Von Karman vortex street

Meanwhile, the flow near the cylinder curls towards the cylinder and forms a new vortex that takes the place of the original. As time goes on, the vortices on either side of the cylinder take turns breaking off and traveling down stream. A snapshot of this behavior is shown schematically in figure 9.3. This stream of successively broken-off vortices is known as a von Karman vortex street [trittSS]. 

A little bit of physical intuition as to how the vortices form in the first place may help in explaining the behavior as TZ is increased still further. We know that u = 0 at the cylinder s surface. We also know that the velocity increases rapidly as we get further from that surface. Therefore vortices are due to this rapid local velocity variation. If the variation is small enough, there is enough time for the vorticity to diffuse out of the region just outside the cylinder s surface and create a large von Karman vortex street of vorticity down stream [feyn64]. 

When a bluff body is interspersed in a fluid stream, the flow is split into two parts. The boundary layer (see Chapter 11) which forms over the surface of the obstruction develops instabilities and vortices are formed and then shed successively from alternate sides of the body, giving rise to what is known as a von Karman vortex street. This process sets up regular pressure variations downstream from the obstruction whose frequency is proportional to the fluid velocity, as shown by Strouai. 9. Vortex flowmeters are very versatile and can be used with almost any fluid — gases, liquids and multi-phase fluids. The operation of the vortex meter, illustrated in Figure 6.27, is described in more detail in Volume 3, by Gjnesi(8) and in a publication by a commercial manufacturer, Endress and Hauser.10 ... 

A special case of chaotic advection occurs in open flows in which the time-dependence of the flow is restricted to a bounded region (Tel et al., 2005). This kind of flow structure with an unsteady mixing region and simple time-independent inflow and outflow regions is typical for example in stirred reactors or in a flow formed in the wake of an obstacle. A well known example is the von Karman vortex street behind a cylinder at moderate Reynolds numbers (Jung et al., 1993 Ziemniak et al., 1994), where around the cylinder the flow is time-periodic, but at some distance from it upstream or downstream the velocity field is time independent. 

When a fluid flows past a bluff body, the wake downstream will form rows of vortices that shed continuously from each side of the body as illustated in Figure 4.16. These repeating patterns of swirling vorticies are referred to as Karman vortex streets named after the fluid dynamicist Theodore von Karman. Vortex shedding is a common flow phenomenon that causes car antennas to vibrate at certain wind speeds and also lead to the collapse of the famous Tacoma Narrows Bridge in 1940. Each time a vortex is shed from the bluff body it creates a sideways force causing the body to vibrate. The frequency of vibration is linearly proportional to the velocity of the approching fluid stream and is independent of the fluid density. 

Strouhal foimd the Strouhal Niunber (Sj) to be about %. Actually the constant varies between 0.2 and 0.5 depending on the shape of the body, but has a constant value for a given shape. In 1911, von Karman showed anal5 ically lhat the only stable vortex configuration was that given by the Strouhal Niunber. These vortices are, therefore, sometimes called the Karman Vortex Street. 

Karman vortex street A phenomenon in which vortices of a moving fluid form as repeating patterns. They are caused by the unsteady separation of flow of a fluid as it passes around an object such as a wire and observed over Reynolds numbers of around 90. It is named after Hungarian-American mathematician and physicist Theodore von Karman (1881 -1963) and is also known as the von Kton n vortex street. 

---