Abstracts - KTH Mechanics

Super-late stages of boundary-layer transition
and deterministic post-transitional turbulence
V. I. Borodulin a, Y. S. Kachanov a and A. P. Roschektayev a
The paper is devoted to an experimental study of super-late stages of laminarturbulent
transition in a boundary layer with a streamwise adverse pressure gradient
with Hartree parameter H = 0.115. The experiments were performed at controlled
disturbance conditions in a low-turbulence wind-tunnel T-324 of ITAM SB RAS. The
measurements were carried out by means of a hot-wire anemometer in a broad spatial
region starting with stages of small-amplitude instability waves, developing in the
laminar boundary layer, and ending with the post-transitional turbulent flow. The
‘deterministic noise’ method and a universal disturbance source of instability waves 1
were used in these experiments to excite the flow. The transition was initiated by a
mixture of a quasi-2D Tollmien-Schlichting (TS) wave and 3D broadband
perturbations (a “noise” of TS-waves). The broadband perturbations were random
within 20 periods of the fundamental TS-wave but then repeated periodically at very
large time scales, during which the flow passed the model several times. Thus, the
“noise” was random from the viewpoint of the flow but it was deterministic (even
periodic) from the viewpoint of data processing giving us the possibility to perform
ensemble averaging of hot-wire signals.
It is found that the instability waves leaded to transition with formation of
characteristic vortical structures. Father downstream formation of post-transitional
turbulent boundary layer was observed. At this stage the mean velocity profiles, the
profiles of rms velocity fluctuations, and the disturbance spectra corresponded to
those observed in developed turbulent boundary layers. At the same time it was found
that the flow remained deterministic to a considerable degree. The coherence
coefficient, determined as a ratio of the rms intensity of the ensemble-averaged
(deterministic) and total (non-averaged) velocity fluctuations, remained very large even
in the post-transitional flow (between 80 and 60%). This circumstance gave us the
possibility to obtain instantaneous velocity and vorticity fields in the (x, y, z, t)-space
and to perform a computer-aided, quantitative visualization of the instantaneous flow
structure in the post-transitional turbulent boundary layer both in near-wall and in the
outer region. It is found that the structures resemble very much the vortical structures
found earlier at later stages of transition 2, as well as the coherent vortical structures
observed in developed turbulent boundary layers. A conclusion is made that the post
transitional turbulent flow is mainly deterministic and can be simulated (modeled)
experimentally. Such model turbulence can possess all main average statistical
properties characteristic of the wall turbulence but, simultaneously, the instantaneous
structure of this turbulence can be deterministic and reproducible.
This work is supported by Russian Foundation for Basic Research.
a Institute of Theoretical and Applied Mechanics of SB RAS, 630090, Novosibirsk, Russia.
1 Borodulin et al., Proc. Intl. Conf. Methods. Aerophysical. Research. Novosibirsk: ITAM, Part 2, 39 (1996).
2 Borodulin et al. Thermophysics and Aeromechanics. 10, 1 (2003).
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