Turbulent Shear Flows 7 pp 173-194 | Cite as

# Three-Dimensional Aspects and Transition of the Wake of a Circular Cylinder

## Abstract

Three-dimensionality in the wake of a cylinder is an intrinsic feature, not only in the transition regime when small-scales appear, but also when the vortex shedding is laminar. Certain features associated with this laminar regime also have relevance to the flow at higher (turbulent) Reynolds numbers.

In the laminar shedding regime (for *Re <* 180) two characteristics of the wake, which have received a great deal of debate in the past, are found to be related to each other; in the present paper the existence of a discontinuity in the Strouhal-Reynolds number relationship is explained by a transition between different modes of oblique vortex shedding. Oblique shedding is shown to be caused by the end boundary conditions in the case of cylinders of even hundreds of diameters in length. By manipulating the end conditions, parallel shedding can be induced, which then results in a completely-continuous Strouhal curve. It is also shown that this curve is “universal” in that all the oblique-shedding and parallel-shedding frequency data can be collapsed onto one continuous curve using a simple relationship. The case of parallel shedding represents *two-dimensional* vortex shedding, and therefore the “universal” Strouhal curve is compared with data from two-dimensional numerical computation.

The transition to three-dimensionality in the wake, at higher Reynolds numbers, is shown to involve two successive stages, each of which corresponds with a discontinuity in both the character of wake formation and also the *S-Re* relationship. The first discontinuity (near *Re =* 180) is associated with the inception of vortex loops, and it is hysteretic. The second discontinuity (between *Re =* 230–260) corresponds with a change to a finer-scale streamwise vortex structure, and in this case there is no hysteresis. There are fundamental differences between the development of three-dimensionality in this separated wake as compared with that found in other “unseparated” shear flows.

Finally, it is shown (in the laminar shedding regime) that a larger-scale wake evolves far downstream of the cylinder (and at roughly the same downstream location whether the shedding be parallel or oblique). In the case of the oblique shedding, the large-scale structure involves oblique instability “waves” at an angle of typically around twice the (upstream) oblique-shedding angle.

### Keywords

Vortex Convection Assure Vorticity Peaked### Nomenclature

*L/D*Length/Diameter of cylinder

*Re*Reynolds number

*S*Strouhal number

*θ*Oblique vortex shedding angle

*U*_{c}Convection speed of the vortices downstream

*U*_{∞}Free stream speed

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