Experimental detection of deterministic turbulence

Abstract

This paper is devoted to an experimental investigation of transitional and turbulent, post-transitional boundary layer initiated by fully controlled 3D broadband perturbations. A self-similar laminar boundary layer with an adverse pressure gradient was used as a primary base flow. The excited controlled disturbances initially represented Tollmien–Schlichting (TS) waves, which had a spectral component that was random at small and moderate time scales but periodical at very large time scales, during which the flow passed the experimental model several times. Detailed measurements were carried out by means of a hot-wire anemometer in a broad spatial region starting with stages of small-amplitude instability waves and ending with stage of a developed post-transitional turbulent flow. It was found that average characteristics of the produced post-transitional flow corresponded to the developed wall turbulence; meanwhile, the instantaneous flow structure there still remained deterministic, i.e. basically reproducible from one long signal realization to another. This instantaneous structure was measured in detail and compared with the one known from previous investigations of turbulent and transitional flows. A conclusion was drawn that the deterministic (reproducible) wall turbulence did exist in nature and could be generated experimentally in boundary layers. Besides important philosophical meaning, this result provided investigators with a very powerful methodological tool for subsequent turbulence research.

Keywords:

• boundary layer
• laminar-turbulent transition
• broadband controlled perturbations
• vortical structures
• post-transitional deterministic turbulence

Acknowledgements

This work is supported by the international project of the Russian Foundation for Basic Research and the Deutsche Forschungsgemeinschaft (grant RFBR-DFG 08-01-91951) and the Russian Academy of Sciences.

Notes

1. Some of those ideas are discussed in [9].

2. Note that here the direction of the time axis is from right to left, as well as in all other time-traces presented below, in order to correspond to contour plots in the (t, z)- and (t, y)-planes like those shown in Figures 6, 23 and others.

3. The experimental results obtained in [22] are presented here by their line approximation.

4. Note that the periodicity of the structures at very large time scales (with the period of T _r) is observed very distinctly, but, at the same time, any structure (including the longest one) is considerably shorter than this period.

5. Note that only coherent part of total velocity disturbances is presented in Figures 21 and 22.

6. The process of production of ring-like vortices by Λ-structures is discussed in detail in [8, 9, 10].