(vc_flow_over_cylinder)=

# Flow Over Cylinder

## Why this case matters

The flow over a circular cylinder is the reference case for unsteady, separated bluff-body wakes. Above a critical Reynolds number {eq}`vc_reynolds_flow_over_cylinder` it sheds the Von Karman vortex street, a periodic wake whose shedding frequency and fluctuation statistics are a stringent test of whether the solver sustains the right unsteady dynamics rather than only a correct mean. The well-resolved experiment of {footcite:t}`parnaudeau2008experimental` at $\mathrm{Re} = 3{,}900$ provides mean and fluctuating velocity profiles in the near wake for direct comparison. For computational wind engineering this validates the vortex shedding that drives fluctuating cross-wind loads on towers, chimneys, cables and other slender structures.

The flow around an infinite cylinder is frequently found in literature as validation case for numerical models. After certain Reynolds number this flow is known to exhibit the Von Kármán vortex street, a repeating pattern of swirling vortices which are shed from alternating sides of the object as illustrated below:

```{figure} /_static/img/solver/validation/cases/flow_over_cylinder.svg
---
width: 70%
align: center
---
```

This case is frequently used as validation for numerical models since its flow velocity profile for certain Reynolds numbers was well-estabilished in literature through experiments. The Reynolds number in this case is defined as:

```{math}
---
label: vc_reynolds_flow_over_cylinder
---
\mathrm{Re}=\frac{U_{\infty}d}{\nu}
```

Experimental results of the averages and standard deviation of longitudinal and transversal velocity are found in {footcite:t}`parnaudeau2008experimental` for a Reynolds number $\mathrm{Re}=3,900$.

```{toctree}
---
hidden:
---
02_flow_over_cylinder.ipynb
```

```{footbibliography}
```