# Vortex street and Reynolds number

Its been stated in Wikipedia regarding Reynolds number(Re) that "laminar flow occurs when Re<2300 and turbulent flow occurs when Re>4000. In another wiki file related to Kármán vortex street it has been stated that "A vortex street will only be observed over a given range of Reynolds numbers (Re), typically above a limiting Re value of about 90. According to Wiki "The term Kármán vortex street (or a von Kármán vortex street) is used in fluid dynamics to describe a repeating pattern of swirling vortices caused by the unsteady separation of flow of a fluid over bluff bodies".Doesn't this "unsteady" refer to turbulence? If so then how is it possible for vortices to have so low value of Re? Is 'more the turbulence higher is the vortex effect' a right statement?

Turbulence isn't the same as unsteadiness - a vortex street is not necessarily a turbulent phenomenon. As an analogy that (for some reason) I find easier to understand, consider a convection experiment where we heat a fluid at the bottom and cool it at the top. Below a certain threshold value for the temperature difference, the heat is transferred only by diffusion and there is no bulk flow. A little higher and we get an instability, resulting in the formation of a convection cell. In this case the fluid is moving, but it is still moving in a laminar way. As we increase the temperature difference, the speed of the flow increases, and it's only when we've increased the temperature quite a bit more that the flow becomes turbulent.

Vortex streets are similar. Above a certain value of the Reynolds number, the vortex street forms. The flow is now time-dependent, but it's periodic and still relatively easy to predict. If the flow is increased even further then the vortices spin so fast that smaller vortices form to dissipate their kinetic energy. It's only at this point that the flow becomes unpredictable and chaotic, which is when we call it turbulent. I guess you can say something like, a Kármán vortex street is a flow that's unsteady on one spatial scale, but in order for a flow to be called turbulent it has to be unsteady across a wide range of scales.

• Indeed a common misconception that a vortex is necessarily turbulent. Commented Jun 10, 2012 at 9:25

The point at which the flow becomes turbulent is very sensitive to the flow geometry. The value of 2,300 you quote applies to flow in smooth pipes. To take an example, the flow round a sphere becomes ceases to be laminar at an Re of about 1. The flow becomes increasing turbulent as you raise the Reynold's number until vortex shedding starts around Re = 50.

• This is partially due to the choice of the length scale that goes into the calculation of the Reynolds number. We choose one that is "characteristic" of the system, but it is not obvious that this term is well defined. Commented Jun 9, 2012 at 15:43