Vortex Shedding: Strouhal Number & Lock-In Resonance

simulator intermediate ~12 min
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f_s = 2.0 Hz — LOCK-IN at 10 m/s with D = 1 m

At 10 m/s with a 1 m diameter body (St=0.2), the vortex shedding frequency is 2.0 Hz — exactly matching the 2.0 Hz natural frequency. This is the lock-in condition where resonant vortex-induced vibrations become dangerous.

Formula

f_s = St × V / D (shedding frequency)
V_cr = f_n × D / St (critical wind speed for lock-in)
St ≈ 0.198(1 − 19.7/Re) for circular cylinder

The von Kármán Vortex Street

Theodore von Kármán described one of fluid mechanics' most beautiful phenomena: when a steady flow encounters a bluff body, it does not remain steady. Instead, vortices detach alternately from each side of the body in a remarkably regular pattern — the von Kármán vortex street. Each departing vortex creates a lateral impulse, generating an alternating lift force perpendicular to the wind direction. This alternating force is the root cause of vortex-induced vibrations in chimneys, towers, cables, and bridge decks.

The Strouhal Number

The frequency of vortex shedding is governed by the Strouhal number: f_s = St × V / D. For circular cylinders, St ≈ 0.2 across a remarkable range of Reynolds numbers (300 to 300,000). This universality makes Strouhal number prediction reliable: given the wind speed and body diameter, the shedding frequency is predictable. In this simulation, adjusting wind speed or diameter changes the shedding frequency, and you can see the vortices form and shed at the predicted rate.

The Lock-In Phenomenon

The most dangerous condition occurs when the shedding frequency approaches a structure's natural frequency — the lock-in zone. Instead of the shedding frequency increasing linearly with wind speed, the structural motion takes control: the oscillating structure synchronizes the vortex shedding to its own natural frequency over a range of wind speeds. Vibration amplitudes grow dramatically, limited only by structural damping. The Tacoma Narrows Bridge collapse, while driven by flutter rather than vortex shedding, popularized awareness of wind-structure resonance. True vortex lock-in has caused failures of cooling tower stacks, marine risers, and suspension bridge hangers.

Engineering Countermeasures

Preventing vortex-induced vibration requires either separating the shedding frequency from the natural frequency or disrupting the vortex coherence. Helical strakes — spiral fins wrapped around the body — break up the spanwise correlation of vortex shedding, reducing the net alternating force by 90%. Tuned mass dampers add damping at the critical frequency. Aerodynamic fairings streamline the cross-section, preventing regular shedding entirely. For bridge decks, vortex shedding is often the controlling dynamic load case for fatigue of hangers and deck elements.

FAQ

What is vortex shedding?

When wind flows past a bluff body (cylinder, tower, bridge deck), vortices detach alternately from each side forming a von Kármán vortex street. Each vortex creates a lateral force, producing an alternating lift that oscillates at the shedding frequency f_s = St × V / D.

What is the Strouhal number?

The Strouhal number St = f_s × D / V is a dimensionless frequency relating shedding frequency to wind speed and body size. For circular cylinders, St ≈ 0.2 over a wide Reynolds number range. For rectangular sections, St varies from 0.1 to 0.2 depending on the aspect ratio.

What is lock-in?

Lock-in occurs when the shedding frequency approaches the structure's natural frequency (typically within ±20%). The structure's motion organizes the vortex shedding, synchronizing it to the natural frequency over a range of wind speeds. This creates resonant amplification with potentially catastrophic vibration amplitudes.

How is vortex-induced vibration prevented?

Mitigation strategies include: helical strakes that disrupt vortex coherence, tuned mass dampers that absorb vibration energy, aerodynamic shaping (fairings) that prevent regular shedding, and structural stiffening to move the natural frequency away from expected shedding frequencies.

Sources

Embed

<iframe src="https://homo-deus.com/lab/wind-engineering/vortex-shedding/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub