Turbulence production in an APG-boundary-layer transition induced by randomized perturbations

This paper is devoted to an experimental investigation of formation and development of coherent vortical structures at late stages of a laminar-turbulent transition initiated by a harmonic, almost two-dimensional Tollmien-Schlichting (TS) wave perturbed by weak (initially) broadband disturbances. The initial base flow represented a self-similar boundary layer with an adverse pressure gradient (APG) with Hartree parameter β_H = −0.115. Experiments were performed at controlled disturbance conditions with the help of the ‘deterministic noise’ method and a universal disturbance source of instability waves. The main measurements were carried out by means of a hot-wire anemometer in a broad spatial region of the flow starting with stages of quasi-sinusoidal small-amplitude instability wave and ending with final stages of transition characterized by formation of concentrated localized vortical structures. The excited perturbations were partly random (within 20 TS-wave fundamental periods) but periodical at very large time scales during which the flow passes the model several times. The detailed measurements and the experimental data processing gave us the possibility to obtain instantaneous velocity and vorticity fields in the (x, y, z, t)-space and to perform computer-aided ‘visualization’ of the instantaneous flow structure. Specific features of the turbulence production mechanism occurring at late stages of transition are studied and compared with previously reported data obtained at sinusoidal excitation. A qualitative similarity is found between essentially nonlinear stages of transition observed in the present (randomized) case and those studied previously in cases of transition initiated by a harmonic TS wave or by a TS wave packet. It is found that interaction of primary wave with a broadband ‘noise’ of 3D TS waves leads at late stages of transition to formation of Λ-vortices, intensive Λ -shaped high-shear (HS) layers, Ω -shaped vortices, ring-like vortices and associated ‘spikes’ in time-traces, and other phenomena. These structures are found to be disposed in a random order in time and space and have somewhat distorted shapes (in contrast to the periodic-excitation case studied earlier). However, their general properties are qualitatively similar. The obtained instantaneous pictures of velocity and vorticity fields seem to correspond qualitatively to those present in the near-wall region of the developed turbulent boundary layer.

Acknowledgements

This work is supported by Russian Foundation for Basic Research (grant 00-01-00835) and Russian Academy of Sciences.

Notes

¹ Other names of this scenario are S-type of transition [18], or C- and H-mode of transition for Craik's [19] and Herbert's [20] studies. Discussion about the terminology can be found, in particular, in papers [7, 8, 18].

Note that transition of this flow turned out to be very similar to that observed in a flat-plate boundary-layer.

The base-flow calculations presented in this study have been performed by B. V. Smorodsky.

⁴ Note that the direction of the time axis is from right to left here, as well as in all other time-traces presented below, in order to correspond to contour plots in the (−t, z)-plane like those shown in figure 16 and others.

⁵ For contour plots of the flow velocity this style of data representation is used throughout the present article.

⁶ Here x′ = (t ₀−t)U _e is an effective streamwise coordinate introduced in [58], where U _e is the boundary-layer edge velocity and time instant t ₀ is different for every individual Λ -structure and corresponds approximately to its tail.

Note that the same spline approximation was also used in movie 4 (bottom) discussed below.