The instability and breakdown of a near-wall low-speed streak

Abstract

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 in ectional 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 rate of the symmetric mode is very sensitive to the streak width and is rapidly reduced as the velocity defect decreases flowing 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.

Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

“…The sinuous mode is antisymmetric with respect to the base flow, with transversely oscillating perturbation streamlines. The sinuous mode was more rapidly growing, and was related to spanwise shear, whereas the varicose mode was associated with wall-normal shear (Saric 1994;Asai, Minagawa & Nishioka 2002).…”

Growth of boundary-layer streaks due to free-stream turbulence

“…The same definition has been employed by Asai et al [3]. The positive and negative streaks are therefore defined as follows,…”

Streak interactions and breakdown in boundary layer flows

“…[4][5][6][7] These studies confirmed that the instability is of inflectional type and that the dominating instability appears as spanwise ͑sinuous͒ oscillations of the streaks. For zero-pressure-gradient boundary layers, the spatial response of a single low-speed streak submitted to a time-harmonic excitation of sinuous or varicose type has been more recently examined experimentally by Asai et al 8 The growth of the sinuous mode was observed to evolve into a train of quasi-streamwise vortices with vorticity of alternate sign. By contrast, the varicose mode led to the formation of hairpin structures made up of a pair of counterrotating vortices.…”