Math 2.0

Fluid mechanics Ideal fluids Example

Kármán vortex street

Builds on VorticityReynolds numberStrouhal numberCirculation

Example

A Kármán vortex street is the double row of vortices in the wake of a bluff body, such as a cylinder, in a steady stream. Vortices are shed alternately from the two sides of the body. The vortices of the two rows turn in opposite senses, so the vorticity of the wake alternates in sign. For a circular cylinder the street appears once the Reynolds number based on the diameter exceeds a critical value of about 4747. Let DD be the diameter and UU the speed of the stream. Over a wide range of Reynolds numbers above this value, the shedding frequency ff satisfies fD/U≈0.2f D / U \approx 0.2. So the Strouhal number of the flow stays nearly constant.

Remarks

Von Kármán studied an idealised model: two infinite rows of point vortices in an ideal fluid. One row has vortices of circulation Γ\Gamma at the points (na,h/2)(na, h/2), and the other has vortices of circulation −Γ-\Gamma at the points ((n+12)a,−h/2)((n + \tfrac{1}{2})a, -h/2), for all integers nn. This staggered array moves as a whole, parallel to the rows, with speed Γ2atanh⁡(πha)\frac{\Gamma}{2a} \tanh\left(\frac{\pi h}{a}\right). A linear stability analysis shows that the staggered array is neutrally stable only when sinh⁡(πh/a)=1\sinh(\pi h / a) = 1, that is h/a≈0.281h / a \approx 0.281, and unstable otherwise. The symmetric arrangement, with the two rows facing each other, is always unstable.

Reading path

To understand this page from the ground up, read these 5 pages in order. The foundations come first.

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Circulation, concept, no evidence levelCirculationconceptReynolds number, concept, no evidence levelReynolds numberconceptStrouhal number, concept, no evidence levelStrouhal numberconceptVorticity, concept, no evidence levelVorticityconceptKármán vortex street, example, no evidence levelKármán vortex streetexample
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
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  1. Circulation concept
  2. Reynolds number concept
  3. Strouhal number concept
  4. Vorticity concept
  5. Kármán vortex street example

Further reading

  1. Web https://en.wikipedia.org/wiki/K%C3%A1rm%C3%A1n_vortex_street
About this page
TagNZKHXG3YQ0
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Kindexample
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MSC76D25, 76B47
IllustratesStrouhal number
UsesVorticity, Reynolds number, Strouhal number, Circulation
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Changed3 November 2026

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