wall boundary layers or the drag crisis.

Physics tutorial

Kármán Vortex Street: why a symmetric wake breaks itself

BackgroundWhen a slow incompressible flow passes a cylinder, vorticity made at the cylinder surface flows into the wake along two shear layers. The Reynolds number captures the contest between inertia, viscosity and the size of the body.

Why it mattersChimney stacks, bridge cables, flow meters and aquatic propulsion all meet periodic shedding. Seeing how speed and diameter set its frequency is the first step toward understanding fluid–structure interaction.

Start with the essentials

Focus question: Why does the wake behind a perfectly symmetric cylinder not stay symmetric forever?
One-sentence intuition: Once $\mathrm{Re}_D$ passes a critical value, the symmetric wake cannot survive small disturbances. Vorticity gathers and breaks away from each side in turn, and the lift reverses at $f=\mathrm{St}U_\infty/D$ .

Core mathematical model

Reynolds number

\mathrm{Re}_D=\frac{U_\infty D}{\nu}

It compares inertial transport with viscous diffusion. Its value decides whether the wake crosses the linear instability threshold for periodic shedding.

Strouhal relation

\mathrm{St}=\frac{fD}{U_\infty}

It turns the shedding frequency into a dimensionless number. In the classic subcritical cylinder wake it changes only slowly with Reynolds number.

Periodic transverse load

C_L(t)\approx \widehat C_L\sin(2\pi f t)

The upper and lower shear layers release vortices in turn, so the lift changes sign every half-cycle.

Common difficulties

The cylinder does not need to oscillate first

Typical misconceptionThe cylinder has to be shaken side to side before the shedding alternates.

Better mental modelThe steady symmetric flow past a fixed cylinder becomes unstable on its own. Background noise only picks the starting phase.

The drawn vortices are not grid-resolved CFD

Typical misconceptionEvery rendered core is a directly resolved Navier–Stokes vortex.

Better mental modelThe reduced wake keeps the alternating sign, convection, spreading scale and force phase of the vortices, but it does not resolve the full boundary layer.

Run the experiment

01
Stay below onset
Choose Steady pair and look at the lift and Strouhal readouts.
What to observe: The wake stays nearly symmetric, and the periodic shedding frequency drops to zero.
02
Cross the instability
Choose Classic street with streamlines and lift history visible.
What to observe: Positive and negative cores alternate, and the lift trace rises and falls in step with their release.
03
Check how frequency follows speed
Raise only the free-stream speed and keep diameter and viscosity fixed.
What to observe: The Reynolds number rises, and the shedding frequency grows roughly in proportion to the inflow speed.