Vortices shed alternately behind a body and apply an oscillating side force to it. The frequency is given by the dimensionless Strouhal number (St = f·D/U), which for a circular cylinder stays around 0.2 over a wide Reynolds range [1].
Why that is useful
As a design check. If the shedding frequency is close to a structural natural frequency there is a resonance risk. This is the classical cause of damage in heat exchanger tubes, stacks and masts, and scaffolding members.
As an analysis check. If a transient solution does not reproduce the expected Strouhal number, the cause is usually not the physics but the mesh: the wake is under-resolved, or numerical diffusion has damped the vortices. This is one of the cheapest verification tests available.
Modelling requirements
Steady state will not do. The phenomenon is transient by definition; a steady solution gives a symmetric and wrong wake. See the steady versus transient note.
Do not use a symmetry plane. The wake is not symmetric; a half model forbids shedding and returns zero side force. See the symmetry note.
Time step from the frequency. At least twenty steps per shedding period. An oscillation sampled with five steps loses its amplitude.
Three-dimensionality. Above a certain Reynolds number the vortex tubes break down along the span; a two-dimensional model markedly overpredicts the oscillation amplitude.
Lock-in
If the body is free to vibrate and the shedding frequency approaches its natural frequency, shedding locks on to the structural frequency and the amplitude grows. That is no longer a one-way problem. See the fluid-structure interaction note.
References
- Williamson, C. H. K. (1996). Vortex dynamics in the cylinder wake. Annual Review of Fluid Mechanics, 28, 477–539. DOI: 10.1146/annurev.fl.28.010196.002401
- Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32(8), 1598–1605. DOI: 10.2514/3.12149