Strouhal Number & Vortex Shedding Simulator — Karman Vortices and Lock-on
Compute the Karman vortex shedding frequency behind a cylinder from velocity, diameter and viscosity. Strouhal number is switched automatically by Reynolds number regime and lock-on resonance against the structural natural frequency is diagnosed in real time.
Parameters
Flow velocity U
m/s
Cylinder diameter D
m
Kinematic viscosity ν
m²/s
Natural frequency f_n
Hz
Defaults correspond to flow of water at 20 °C around a cylinder. ν uses a linear slider, displayed in scientific notation.
Results
—
Reynolds number Re
—
Strouhal number St
—
Shedding frequency f
—
f / f_n (resonance ratio)
Lock-on risk: low
Flow around cylinder and Karman vortex street
Gray circle = cylinder cross section / red and blue circles = alternating shed vortices / left arrows = upstream velocity vectors
Theory & Key Formulas
Strouhal number St non-dimensionalizes the shedding frequency by velocity and size. Here f is the vortex shedding frequency [Hz], D is the cylinder diameter [m] and U is the flow velocity [m/s]:
$$St = \frac{f\,D}{U}\quad\Longleftrightarrow\quad f = St\,\frac{U}{D}$$
Reynolds number. ν is the kinematic viscosity [m²/s]:
$$Re = \frac{U\,D}{\nu}$$
For flow around a cylinder, St falls into the following Reynolds number regimes (simplified model):
Lock-on resonance risk is flagged when |f − f_n|/f_n < 0.1 relative to the structural natural frequency f_n.
About the Strouhal Number & Vortex Shedding Simulator
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Why do chimneys and power lines hum and sway in the wind? It looks like the wind is just hitting them.
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That is the Karman vortex effect. When wind passes a round bluff body, the wake sheds alternating clockwise and counterclockwise vortices, one after another. Each shedding event pushes the cylinder sideways, so you get periodic lateral forces that make the structure vibrate and sing. Hit "Shed vortices" above and you will see the red and blue vortices arrange themselves in a staggered street.
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What sets how fast the vortices come off? Surely it is not just "faster wind, faster shedding"?
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Good catch. The dimensionless Strouhal number organizes it: $St = f\,D/U$. Across the wide subcritical range, St is roughly 0.20, so once you fix the diameter, the shedding frequency scales linearly with velocity. For a 5 cm cylinder in 5 m/s flow, $f = 0.20 \times 5/0.05 = 20$ Hz, that is twenty vortices per second.
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Wait, so St itself changes with Reynolds number? When I move the diameter or viscosity sliders the value really shifts.
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Right. For Re < 47 nothing sheds; the wake is steady. From 47 to 250 we use the Roshko fit $St \approx 0.21(1 - 21.2/Re)$. Above 250 we sit in the subcritical regime with St ≈ 0.20, then beyond $2 \times 10^5$ the separation point migrates and St jumps around before settling near 0.27 in the supercritical range. Engineering wind and water flows usually sit in subcritical territory, so 0.20 is a good default to memorize.
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I just got a "Lock-on risk" warning. What does that mean?
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It means the shedding frequency f got within 10 % of the structure's natural frequency f_n. When that happens, the flow synchronizes with the structural motion and the shedding locks to the vibration, sustaining large oscillation across a band of wind speeds. The Tacoma Narrows collapse, plus countless fatigue failures of chimneys, bridge decks and transmission lines, are tied to this lock-on. Vibration design fundamentally aims to keep f and f_n apart in the design wind range.
FAQ
Yes, but both the choice of characteristic dimension D and the value of St depend on the shape. Cylinders sit near 0.20 in the subcritical range, a square section (with the cross-stream side as D) is about 0.12 to 0.13, and streamlined sections drop further and can even suppress shedding. You must look up shape-specific St values from experimental data.
St is dimensionless, so the same formula applies to both. What differs is Reynolds number: for the same diameter and velocity, air (ν ≈ 1.5×10⁻⁵ m²/s) gives an order-of-magnitude lower Re than water (ν ≈ 1.0×10⁻⁶). At lab scale, air experiments tend to sit between the laminar vortex street and subcritical regimes, while water more easily reaches the subcritical regime.
There are three main mitigations. (1) Separate the structural natural frequency f_n far enough from the shedding frequency f in the design wind range. (2) Add helical strakes around chimneys to disrupt spanwise coherence of the shedding. (3) Increase damping with a tuned mass damper or other dissipative device. Separating the frequencies is fundamental; strakes are a common retrofit.
Because D/U is the characteristic convective time, the time it takes a fluid particle to traverse the body. The Strouhal number is the ratio of the shedding time scale 1/f to D/U, and on geometrically similar bodies this dimensionless quantity should be constant. Empirically St for cylinders is indeed nearly constant over a very wide range of Re, which makes it a textbook example of similarity laws.
Real-world Applications
Wind design of tall chimneys and skyscrapers: Tall RC chimneys and high-rise cylindrical towers can experience vortex-induced cross-wind vibration in their design wind range. Designers compare the natural frequency f_n with the shedding frequency f at each wind speed and check whether lock-on develops dangerously. Helical strakes or tuned mass dampers are added where needed.
Self-excited oscillation of power lines and bridge cables: Conductor galloping and stay-cable vibration involve vortex excitation. Tacoma Narrows (1940) was technically a torsional flutter, but ever since, bridge design has used wind-tunnel testing and dimensionless analysis based on St and f_n to quantify vortex-induced vibration risk.
Vortex flow meters: A bluff body inserted into a pipe sheds vortices whose frequency f is measured by a piezo sensor, and $U = f\,D/St$ recovers the flow velocity. Because St ≈ 0.2 stays nearly constant across the subcritical regime, vortex flow meters are insensitive to viscosity and density, and are widely used in industrial process measurement.
Heat exchangers and reactor fuel rods: Tube bundles in heat exchangers and fuel assemblies in nuclear reactors experience cross-flow that drives vortex shedding, which is a leading cause of vibration, wear and fatigue failure. Design codes use array-corrected St values to compute shedding frequencies and verify adequate separation from tube natural frequencies.
Common Misconceptions
The most common misconception is that "the Strouhal number is always a constant 0.2." Across the broad subcritical range (roughly $250 \le Re < 2 \times 10^5$) St ≈ 0.20 is indeed nearly constant, but for Re < 47 nothing is shed at all, from 47 to 250 St rises with Re, and in the transition range past $2 \times 10^5$ the separation point migrates and St scatters strongly before settling near 0.27 in the supercritical range. Try sweeping the viscosity or diameter sliders in this simulator and you will see the displayed St snap between regimes.
The next most common mistake is to assume that "there is no resonance unless f matches f_n exactly." Lock-on synchronizes the shedding with structural motion over a finite frequency band (commonly 10 to 30 %), and within that band the frequency stays pinned even as the wind speed changes, sustaining large amplitudes. This tool uses |f − f_n|/f_n < 0.1 as a warning threshold, but for real structures a wider band is usually considered dangerous.
Finally, "the cure for lock-on resonance is just to make it stiffer" is a dangerous instinct. Raising f_n only moves the same problem to a higher wind speed. The genuine remedies are (1) separating f and f_n across the design wind range, (2) disrupting shedding coherence with helical strakes, and (3) raising the damping ratio with dampers. The simple check shown here is only a first-order screen; real designs need wind tunnel tests, CFD and vibration response analysis.