I. Theoretical Transitions Between Flow Patterns

A cylinder with a diameter D is placed in a flow with a velocity U in the direction of the x-axis, as shown on figure 1 below :

Figure 1 : Flow past the cylinder

The Reynolds number Re = UD/n characterizes the flow pattern past the cylinder, and the following transitions have been experimentally observed (e.g. see figure 2) :

• For Re lower than 4, the flow past the cylinder remains uniform with both an upstream/downstream symmetry and a right-hand/left-hand one. This flow pattern is called a creeping flow
• From Re = 4 to a critical Reynolds number approximatively equal to 40, vortices appear in the immediate wake of the cylinder, yet they stay closely attached to it. This area is called the recirculation zone, since the two vortices rotate in opposite senses, and the x-axis symmetry is the only one to remain. Furthermore, the size of the vortices increases with the Reynolds number.
• For Reynolds numbers lower than 200, the flow downstream the cylinder becomes unsteady, even though all the imposed conditions are being held steady. Two rows of vortices appear on either sides of the wake : all those on one side rotates in the same sense, whereas all those on the opposite side rotate in the opposite sense. It can be noticed that the flow remains bi-dimensional.This new pattern turns out to be periodic, and the period can be calculated by determining the length of time between the formation of two vortices. This period increases with the Reynolds number, and according to the dependency of the Strouhal number on this adimensional variable.
• For Reynolds number greater than 200, the flow looses its bi-dimensional characteristics, and for Re = 400, vortices themselves become turbulent from their very point of generation.
• For higher values of Reynolds number, vortices loose their regular shape and their coherency, therefore visualization is difficult.

Figure 2 : Streaklines in the wake behind a cylinder for different Reynolds numbers.

Figure 3 : Vortices in the wake behind the cylinder (click on picture to animate)

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