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3.1 The unforced wall jet

Figure 3 shows smoke visualisations for the unforced wall jet at three different Reynolds numbers, Re_j = 2500, 5000, 10000, respectively. At all Reynolds numbers, the smoke filament leaves the nozzle as a nearly straight line, indicating that the flow is laminar. The Kelvin-Helmholtz instability leads to the formation of shear-layer vortices, which subsequently undergo one ore more stages of vortex pairing. With increasing Reynolds number, the shear-layer instability and roll-up move upstream. The breakdown of the shear-layer vortices results in large-scale turbulent structures.

At Re_j = 2500 two separate shear-layer vortices can be seen at x/b $\approx$ 5. At x/b $\approx$ 8 a pairing process takes place, and at x/b $\approx$ 12 a vortex after the first stage of pairing can be observed.

At Re_j = 5000 the processes are the same but take place closer to the wall jet nozzle. The first pairing process occurs at x/b $\approx$ 5, a second pairing at x/b $\approx$ 10, and the third pairing process at x/b $\approx$ 15.

At Re_j = 10000 the individual shear-layer vortices cannot be distinguished anymore, since the pairing processes had taken place too rapidly. The resulting coherent structures can, however, still be seen clearly.

Figure 3: Visualisation of shear layer structures (unforced) ( 0 $\leq$ x/b $\leq$ 17): a) Re_j = 2500; b) Re_j = 5000; c) Re_j = 10000.

It has been shown by [Wygnanski, Katz & Horev (1992)] that a ``certain'' threshold Reynolds number has to be reached to ensure that the wall jet is self-similar with respect to the mean and fluctuating velocities. A Reynolds number of Re_j = 5000 is about the lower limit at which this self similarity can be reached. [Abrahamsson, Johansson & Löfdahl (1994)] showed that a Reynolds number of Re_j = 10000 is well above this threshold. Since the flow visualisation becomes more and more difficult towards higher exit velocities, Re_j = 5000 was chosen as a compromise between physical requirements and experimental constraints.

For a better understanding of the dynamics of the shear-layer roll-up and the pairing processes, figure 4 shows a flow-visualisation movie at Re_j = 5000. The frequency of the natural shear-layer roll-up is $\approx$ 1000 Hz.

Figure 4: Visualisation of shear layer structures (unforced) (movie 850kB).

Since the unforced shear-layer roll-up is affected by background disturbances, the process is not perfectly periodic. Therefore, the pairing processes cannot be observed very clearly.

In order to facilitate the observation of the shear-layer roll-up, the wall jet was exposed to a slight acoustical forcing by a loudspeaker located approximately one meter away from the test section. The excitation frequency was about four times the video framing frequency (f_e = 100 Hz).

Figure 5: Visualisation of shear layer structures (slight acoustical forcing) (movie 500kB).

The stages of transition are more easily observed in figure 5, which shows a movie of the acoustical forced wall jet. Due to the forcing, the shear-layer roll-up moves upstream. The formation and subsequent pairing of the shear-layer vortices is now clearly visible.

The present results are in good agreement with [Bajura & Catalano (1975)], although their Reynolds numbers did not exceed Re_j$\le$600. They describe the process of transition as (1.) the formation of discrete shear-layer vortices, (2.) the coalescence of adjacent vortices, (3.) the eruption of the wall jet into the ambient fluid and (4.) the dispersion of these vortex-patterns into three-dimensional turbulent structures.

We cannot confirm the occurence of dipolar structures observed by [Gogineni & Shih (1997)] at Re_j = 1450. The reason is probably the different the velocity profiles at the nozzle of the wall jet. [Gogineni & Shih (1997)] had a channel flow with a parabolic velocity profile at the exit. The vorticity in the boundary layer and the shear layer region are thus of equal strength but of opposite sign, allowing the formation of dipols out of one shear layer and one boundary layer vortex. In the present investigation, the shear layer at the nozzle was separated from the boundary layer by a thick potential core, as described in detail by [Michalke & Schober (1999)]. This potential core inhibits interaction between the boundary layer and the shear-layer region in the early stages of the wall-jet development.

We conclude therefore, that in a wall jet emanating with a thick potential core, laminar to turbulent transition of the wall jet is driven by the growth, pairing and decay of the shear-layer vortices. The boundary layer region plays no important role at these early stages.

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