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Transition and Turbulence

1. Instability and Breakdown of a Near-Wall Low-Speed Streak

Sinuous Instability/Varicose Instability

The instability of the three-dimensional high-shear layer associated with a near-wall low-speed streak is investigated experimentally. A single low-speed streak, not unlike the near-wall low-speed streaks in transitional and turbulent flows, is produced in a laminar boundary layer by using a small piece of screen set normal to the wall. In order to excite symmetric and anti-symmetric modes separately, well-controlled external disturbances are introduced into the laminar low-speed streak through small holes drilled behind the screen. The growth of the excited symmetric varicose mode is essentially governed by the Kelvin-Helmholtz instability of the inflectional velocity profiles across the streak in the normal-to-wall direction and it can occur when the streak width is larger than the shear layer thickness. The spatial growth rates of symmetric modes are very sensitive to the streak width and are rapidly reduced as the velocity defect decreases due to the momentum transfer by viscous stresses. By contrast, the anti-symmetric sinuous mode that causes the streak meandering is dominated by the wake-type instability of spanwise velocity distributions across the streak. As far as the linear instability is concerned, the growth rate of the anti-symmetric mode is not so strongly affected by the decrease in the streak width, and its exponential growth may continue further downstream than that of the symmetric mode. As for the mode competition, it is important to note that when the streak width is narrow and comparable with the shear-layer thickness, the low speed streak becomes more unstable to the anti-symmetric modes than to the symmetric modes. It is clearly demonstrated that the growth of the symmetric mode leads to the formation of hairpin vortices with a pair of counter-rotating streamwise vortices, while the anti-symmetric mode evolves into a train of quasi-streamwise vortices with vorticity of alternate sign. [Asai, M., Minagawa, M. and Nishioka, M., J. Fluid Mech. 455 (2002) 289-314]

2. Instability of Spanwise-Periodic Low-Speed Streaks

Nonlinear evolution of subharmonic streak instability
Nonlinear evolution of subharmonic streak instability

The streak instability is examined experimentally by artificially generating spanwise-periodic low-speed streaks in a laminar boundary layer on a flat plate.Fundamental and subharmonic modes are excited for each of the sinuous and varicose instabilities and their development is compared with the corresponding result of a single low-speed streak.The development of subharmonic sinuous mode does not strongly depend on the streak spacing and it grows with almost the same growth rate as that for the single streak.By contrast, the development of fundamental sinuous mode is very sensitive to the streak spacing and is completely suppressed when the streak spacing is smaller than a critical value, about 2.5 times the streak width for the low-speed streaks examined.On the varicose instability, the fundamental mode is less amplified than the subharmonic mode, but the growth of both modes is weak compared with the case of the single streak. [Konishi, Y. and Asai, M., Fluid Dyn. Res. 42 (2010)]

3. Growth and Breakdown of Low-Speed Streaks Leading to Wall Turbulence

Development of low-speed streaks downstrem
of the suction strip

Two-dimensional local wall suction is applied to a fully developed turbulent boundary layer such that most of turbulent vortices in the original outer layer can survive the suction and cause the resulting laminar flow to undergo re-transition. This enables us to observe and clarify the whole process by which strong vortical motions give rise to near-wall low-speed streaks and eventually generate the wall turbulence. Hot-wire and PIV measurements show that low-frequency velocity fluctuations, which are once markedly suppressed near the wall by the local wall suction, soon start to grow downstream the suction. The growth of low-frequency fluctuations is of algebraic type, characterizing the streak growth caused by the suction-survived turbulent motions. The low-speed streaks obtain almost the same spanwise spacing as that of the original turbulent boundary layer without the suction even in the initial stage of the streak development. This indicates the suction-survived turbulent vortices to be quite efficient to excite the necessary ingredients for the wall turbulence, namely, low-speed streaks of the right scale. After attaining near saturation the low-speed streaks soon undergo the sinuous instability to lead to re-transition. Flow visualization shows that the streak instability and its subsequent breakdown occur at random in space and time in spite of the fact that the spanwise arrangement of streaks is almost periodic. Even under the high-intensity turbulence conditions the sinuous instability amplifies disturbances of almost the same wavelength as predicted from the linear stability theory though the actual growth is in the form of wave packet with the number of wave periods not more than two. It should be emphasized that the mean velocity develops the log-law profile as the streak breakdown proceeds. The transient growth and eventual breakdown of low-speed streaks are also discussed in connection with the critical condition for the wall turbulence generation. [Asai, M., Konishi, Y., Oizumi, Y. and Nishioka, M., J. Fluid Mech. 586 (2007) 371-386]