Fluid dynamics · unsteady wakes

Kármán Vortex Street

Follow the shear layers destabilizing behind a cylinder in a transparent wind tunnel. Change inflow, diameter, and viscosity to cross the shedding threshold, reverse lift periodically, and lock the wake to 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 uses $\mathrm{St}=fD/U_\infty$ to set the alternating release cadence. It does not resolve three-dimensional transition, turbulent cascade, wall boundary layers, or the drag crisis.

Physics tutorial

Kármán Vortex Street: why a symmetric wake breaks itself

BackgroundIn low-speed incompressible flow past a cylinder, wall-generated vorticity enters the wake through two shear layers. Reynolds number organizes the competition among inertia, viscosity, and body scale.

Why it mattersStacks, bridge cables, flow meters, and aquatic propulsion all encounter periodic shedding. Understanding how speed and diameter lock its frequency is the first step toward fluid–structure interaction.

Start with the essentials

Focus question: Why does a geometrically symmetric wake refuse to remain symmetric forever?
One-sentence intuition: Above a critical $\mathrm{Re}_D$ , the symmetric wake is unstable. Opposite vorticity collects and releases alternately, reversing lift at $f=\mathrm{St}U_\infty/D$ .

Core mathematical model

Reynolds number

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

Compares inertial transport with viscous diffusion and organizes the onset of periodic shedding.

Strouhal relation

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

Compresses shedding into a dimensionless cadence that varies only gradually across the classic subcritical regime.

Periodic transverse load

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

Alternating release from the upper and lower shear layers makes lift reverse sign every half-cycle.

Common difficulties

The cylinder need not oscillate first

Typical misconceptionAlternating shedding requires the cylinder to be driven side to side.

Better mental modelThe steady symmetric fixed-cylinder solution can itself become unstable; ambient noise merely selects the initial phase.

Discrete vortices are not grid-resolved CFD

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

Better mental modelThe reduced wake retains alternating sign, convection, spreading scale, and force phase without resolving the full boundary layer.

Run the experiment

01
Remain below onset
Choose Steady pair and inspect lift and Strouhal readouts.
What to observe: The wake remains nearly symmetric and the periodic shedding frequency vanishes.
02
Cross the instability
Choose Classic street with streamlines and lift history visible.
What to observe: Positive and negative cores alternate while the lift trace synchronizes with their release.
03
Test the scaling
Increase only free-stream speed while diameter and viscosity remain fixed.
What to observe: Reynolds number rises and shedding frequency grows approximately in proportion to inflow speed.